pipes with a copper wire screen mesh (wick) was carried out. Pure water and ... same length (55.5 cm) and the same outer diameter (19.05 mm). The results of ...
NUMERICAL AND EXPERIMENTAL STUDY OF FLOW AND HEAT TRANSFER ENHANCEMENT IN A CYLINDRICAL HEAT PIPE USING NANOFLUID
A THESIS SUBMITTED TO THE COLLEGE OF ENGINEERING UNIVERSITY OF BASRAH IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING (THERMO MECHANICS)
By HASSANAIN GHANI HAMEED )M. Sc. Mechanical Engineering( (2004)
January 2015
1436
Acknowledgments I wish to express my deep gratitude to my supervisor Prof. Dr. AbdulMuhsin A. Rageb. He was always patient, encouraging and enthusiastic. I also would like to thank Assist Prof. Dr. Rabee H. Thejeel Dean of the College of Engineering for his help and support. My thanks go to Assist Prof. Dr. Ameen Ahmed Nassar the Head of the Mechanical Engineering Department. My grateful respect and thanks to Assist Prof. Dr. Alaa M. Hussain Dean of Najaf Technical College and all my friends especially Dr. Dhafeer M. Hicham, Dr. Ali Shakir, Dr. Assad A. Abass, Dr. Wissam Ahmed, Mr. Bassil N. Merza, Mr. Adeel Aziz, Mr. Selah M. Salih and all staff of Automotive Technical Department in Technical College of Najaf and Air Conditioning Workshop in Technical Institute of Najaf for their support and advice. Last but not the least; I would like to express my deep thanks to my family for their support during all my life.
I
Certification I certify that the PhD thesis “Numerical and Experimental Study of Flow and Heat Transfer Enhancement in a Cylindrical Heat Pipe Using Nanofluid” which is submitted by “Hassanain Ghani Hameed” is prepared under my supervision at the University of Basrah, College of Engineering as a partial requirement for the degree of Doctor of Philosophy in Mechanical Engineering.
Signature: Name: Prof. Dr. Abdul-Muhsin A. Rageb Date:
/
/ 2015
In view of the available recommendation, I forward this thesis for debate by the examining committee.
Signature: Name: Assist. Prof. Dr. Ameen Ahmed Nassar Date:
II
/
/ 2015
Examining Committee’s Report We certify that we have read this thesis titled "Numerical and Experimental Study of Flow and Heat Transfer Enhancement in a Cylindrical Heat Pipe Using Nanofluid" which is being submitted by (Hassanain Ghani Hameed) and as Examining Committee, examined the student in its contents. In our opinion, the thesis is adequate for award of degree of Doctor of Philosophy in Mechanical Engineering.
Signature: Name: Prof. Dr. Abbas H. Sulaymon (Chairman) Date: / / 2015
Signature: Name: Prof. Dr. Haroun A. K. Shahad (Member) Date: / / 2015
Signature: Name: Assist Prof. Dr. Salman H. Hammadi (Member) Date: / / 2015
Signature: Name: Assist Prof. Dr. Qais A. Rishack (Member) Date: / / 2015
Signature: Name: Assist Prof. Dr. Mushtaq I. Hassan (Member) Date: / / 2015
Signature: Name: Prof. Dr. Abdul-Muhsin A. Rageb (Member and Supervisor) Date: / / 2015
Approval of the College of Engineering Signature: Name: Assist Prof. Dr. Rabee H. Thejeel (Dean of Engineering College) Date: / / 2015
III
Abstract In this work a theoretical and experimental study of fluid flow and heat transfer in steady state conditions for a constant and variable conductance heat pipes with a copper wire screen mesh (wick) was carried out. Pure water and two types of nanofluid (water based-Al2O3 nanofluid and water based-CuO nanofluid) are used as working fluids. The main objective of this work is to identify the effect of several parameters such as input heat flux, coolant temperature, working fluid type, nanoparticles concentration and the presence of the non – condensable gas on the heat pipe performance. Two dimensional model axi – symmetric was used and the basic equations which were used in the analysis are the mass conservation equation, Navier– Stokes equations and the energy equation. An upwind finite difference approach is used in the development of the numerical scheme. The theoretical results of the constant conductance heat pipe (CCHP) showed that the increment of the input heat flux or the coolant temperature leads to an evident increase in the heat pipe operating temperature and improves the heat pipe performance for both pure water and nanofluids. The improvement in the heat pipe performance which was represented here by the thermal resistance, reached up to 31.49% for water based-Al2O3 nanofluid and 34.04% for water based-CuO nanofluid at input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and nanoparticles concentration (NPC) of 5 Vol.%. For variable conductance heat pipe (VCHP) the same behaviour as in CCHP was noted. The mass of non-condensable gas (air) has maximum effect on the heat pipe thermal performance. The increase in the nanoparticles concentration within the nanofluid led to a small improvement in the heat pipe thermal resistance, which reached up to 4.07% for water based-Al2O3 nanofluid and 4.17% IV
for water based-CuO nanofluid at input heat flux of 2784.86 W/m2, coolant temperature of 26 oC, air mass of 0.5 mg and nanoparticles concentration (NPC) of 5 Vol.%. The experimental part included fabricating and testing two heat pipes with six layers of wire screen mesh lined on the internal wall. These two pipes have the same length (55.5 cm) and the same outer diameter (19.05 mm). The results of CCHP and VCHP showed that the optimum amount of the liquid charge for heat pipe with wire screen wick is about 240% of that the amount theoretically estimated. The increase in the coolant temperature led to decrease in the heat pipe thermal resistance. With using the nanofluids, the increase in the nanoparticles concentration led to an increase in heat pipe thermal resistance improvement. Whereas, for CCHP the improvement reached up to 44.4% and 48.6% for water based-Al2O3 and CuO nanofluids respectively. While, for VCHP, at air mass of 0.5 mg, the improvement reached up to 9.88% and 10.48% for water based-Al2O3 and CuO nanofluids respectively. All these were at input heat flux of 2784.86W/m2, coolant temperature of 26 oC and nanoparticles concentration (NPC) of 5 Vol.%. In the present work, the maximum relative errors between the numerical and experimental results are 8.2% for pure water and 25% for nanofluids. The error associated with nanofluids results is due to the deposition of nanoparticles on the wick surface in the evaporation zone which cannot be considered and modeled in the theoretical work
V
Contents Acknowledgements ………………...…...……………………….……….... I Certification …………….……………...…………………...…..…..….......... II Examining Committee’s Report…………...……………….……..….……… III Abstract ………………………………..……………..…………………….…...I V Contents ……….………………………..…………..………………….........….V I Nomenclature ………….……..……………....……………….…………...….. XI Abbreviations …………....…….........…………..……...…..……………...….X IV Chapter One: Introduction 1.1 Introduction …………….………………………………………………....……1 1.2 Classification of Heat Pipes …………………….…….……………………..…2 1.3 Nanofluid Characteristics …….……………………………………………...…5 1.4 Capillary Structure ……………...…………………………………………...…6 1.5 Heat Pipe Limitation …….…...……………………………...…………..…..…9 1.6 Objectives of the Study …….…………………………...………...……….….11 Chapter Two: Literature Review 2.1 Literature Related to conventional working fluid …..…………………….….17 2.1.1 Theoretical literature ……………………………………...…………..…..17 2.1.2 Experimental literature ………………………………………………...….21 VI
2.1.3 Theoretical and Experimental literature ………………………...……...…31 2.2 Literature Related to working fluid with nanoparticles ……….....………...…38 2.2.1 Theoretical literature …………………………………………...………....38 2.2.2 Experimental literature ………………………………………….……...…39 2.2.3 Theoretical and Experimental literature ……………………………….….48 2.3 Summary ……………………….……………………..……………..…….….48 Chapter Three: Theoretical Work 3.1 Introduction………………………………...……………………...……….….54 3.2 The Physical Model ……………..........................................………………....54 3.3 Mathematical Formulation and Governing Equations of CCHP …..………....55 3.3.1 Governing Equations …………………………………...………….……...57 3.3.1.1 Vapor Region ………………….……….………………..….…….….58 3.3.1.2 Wick Structure .………………………...……………………........…..61 3.3.1.3 Wall Region………….………………...………………………….......65 3.4 Mathematical Formulation and Governing Equations of VCHP ………...…...66 3.4.1 Governing Equations ………………………………………….…….…….69 3.4.1.1 Vapour Region ……………………………….………………….……69 3.4.1.2 Wick Structure ……………………………………………….….…….70 3.4.1.3 Wall Region …………………………………………………………...70 3.5 Numerical Modeling ……………………...…………………………………..71 3.5.1 Convergence of Numerical Solution ………………………...……………..71 3.5.2 Numerical Procedure ………………………………………………….……72 Chapter Four: Experimental Work 4.1 Introduction…………………...……………………………………...………..78 4.1.1 Heat Pipe ………………………………………………………………….78 VII
4.1.1.1 The Container and End Caps ……………………………..…….……..79 4.1.1.2 The Working Fluid …………………………………………..………..80 4.1.1.3 The Wick Structure ……………………………………..……….……82 4.1.2 Water Cooling System ……………………………………………....……86 4.1.3 Power Supply System ……………………………………………….……86 4.1.3.1 AC Automatic Voltage Regulator ………………………………........86 4.1.3.2 Variable AC Transformer (Variac) …………………….……………..87 4.1.4 Measuring Instruments …………………………………….……….…….87 4.1.4.1 Power Measuring Instrument …………………………………..……..87 4.1.4.2 Temperature Measuring System ………………………………...…….88 4.1.4.3 Cooling Water Flow Rate Measuring Instrument ………......………...89 4.2 Accuracy and Uncertainty of Measurements …………………………………89 4.3 Experimental Heat Pipes Specification …………………………………........90 4.4 Experimental Procedures …………………………………………….……….91 4.4.1 Experimental Procedure of CCHP Testing ………………………..……..92 4.4.2 Experimental Procedure of VCHP Testing ……………………...……….93 Chapter Five: Results and Discussion 5.1 Introduction ………………………………………………………….………..98 5.2 Validation of the Present Model….…………………………………….........98 5.2.1 CCHP ……………………………………………………………………..99 5.2.2 VCHP ………………………………………….………………………...100 5.3 Numerical Results ……………………………………………………..........100 5.3.1 CCHP ……………………………………………………………………100 5.3.1.1 Temperature Distribution ……………………………………………102 5.3.1.2 Vapour Flow ……………………………..…………………….…….103 5.3.1.3 Liquid Flow …………………………………………………….........107 VIII
5.3.1.4 Axial Conduction ……………………………………..…….……….109 5.3.1.5 The Maximum Heat Transport Capillary Limit …………….……….110 5.3.1.6 Thermal Resistance …………………………………………..……...112 5.3.1.7 Heat Pipe Thermal Performance Enhancement ………...……..…….113 5.3.2 VCHP ………………………………………….………………………...114 5.3.2.1 Temperature Distribution …………………………….……………...119 5.3.2.2 Vapour Flow …………………………………………………...…….121 5.3.2.3 Liquid Flow …………………………………………………….........124 5.3.2.4 Axial Conduction ………………………………………………........127 5.3.2.5 The Maximum Heat Transport Capillary Limit …….……………….128 5.3.2.6 Thermal Resistance ……………………..…………………….……..131 5.3.2.7 Condenser Active Length ………………………….………….……..133 5.3.2.8 Heat Pipe Thermal Performance Enhancement ………………..……134 5.4 Experimental Results ……………………………………….………………..135 5.4.1 CCHP …………………………………………………….…….………..135 5.4.1.1 Effect of Liquid Inventory on Heat Pipe Thermal Behavior ………..135 5.4.1.2 Effect of Heat Transfer Rate on Heat Pipe Thermal Behavior ….......136 5.4.1.3 Effect of Coolant Temperature on Heat Pipe Thermal Behavior ........136 5.4.1.4 Effect of Nanoparticles Concentration on Heat Pipe Thermal Behavior ……………………………………………………………………........137 5.4.1.5 Comparison between Numerical Predictions and Experimental Results…………………………………………………………………..………..138 5.4.2 VCHP ………………………………………………...………………….139 5.4.2.1 Effect of Liquid Inventory on Heat Pipe Thermal Behavior ………..139 5.4.2.2 Effect of Heat Transfer Rate on Heat Pipe Thermal Behavior ….......139 5.4.2.3 Effect of Coolant Temperature on Heat Pipe Thermal Behavior ........140
IX
5.4.2.4 Effect of Mass of Non-Condensable Gas on Heat Pipe Thermal Behavior ……………………………………………………………………........140 5.4.2.5 Effect of Nanoparticles Concentration on Heat Pipe Thermal Behavior ……………………………………………………………………........141 5.4.2.6
Comparison
between
Numerical
Predictions
and
Experimental
Results…………………………………………………………………..………..142 Chapter Six: Conclusions and Recommendations 6.1 Conclusions…………………………………...…...……………………........218 6.1.1 Theoretical Results of CCHP and VCHP…...…...……………………........218 6.1.2 Experimental Results of CCHP and VCHP…...……………………….......219 6.2 Suggested Future Work …………………………………...……..…….…….220 References…………………………….…………………...…...……………….2 21 Appendices Appendix A
Heat Pipe Working Fluid Properties
A1
Appendix B
Governing Equations Discretization Using the Upwind
B1
Differencing Scheme Appendix C
Nanofluid Preparation
C1
Appendix D
Heat Pipe Losses Calculations
D1
Appendix E
Specific Latent Heat of Vaporization and
E1
Surface Tension Measurements Appendix F
Calibration of Rotameter
F1
Appendix G
Specific Latent Heat of Vaporization and Surface Tension
G1
Measurements Appendix H
Publish Paper from Thesis
H1
Appendix I
Publish Paper from Thesis
I1
X
Appendix J
Publish Paper from Thesis
J1
Appendix K
Publish Paper from Thesis
K1
Nomenclature Symbol A Av Aw Cp dw Da Er F G hfg h k keff Kp L Lca Lcia leff M Mncg ̇ ̇ N P
Description Area Vapor area in the condenser inactive length Cross section area of screen wick wire heat capacity at constant pressure Wire diameter of wick structure Darcy number= Kp/ro2 The relative error A constant defined by Equation 3-45 Mass flux latent heat of vaporization Heat transfer coefficient Thermal conductivity Effective thermal conductivity of wick structure Wick permeability Length Condenser active length Condenser inactive length Effective length of heat pipe= 0.5(Le+2La+Lc) Merit number Mass of non-condensable gas Mass flow rate of the working fluid Maximum mass flow rate of the working fluid Screen mesh number Pressure XI
(SI)Unit m2 m2 m2 J/kg. K m kg/s.m2 J/kg W/m2. K W/m. K W/m. K m2 m m m m W/m2 kg kg/s kg/s N/m2
Pr Psat(Tsat) Psat(Tset) Psat(Tal) Psat(Ts) Pv(Taa) Pc Q Qe Qc Qc,max q R Re Rth r rc T u U URSS v V x ε φ ѱ ω α υ μ σ
Prandtl number Saturation pressure at saturation temperature (Tsat) Saturation pressure at set temperature (Tset) Saturation pressure at active length temperature (Tal) Saturation pressure at coolant temperature (Ts) Vapour pressure at active length temperature (Tal) Capillary Pressure Heat rate Heat input rate (Heat Load) Heat rejected rate from condenser Maximum heat transfer rate from condenser Heat flux Gas constant Reynolds number Total Thermal resistance Radius Capillary radius Temperature Axial velocity Heat transfer coefficient Root-Sum-Square uncertainty Radial velocity Volume, Reference velocity Axial distance Greek Symbols Wick porosity Inclination angle of heat pipe Nanoparticle volume fraction (%) stream function Vorticity fluid thermal diffusivity kinematics viscosity dynamic viscosity Surface tension XII
N/m2 N/m2 N/m2 N/m2 N/m2 N/m2 W W W W W/m2 J/kg.K K/W m m K m/s W/m2.K m/s m3, m/s m degree m3/s s-1 m2/s m2/s kg/m. s N/m
ρ τ θ ΔP ΔPc,max ΔT a al c bf e eff g ga in int l max ncg nf o r s sat set so v w ¯ +
Density shear stress dimensionless temperature, contact angle Pressure drop Maximum capillary pressure drop Temperature difference Subscripts adiabatic, air active length condenser, capillary base fluid Evaporator effective gravity gas input Interface liquid maximum Non-condensable gas nanofluid out Radial Sink Saturated Set Solid Vapor wick Superscripts average quantity dimensionless term
XIII
kg/m3 N/m2 -, degree N/m2 N/m2 K -
Abbreviations Symbol CCHP DI FCHP HP IMP. MHP NCG NPC PCHP TDS VCHP
Description Constant Conductance Heat Pipe Distilled Water Fixed Conductance Heat Pipe Heat Pipe Improvement Miniature Heat Pipe Non-Condensable Gas Nanoparticles concentration Pressure Control Heat Pipe Total Dissolved Solids (ppm) Variable Conductance Heat Pipe
XIV
Chapter One
Introduction
Chapter One Introduction
1.1 Introduction The heat pipe is a very high thermal conductance device for transferring heat in which latent heat of vaporization is exploited to transport heat over long distances with a corresponding small temperature gradient. The heat transporting is realized by means of evaporating a liquid in the heat inlet region (called the evaporator) and subsequently condensing the vapour in a heat rejection region (called the condenser). Closed circulation of the working fluid is maintained by capillary action and/ or bulk forces [1]. The idea of the heat pipe was first suggested by Gaugler in 1942. However, later it was invented by Grover in the early 1960s that the remarkable properties of the heat pipe became appreciated and serious development work took place in energy savings and design improvements in various applications. Most recently, with heat density of electronic components continually increasing, there is a growing interest in using heat pipes for transferring and spreading heat in conjunction with cooling these components [1]. A simple constant or variable conductance heat pipe consists of a sealed container, a wick structure, and a working fluid. The wick structure is placed on the inner surface of the heat pipe wall and is saturated with the liquid working fluid and provides the structure to develop the capillary action for liquid returning from the condenser to the evaporator section. The difference between constant and variable conductance heat pipes is the presence of non-condensable gas. When heat added at evaporator, the liquid is evaporated as it absorbs an amount of heat equivalent to the latent heat of vaporization, while in the condenser 1
Chapter One
Introduction
section, the vapor is condensed. The added mass in the vapor core of the evaporator section and rejected mass in the condenser end results in a pressure gradient along the vapor channel which drives the corresponding vapor flow. Return of the liquid to the evaporator from the condenser is provided by the wick structure. As vaporization occurs in the evaporator, the liquid meniscus recedes correspondingly into the wick structure, as shown in figure 1-1. Similarly, as vapor condenses in the condenser region, the added mass results in an advanced meniscus. The difference between the capillary radii in the evaporator and condenser ends of the wick structure results in a net pressure difference in the liquid-saturated wick. This pressure difference drives the liquid from the condenser through the wick structure to the evaporator region, thus allows the overall process to be continuous [2]. Due to the two-phase characteristics, the heat pipe is ideal for transferring heat over long distances with a very small temperature drop and for creating a nearly isothermal surface for temperature stabilization, thus it works with a nearly isothermal condition. This nearly isothermal condition offers benefits of transporting large amounts of heat efficiently, decreasing the overall heat transfer area and saving system weight. Additionally, no mechanical pumping systems are required due to the capillary-driven working fluid. Given the wide range of operating temperatures for working fluids, the high efficiencies, the low relative weights, and the absence of external pumps in heat pipes, these systems are seen as attractive options in a wide range of heat transfer applications [2].
1.2 Classification of Heat Pipes Under different conditions, heat pipes classifications can be divided into different categories depending on the geometries, applications and so on. Primarily, the heat pipes are classified by two ways. These are based on the working fluids operating temperatures and the types of control. 2
Chapter One
Introduction
For each application, there will be a temperature range for heat pipe particular operating conditions as shown in figure 1-2. Therefore, it is necessary to choose a suitable working fluid, which not only considers the operating temperature, but also concerns the compatibility with heat pipe container and wick materials. Classification of the heat pipes to the following four different types based on the operating temperature, as shown in table 1.1. Table 1.1 Classifications of heat pipes by operating temperature [3]. Type
High temperature (liquid-metal)
Temperature
>700 K
Medium temperature
550-700 K
Room temperature
200-550 K
Cryogenic (low temperature)
Specification
range
1-200 K
Using liquid metals, very high heat fluxes can be obtained due to the inherent properties of the fluid, namely, very large surface tensions and high latent heats of vaporization. Potassium, sodium, and silver are the examples of commonly used liquid metals. Some special organic fluids, such as naphthalene and biphenyl can be used for medium temperature applications. The working fluids typically used methanol, ethanol, ammonia, acetone, and water. With working fluids such as helium, argon, neon, nitrogen, and oxygen. Due to very low values of the latent heat of vaporization, and low surface tensions of the working fluids, they usually have relatively low heat transfer capabilities.
Also, Control is often necessary, for heat pipe operation, because a heat pipe without control will self-adjust its operating temperature in accordance with the
3
Chapter One
Introduction
heat source at the evaporator end and the heat sink at the condenser end. Thus, there are four major control approaches that are described as follows: 1. Gas-loaded heat pipe. The performance of a condenser is significantly affected by the presence of a non-condensable gas. This effect was utilized for heat pipe control. In other words, that any non-condensable gas presents in the vapor space is swept to the condenser section during operation, and gas will block a portion of the condenser surface. Thus, the heat flow at the condenser can be controlled by controlling the volume of the non-condensable gas. 2. Excess-liquid heat pipe. Condenser flooding with excess working fluid can also be used for control. Whereas, a portion of the condenser was blocked due to drifting the excess working fluid in the liquid phase into the condenser. 3. Vapor flow–modulated heat pipe. The flow of vapor through the adiabatic section, as in figure 1-3, controls the heat pipe performance, thus any increase in the temperature of the evaporator surface, due to increasing the heat input, causes a rise in the temperature and pressure of the vapor in the evaporator section. When this vapour flows through the throttling valve causes a reduction in the magnitudes of temperature and pressure of the vapour in the condenser section. Thus, the condensing temperature and pressure can be held at values that yield the required condenser performance even though the temperature at the heat source has increased. In the event that the heat input increases, the condenser can keep track of this increase and adjust its performance by means of the throttling valve. 4. Liquid flow–modulated heat pipe. Heat pipe performance control also effectively achieved by Liquid flow control. As shown in figure 1-4, using of a liquid trap represents a one way of controlling liquid flow. This trap represents a wick-lined reservoir connected to the evaporator end. The trap wick is separated from the operating wick in the rest of the heat pipe. Standardly, in the normal mode of the heat pipe operating the wick of trap is dry. If the heat input increases or the attitude 4
Chapter One
Introduction
of the heat pipe changes, condensation may occur in the trap and the liquid trap may become an alternate condensing end of the pipe. As liquid accumulates in the trap, the main wick begins drying out which results in operational failure [2, 3].
1.3 Nanofluid Characteristics Heat pipe performance depends on several parameters, one of them is the working fluid which has essential importance to achieve the enhancement of the thermal performance since the heat pipe utilizes phase change phenomenon of the working fluid. Thus, the researches focused on enhancing the traditional working fluid properties until Argonne National Laboratory has developed a new class of heat transfer fluids called ‘‘Nanofluids”, which are engineered by suspending ultrafine metallic or nonmetallic nanometer dimension particles in traditional fluids such as water, engine oil, ethylene glycol. While, several experimental investigations have revealed that nanofluids have remarkably higher thermal conductivity and greater heat transfer characteristics than conventional pure fluids, some of these investigations are summarized in table 1.2. Table 1.2 Summery of measured thermal conductivity (k) enhancement for different nanofluids [4]. Maximum Maximum Basie NanoResearchers Diameter concentration enhancement fluid particles (Vol.%) in k (%) Water Al2O3 33 nm 5 30 Eastman et al. [5] Water Al2O3 13 nm 4.3 32 Pak and Cho [6] Water Al2O3 28 nm 4.5 14 Wang et al. [7] Ethylene Al2O3 28 nm 8 40 Wang et al. [7] Glycol Pump Oil Al2O3 28 nm 7 20 Wang et al. [7] Engine Al2O3 28 nm 7.5 30 Wang et al. [7] Oil Water Al2O3 24.4 nm 4.3 10 Lee et al. [8] 5
Chapter One
Introduction
Table 1.2 Continue. Researchers
Basie fluid
Water Das et al. [9] Water Xie et al. [10] Li and Peterson Water [11] Water Krishnamurthy et al. [12] Eastman et al. Water [5] Water Lee et al. [8] Ethylene Lee et al. [8] Glycol Water Wang et al. [7] Water Das et al. [9] Li and Peterson Water [11] Ethylene Liu et al. [13] Glycol
38 nm 60 nm 29 nm
Maximum concentration (Vol.%) 4 5 10
Maximum enhancement in k (%) 25 20 30
Al2O3
20 nm
1
16
CuO
36 nm
5
60
CuO CuO
18.6 nm 18.6 nm
4.3 4
10 20
CuO CuO CuO
23 nm 28.6 nm 36 nm
10 4 6
35 36 52
CuO
25 nm
5
22.4
Nanoparticles
Diameter
Al2O3 Al2O3 Al2O3
1.4 Capillary Structure The selection of the wick for a heat pipe depends on many factors, several of which are closely linked to the properties of the working fluid. The maximum capillary head generated by a wick increases with decreasing of pore size. The wick permeability, another desirable feature which can be calculated as in table 1.3 for different wick types, increases with increasing of pore size. However, for homogeneous wicks as shown in figure 1-5, there is an optimum pore size, which is a compromise. Where pumping capability is required against gravity, small pores are needed. In space the constraints on size and the general high-power capability needed necessitates the use of composite (see figure 1-6) or arterial wicks aided by small pore structures for axial liquid flow. 6
Chapter One
Introduction
Table 1.3 Expressions of wick permeability Kp for several wick structures [2]. Wick Structures
(m2)
Data
Circular artery
Open rectangular grooves
Circular annular wick Wrapped screen wick
(
(
)
( )
(
)
( )
) /m
7
Chapter One
Introduction
Another feature of the wick, which must be optimized, is its thickness. The heat transport capability of the heat pipe is raised by increasing the wick thickness. It is important to select the proper wick structure depending on the application. Mesh screen, fiberglass, sintered porous metal and narrow grooves cut in the inner surface of the container wall have been used as wick materials. The first type has been widely used in heat pipes. This type of wick structure is designated by its mesh number, which is an indication of the number of pores per unit length or unit surface area. The surface pore size is inversely proportional to the mesh number and the liquid flow resistance can be controlled by the tightness of the wrapping. The pressure-drop diagram along the length of a heat pipe working under low heat flux is illustrated in figure 1-7. The maximum capillary pressure ∆Pc developed within the heat pipe wick structure is given by: (
)
(1-1) Whereas, the maximum capillary pressure must be greater than the sum of
all pressure losses inside the heat pipe: (
)
(
)
(1-2)
Where; (1-3) The values of the effective capillary radius reff, also may be named rc, for different wick structures are provided in table 1.4. If the total pressure drop exceeds the maximum capillary pressure, the return rate of liquid to the evaporator will be insufficient and the heat pipe will experience drying out of the wick [1,2].
8
Chapter One
Introduction
Table 1.4 Expressions for the effective capillary radius rc for several wick structures [2]. Wick Structures rc (m) Data Circular Cylinder
r= radius of liquid flow passage
Rectangular groove
w= groove width w= groove width
Triangular groove
= half included angle
Parallel wires
w= wire spacing N= screen mesh number/m
Wire screen
w= wire spacing dw= wire diameter
Packet spheres
rs= sphere raduis
1.5 Heat Pipe Limitations Limitations of the heat that may be transported by a conventional heat pipe can be divided into two primary categories: limits that led to heat pipe failure and limits that do not. For the limitations which led to heat pipe failure, all are characterized by insufficient liquid flow to the evaporator for a given heat input, thus resulting in dryout of the evaporator wick structure. While, limitations not resulting in heat pipe failure does require that the heat pipe operates at an increased temperature for an increase in heat input. These categories and basic phenomena for each limit may be summarized as follows [2]: i- Limitations (Failure) 1. Capillary limit. Development of the net capillary forces which generated by the liquid–vapor interfaces in the evaporator and condenser are represent the fundamental phenomenon governing the heat pipe operation. Thus, the capillary limit occurs when the driving capillary pressure is not large enough to provide 9
Chapter One
Introduction
adequate liquid flow from the condenser to the evaporator, therefore evaporator wick dry out will occur. 2. Boiling limit. In heat pipes, the heat flux limit or the boiling limit occurs when the heat flux applied at the evaporator surface is sufficient to cause the nucleation of vapor bubbles on the inner surface of the container or the surface the wick. These vapor bubbles that partially obstruct the liquid flow, and can lead to wick dryout, in the evaporator section. 3. Entrainment limit. The entrainment limit in heat pipes occurs when high shear forces, due to large vapour mass flow rate, developed at the liquid-vapour interface. Whereas, the liquid may be entrained by the vapor and returned to the condenser. This results in dry-out in the evaporator due to insufficient liquid flow to the wick structure. ii- Limitations (Nonfailure): 1. Viscous limit. The viscous limit or the vapor pressure limit develops at low operating temperatures, when the pressure drop in the vapor core along the heat pipe reaches the same order of magnitude as the saturation vapor pressure in the evaporator. This results in an extremely low pressure available to drive the vapor through the condenser section. 2. Sonic limit. The sonic limit can occur in heat pipes during start-up at low temperatures which produces low vapor densities. Thus, a sufficiently high mass flow rate in the vapour core may result in very high velocities and generate a shock wave that chokes the flow in the vapor passage and reduce the ability of heat pipes to transfer heat from evaporator to the condenser. 3. Condenser limit. The cooling limitations, such as convection or radiation, are specifying the condenser limit. For example the heat pipe transport, in the case of cooling by radiation, can be governed by the condenser surface area, emmissity, and operating temperature. 10
Chapter One
Introduction
Additionally, the capillary, viscous, entrainment, and sonic limits are axial heat flux limits, that are, functions of the axial heat transport capacity along the heat pipe, while, the boiling limit is a radial heat flux limit occurring in the evaporator. Using the analysis techniques for each limitation independently, the heat transport capacity as a function of the mean operating temperature (the adiabatic vapor temperature) can be determined. This procedure yields a heat pipe performance region similar to that shown in figure 1-8.
1.6 Objectives of the Study In this study, the main purpose is to develop a numerical model by which one can predict the thermal behavior of constant conductance heat pipe (CCHP) and variable conductance heat pipe (VCHP) with wire screen mesh as wick and water and nanofluid as working fluid at steady – state conditions. Moreover, it includes an experimental study to investigate the effects of some parameters on the heat pipe performance, using a locally manufactured heat pipe. The specific objectives of the present study may be summarized as follows: 1. Investigating the effect of filling ratio on the performance of a wicked heat pipe to select the optimal ratio which gives the best heat pipe thermal performance. 2. Investigating the effect of heat flux on the performance of a wicked heat pipe. 3. Studying the effect of the heat sink temperature on the heat pipe performance. 4. Studying the effect of nanoparticles concentration (Al2O3 and CuO) on the heat pipe performance. 5. Studying the effect of the mass of non-condensable gas on the heat pipe performance. 11
Chapter One
Introduction
6. Prediction of the maximum heat transfer rate for constant conductance and variable conductance horizontal cylindrical heat pipes.
Figure 1-1 (a) Typical heat pipe construction and operation; (b) radii of curvature of the liquid–vapor interface in the evaporator and condenser [2].
12
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Introduction
Figure 1-2 Operating temperature range of common working fluids [3].
Figure 1-3 Representative vapor flow-modulated heat pipes [2].
Figure 1-4 Representative liquid flow-modulated heat pipes [2]. 13
Chapter One
Introduction
(a) Wrapped screen
(d) Annular
(b) Sintered metal
(c) Axial groove
(e) Crescent
(f) Artery
Figure 1-5 Cross sections of homogeneous wick structures [2].
(a) Composite
(b) Screen-covered groove
(c) Slab
(d) Tunnel
Figure 1-6 Cross sections of composite wick structures [2]. 14
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Figure 1-7 Pressure variation along the length of a heat pipe working under low heat flux [2].
Figure 1-8 Typical heat pipe performance map [2].
15
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Chapter Two Literature Review
Heat pipes have gradually being recognized as a highly-effective heat transfer element in almost all industrial fields. Originally, the heat pipe was invented by Gaugler of the General Motors Corporation in 1944, but remains without significant attention within the heat transfer community until the concept resurrected by the space program in the early 1960's. Since then, a great deal of literature has been published concerning experimental, numerical, and analytical work involving heat pipes. Also, the available literature states that the working fluid transport properties limit the heat transfer capability of the all heat transfer devices including heat pipe. To overcome these limitations, a new method is used to improve the fluid transport properties by adding additives to the working fluids. This method was demonstrated firstly by Choi in 1995, when he predicted that nanofluids, a suspension of nanoparticles (less than 100 nm in diameter) in a liquid, could improve the thermal conductivity of the base fluid about 3.5 times. This led finally to improve the thermal performance of many devices such as heat pipe. Nevertheless, a description of the performance of prototype heat pipe systems for aerospace applications, heat recovery systems, solar energy and electronics cooling is mainly represented within this literature. A review of previous literature related to the present study is presented in this section, according to working fluid specification, to provide a historical background for the work discussed in this thesis.
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2.1 Literature Related to Conventional Working Fluid 2.1.1 Theoretical Literature Zhu and Vafai (1999) [14] presented a two dimensional analytical model to study low-temperature cylindrical heat pipes. They obtained a closed-form solution for predicting the vapor and liquid velocities and pressure distributions. This model incorporated liquid-vapor interfacial hydrodynamic coupling and non-Darcian transport through the porous wick. Also, they obtained the steady-state vapor and wall temperatures for a given input heat load in the evaporator region and a convective boundary condition in the condenser region. At the same time, a closedform solution of the heat pipe capillary limit during steady state operation was obtained. These closed-form analytical solutions provided a quick, accurate prediction method for low-temperature heat pipe operation which was found to be in very good agreement with both experimental and numerical results. Finally, the results showed that the interfacial effects are small and can be neglected. Facăo and Oliveira (2002) [15] presented a numerical study of a hybrid flatplate solar collector using cylindrical heat pipes. The hybrid collector used solar radiation and hot gases (gas burner) as energy inputs. The obtained results of the hybrid collector efficiency were quantified for all possible operating conditions. The results showed that the hybrid solar collector has an efficiency of 63% for an incident solar radiation of 1000 W/m2 and an inlet gas temperature of 300 oC. Also, the heat pipes had a very small thermal resistance. Therefore, the condenser temperature can be considered similar to the evaporator temperature. A numerical method based on the SIMPLE algorithm has been developed by Borujerdi and Layeghi (2004) [16] for the analysis of vapor flow in a concentric annular heat pipe (CAHP). They studied the response of a CAHP in the steady-state for various heat fluxes in the evaporator and condenser sections. Navier-Stokes equations were used to simulate the fluid flow and heat transfer in the annular vapor 17
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space. The governing equations were solved numerically, using finite volume approach. The vapor pressure and temperature distributions along a concentric annular heat pipe were predicted for a number of symmetric test cases. They also predicted the vapor flow reversal and transition to turbulence phenomena (Rea,z=2300). The results were compared with the available numerical data and have shown good agreement in all cases. Therefore, the vapor flow model developed in this study had shown good accuracy and convergence behavior in the range of low to moderate radial Reynolds numbers. Finally, the results showed that due to the small pressure drop along the heat pipe at low and moderate radial Reynolds numbers, the present analysis predicted very small vapor temperature drop along the heat pipe. A significant energy saving in domestic sector was attained when heat pipe fin stack was utilized in the drying cycle of domestic appliances for heat recovery. In this work, a design method by using CFD simulation of the dehumidification process with heat pipe heat exchangers was presented by Lin et al. (2004) [17]. They presented the strategies of simulating the process with heat pipes. The results showed that the method can be further used to optimize the design of the heat pipe fin stack. The study suggests that the CFD modeling is able to predict thermal performance of the dehumidification solution with heat pipe heat exchangers. Mahjoub and Mahtabroshan (2008) [18] presented a numerical solution of the steady incompressible flow in cylindrical coordinates in both vapor region and wick structure. The governing equations that they used in vapor region were continuity, Navier-Stokes and energy equations. They used SIMPLE algorithm to solve these equations. For a parametric study on heat pipe operation, a benchmark had been chosen and the effect of changing one parameter had been analyzed when the others are fixed. The results that they obtained showed that: 18
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Wick porosity, wall thermal conductivity and heat pipe radius had significant effects on the thermal resistance of a conventional cylindrical heat pipe. It increased with wick porosity and decreased with wall thermal conductivity and heat pipe radius. The temperature difference between evaporator and condenser remained nearly constant with increasing heat pipe length. Consequently the thermal resistance of heat pipe remained constant. Also, the pressure drop increased with heat pipe length. With increasing the transmitting heat the temperature difference in evaporator and condenser section increased. Also, the pressure drop in liquid region increased since the flow rate of liquid increased. Shabgard and Faghri (2011) [19] presented a steady-state analytical model for cylindrical heat pipe subject to multiple uniform heat sources, as in figure 2-1, and subjected to either constant heat flux or convective cooling in the condenser. The proposed model coupled two-dimensional heat conduction in the heat pipe‟s wall with the liquid flow in the wick and the vapor hydrodynamics. They considered two heat pipes; the first with 1m length and 0.0254m outer diameter and the other with 0.89m length and 0.0191m outer diameter to study the effects of multiple heat source and axial conduction on heat pipe operation. They obtained a very good agreement between the results of the analytical model when compared with full numerical simulations. The effect of the axial heat conduction in the heat pipe wall was assessed by carrying out a parametric study of heat pipe length, wall thickness, wick thickness and heat transfer rate. The results showed that in certain cases exclusion of the axial heat conduction in the wall can causes an error more than 10% in the calculated pressure drop in heat pipe, while, considering axial heat conduction was important to obtain the accurate temperature distribution along the heat pipe wall. Finally, they showed that a significant saving in computational time 19
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was achieved by use of the proposed analytical model compared to full numerical simulations. Therefore, the developed model provided a useful tool to evaluate the capillary limit of the cylindrical heat pipe and can be used for optimization and design applications. The two-dimensional heat transfer and fluid flow in a heat pipe at steady state was numerically simulated by Thuchayapong et al. (2012) [20] using the Finite Element Method (FEM). They considered a heat pipe with 18.8mm, 890mm and 0.15mm as outer diameter, length and thickness respectively. The wick was a double-layer of a 150 mesh copper screen. The liquid-wick thickness was assumed to be 0.75 mm. A vapor core, wick, wall of container, and water jacket may are considered as the domains of calculation. In this work, the researchers developed a study that coupled the liquid and vapor pressures in their model by applying the capillary pressure model at the liquid-vapor interface. Whereas, the capillary radius variation was assumed to be a simple linear function, of the wick effective pore radius (Reff) and the vapour core radius (Rv), along the heat pipe and applied in the capillary model. They used this assumption for investigating the effect of capillary pressure on performance of a heat pipe. It also affected on the wall temperature distributions at the end of evaporator section. The results showed that the capillary pressure gradient inside the wick at the end of the evaporator section was very large. This may have been a result of fast liquid motion at the end of the evaporator section, thus, providing efficient heat transfer by convection. The numerical results of the vapor and wall temperature distribution were compared with experimental data of heat pipes with the coppermesh wick obtained by Huang et al., cited by [20], to confirm the validity of the simulations. The standard deviations of vapor and wall temperature were 0.48 C and 1.78 C, respectively. 20
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Finally, they showed that, experimentally-validated heat pipe temperature distributions were successfully simulated in two dimensions, which may help to improve the accuracy and efficiency of heat pipe design.
2.1.2 Experimental Literature Minimization of thermal distortions, in most precision engineering applications, is done by the use of either active control using temperature controlled air or liquid showers, artificial heaters or ultra-low expansion materials such as Invar, Zerodur. Thus, Borundia and Tran (1999) [21] explored the use of heat pipes as a means of passive cooling at low power inputs (0.1 W – 5 W) encountered in the lithography process and other precision engineering applications where the requirement of stable and near uniform temperature is stringent. They performed their experiments on a commercial heat pipe with 4mm diameter and 125 mm length. The entire set up was placed in a vacuum chamber to further reduce the heat loss through convection and radiation to the surrounding environment as shown in figure 2-2. Hence, the heat pipe performance characteristics such as effective thermal conductivity, transient response and temperature gradient at steady state were determined. The experimental results of the effective thermal conductivity, transient response and steady state temperature distribution of the heat pipe at operating temperatures of 0 oC and 17 oC respectively, are shown below: The effective thermal conductivity of the heat pipe was found to be equal to that of copper at 0.4 W and 0.1 W of power input at 0 oC and 17 oC respectively. The heat pipe time constant was found to be ranging from 60 to 70 secs for both the cases thus indicating that the transient response was independent of the operating temperature of the heat pipe at low power inputs.
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The temperature gradient along the adiabatic section of the heat pipe at steady state was found to be varying linearly from 0.068 oC /mm to 0.28 o
C/mm at 0 oC and from –0.03 oC/mm to –0.26 oC/mm at 17 oC between
power inputs 0.1 W to 5 W respectively. This showed that the temperature gradient was not very sensitive to the operating temperature of the heat pipe. Seok et al. (2000) [22] performed an experimental study for miniature heat pipe (MHP) with woven-wired wick, as shown in figure 2-3, which was used to cool the CPU of a notebook PC. The used pipe in this study with circular crosssection was pressed and bent for packaging the MHP on the very limited space of a notebook PC. When the MHP with 4mm diameter is pressed to 2mm thickness the pipe cross-sectional area was reduced about 30%. In this study, they performed a performance test in order to show the change of operating performance according to the pressed thickness variation and the heat dissipation capacity of MHP cooling module that is packaged on a notebook PC. Also, they considered new wick type in their study for overcoming low heat transfer limit when MHP is pressed to thin-plate. Whereas, the limitation of the pressed thickness during the performance test was shown to be within the range of 2mm – 2.5mm. The results obtained from the performance test were as follows: MHP with woven-wired wick showed the normal operating performance up to the pressed thickness of 2.5mm.
However, cooling performance is
significantly decreased when the pressed thickness is 2mm. Therefore, the limitation of pressed thickness of MHP with woven-wired wick was between 2mm and 2.5mm. About 10% improvement in the maximum heat transfer limit and thermal resistance can be achieved as the wall thickness of MHP is reduced from 0.4mm to 0.25mm. 22
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MHP with central type wick had a maximum heat transfer limit and thermal resistance lower than that of the MHP whose wick is attached along the inner wall. The results of performance test were satisfied the requirement of Tj (Junction Temperature of Processor) of 0°C - 100°C under the operating condition, 11.5W of a CPU thermal load. Experimental investigations were carried out by Sreenivasa et al. (2005) [23] for optimizing the fluid inventory in a typical heat pipe. Generally as known, a flooded, with exceedingly large amount of working fluid, heat pipe has slow response and has limited lower range of operation in terms of operating temperature. While starving, with too little amount of working fluid, heat pipe although exhibits fast response to heat loads, shows severe limit at high temperature conditions. In this study, the attempt was made by the researchers to design, fabricate and test a miniature heat pipe with 5 mm diameter and 150 mm length with a thermal capacity of 10 W. The working fluids used in this study were same as those commonly used namely, water, methanol and acetone. Thermocouples are used for measuring and recording the temperature distribution along the heat pipe. Experiments were conducted with and without working fluid for different thermal loads, 2, 4, 6, 8 and 10W, to assess the performance of heat pipe. Whereas, the heat pipe performance was quantified in terms of response time for surge loads, thermal resistance and overall heat transfer coefficient. The amount of liquid was varied and the results were showed as follows: Steady state of the system occurred earlier in case of wet run when compared to dry run. The steady state temperature increases with increased heat loads. The wet run showed an averaged constant axial temperature gradient. While, gradient of temperature distribution in dry run increased with the heat input. 23
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The operating heat pipe with wet run had lower overall resistance when compared to dry run. The thermal resistance observed in the dry run was 10 o
C/W and that in wet run was 6 oC/W, for a 2W heat input capacity.
Increasing the heat input led to increase the overall heat transfer coefficient of heat pipe, in the range of inputs tested for acetone and methanol, while water filled heat pipe showed a nearly constant coefficient. The filling ratio of working fluid as 85% of evaporator volume was shown to have minimum effect on the performance of heat pipe with respect to the temperature difference when water and methanol are used as working fluids. However, in case of acetone, the temperature difference across evaporator and condenser continues to drop down with an increase in the fill ratio. With acetone as the working fluid, 100% fill ratio of evaporator volume shows the best result with minimum temperature difference across the evaporator and condenser. In general, fill ratio of working fluid greater than 35% of volume of evaporator showed better results in terms of increased heat transfer coefficient, decreased thermal resistance and reduced temperature difference across the evaporator and condenser. The effect of length to internal diameter (L/di) ratio of heat pipe on the performance of heat pipe solar collector was experimentally investigated by Sivaraman and Mohan(2005) [24]. They designed and fabricated two solar collectors with different L/di. Also, they replaced the transport tubes of the solar collector by stainless steel wick heat pipe. The material of container and wick are fabricated from copper and stainless respectively, while methanol was used as working fluid of heat pipe. For the experiments, the heat pipes were designed to have heat transport factor of around 194 W and 260 W of thermal energy. Experiments were conducted during summer season with a collector tilt angle of 24
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13o to the horizontal. The collector with L/di ratio of 52.63 was found to be more efficient, by 68%, than the collector with L/di ratio of 58.82. This improving in the efficiency is due to increase in heat transport factor of heat pipe, which increase with decrease in L/di ratio. An experimental study has been performed by Kempers et al. (2006)[25] to determine the effect of the number of mesh layers and amount of working fluid on the heat transfer performance of copper–water heat pipes with screen mesh wicks for different orientation. They fabricated the tested heat pipes from copper tubing with an outer, inner diameter and length of 9.53, 6.22 and 177.8 mm respectively. While, the wicks for each heat pipe were made from a woven copper wire screen mesh with wire diameter of 0.109 mm and 3940 strands per m. Fluid loadings that corresponded to 50%, 80%, 100%, 120% and 150% of the amount of water required to saturate the wick, which corresponded to 0.63 g, 1.01 g, 1.27 g, 1.52 g, and 1.9 g of water, respectively are used in the tests which performed for the heat pipes. Also, they considered 1, 2, 3 and 6 layers of wire screen mesh in the tests. At low heat fluxes, the effective thermal resistance variation was non-linear for the heat pipes with the smaller number of mesh layers. The non-linearity is more significant as the number of layers is decreased. The thermal resistance decreased significantly with the heat flux, and then approaches a constant value. In the nearly constant region, the thermal resistance increase with the number of mesh layers. However, a six fold increase in the number of mesh layers resulted in only a 40% increase in thermal resistance of the heat pipe, and is not consistent with models based on conduction heat transfer through the wick. The maximum heat transport rate before the onset of failure increased with the number of mesh layers.
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Also, as the heat pipes were inclined from vertical, the maximum heat transport capacity of the heat pipes decreased. All heat pipes that tested under the same fluid loading had similar heat transfer characteristics before the onset of failure and exhibited roughly the same non-linearity at low heat fluxes. This indicates that the fluid loading is not the cause of the non-linearity. The thermal resistance of the heat pipes increased with the fluid loading. Whereas, the heat pipes with fluid loadings close to the „„ideally‟‟ loaded case, which defined as the amount of fluid required to fully saturate the wick, exhibited little differences in the effective thermal resistance. In the under-loaded heat pipe, the onset of dry-out resulted in an increase of effective thermal resistance over time. This may be due to liquid accumulating in the wick at the condenser section of the heat pipe causing the evaporator section to remain dry. Under-loading also resulted in a maximum heat transfer rate which is significantly lower at all orientations than that obtained for overloading. This resulted in marginally higher maximum heat transfer rates at all orientations besides vertical. Kempers et al. (2008) [26] investigated experimentally the heat transfer mechanisms in the condenser and evaporator sections of a copper-water wicked heat pipe. They performed their experiments using a 19.05 mm outer diameter copper-water heat pipe with a length of 355.6 mm and a wall thickness of 1.65 mm. A copper wire screen mesh with 3 wraps and a wire diameter of 0.11 mm and 3937 strands per meter was used. The heat pipe was charged with 7.13 ml of water, which approximately corresponds to the amount required to completely saturate the wick based on a standard model for screen mesh porosity. The individual condenser and evaporator thermal resistances obtained where the temperature distributions 26
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measured using thermocouples on the outer wall and within the core of the heat pipe under different operating conditions. The results obtained showed that the heat transfer in the condenser section was found to be only by conduction. This was demonstrated by the experimental results which were in good agreement with the conduction model of Chang, cited by [26]. While, in the evaporator either conduction or boiling heat transfer can occur. Also, the transition between the two modes was found to be dependent on the vapor pressure and heat flux, with boiling occurring even for very low heat fluxes or superheat for operating temperatures above 50 oC. The onset of boiling in the evaporator could be reasonably predicted by the bubble nucleation criterion outlined by Van Stralen and Cole, cited by [26]. The experimental data for the boiling heat transfer in the evaporator was well correlated by: [ ][ ]
[
[
]
]
(2-1)
Where:
(
)
( )
Finally, they proposed a composite heat transfer model for the heat pipe that considers both conduction and boiling heat transfer in the evaporator. The predictions from this model, using the boiling correlation proposed in this study, were in good agreement with the experimental data. Experimental investigation was performed by Xie et al. (2008) [27] for the thermal performance and pressure drop of a novel integrated heat pipe–heat sink with a new kind of wick structure applied in the evaporator and multi-condensers, as shown in figure 2-4. The obtained results indicated that the heat transfer performance was strongly affected by the air flow rate and power input, especially when the air flow rate is less than 40 m3/h. This copper water heat pipe–heat sink reaches the performance of the thermal resistance 0.118 K/W for a total power of 27
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420 W under the maximum temperature difference limit of 50 K when the air flow rate is 71 m3/h (2.9 m/s of frontal velocity) with pressure drop of 30 Pa. It is estimated that by refining the fin-side heat transfer surface structure, this type of heat pipe–heat sink could reach higher heat flux at the same operating conditions. Tsai et al. (2010) [28] developed a novel dynamic test method to shortens the necessary time for determining the thermal performance of heat pipes. A set of new dynamic parameters of thermal performances of heat pipes, as „„decreasing gradient of temperature difference oC s_1”, „„dynamic descending rate s_1”, and „„maximum heating temperature oC” are ideated from the observed transient phenomenon, and their validities are verified. They study the influences of bending angles, fill ratios and shapes of heat pipes on the thermal performances of heat pipes for both steady-state and dynamic tests. Thus, they established a model based on the investigated dynamic test to explain the experimental results. The results of simulation and experiments in dynamic testing are in fine agreement and rational analogies are observed between the steady-state test and the developed dynamic test. The experimental results that they performed show that deformation of heat pipes influence the thermal performances of heat pipes most significantly. Also, they demonstrate that the parameters of the dynamic test effectively reflect the parameters of the steady-state test. Therefore, the dynamic test can be adopted as a serviceable method to determine thermal performances of heat pipes. Finally, the experiments show that only 10–15 minutes are necessary to examine a heat pipe using the dynamic test. This is much more efficient than the steady-state test and would be greatly beneficial to the notebook PC industry or other heat dissipation technologies that use heat pipes. Masaru et al. (1985) [29] described titanium heat pipe design, manufacture and tests. The heat pipes developed are titanium –ammonia heat pipe with axial grooves (FCHP) and a titanium – ammonia – gas loaded variable heat pipe which 28
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has a heated reservoir (VCHP). The groove shape was initially designed so that it would be rectangular and that the groove depth would be more than 0.5 mm. Three grams as initial mass of pure nitrogen 99.99% was charged to the VCHP as noncondensable gas. The results show that there are no problems in welding and pinchoff of titanium and that the grooves made by proposed method have the capability to carry 22.7W heat load for CCHP. This study has clarified that titanium is very desirable as heat pipe material for use in space. For a high power photonic devices, thermoelectric modules (TEMs) are used for precision temperature control. TEMs consume a large amount of power, particularly when subjected to a wide range of ambient temperatures. Thus, the use of variable conductance heat pipes (VCHPs) as a lower power alternative to TEMs was investigated by Cleary et al. (2007) [30]. They characterize the performance of a methanol-argon VCHP with a non-wicked reservoir for both passive and active control. Moreover, they introduce the concept of an “ideal” working fluid for a gasloaded VCHP. An experimental prototype was constructed and the obtained measurements are compared with the predictions of the flat front model. The results that they presented showed that the following: From the comparison between the saturation curve of the ideal working fluid with that of methanol it is clear that perfect passive control of evaporator temperature is unrealistic for varying ambient temperature. A non-dimensional form of presenting the saturation properties of fluids is presented which allows the relative merit of fluids with different liquid-vapor saturation curves to be assessed and to determine their overall effectiveness as VCHP operating fluids. They found that the flat front model offers a reasonably good prediction of the evaporator temperature for an unheated reservoir. However, the flat front
29
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model for a heated non-wicked predicted the performance of this VCHP prototype. Experimentally it was found that it was not possible to control the evaporator temperature at low ambient temperatures due to the high rate of axial conduction through the copper wall and wick of the adiabatic section in the prototype VCHP. Excluding these low ambient temperatures, the VCHP provided a significant power consumption reduction when compared to a TEM. The design and test of a pressure controlled heat pipe (PCHP) for spacecraft thermal management was discussed by Sarraf et al. (2008) [31].The PCHP combines a conventional grooved aluminum–ammonia heat pipe with variable– volume non-condensable gas reservoir to create a heat pipe whose conductance can be precisely controlled, as shown in figure 2-5 for the system block diagram. A PCHP with variable volume control was successfully demonstrated. It approached, all of its design goals, and it is a significant advance over other means of temperature control even in its current non-optimized state. The results show the following: A prototype PCHP was capable of maintaining a stable evaporator temperature within 0.1 oC over changes in heat sink temperature from -70 to -40 oC while the changes of input power from 50 to 250W. A similar-sized conventional variable conductance heat pipe, as in figure 2-6, yielded temperature swings of over 3.5 oC for the same variation of heat load and sink temperature. The PCHP was able to maintain the evaporator temperature within 0.05 K over time. The transient response time of the PCHP evaporator was 30 seconds. While, the response time of a heated-reservoir VCHP, figure 2-7, having similar 30
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power consumption was 20 minutes. Thus, the PCHP had a much faster transient response than the other devices, as well as providing means for changing the set point temperature after assembly. Finally, A PCHP with variable volume control was successfully demonstrated. It met, or approached, all of its design goals, and it is a significant advance over other means of temperature control even in its current non-optimized state.
2.1.3 Theoretical and Experimental Literature Kim et al. (2003) [32] developed a one-dimensional heat and mass transfer model and obtained an analytical solution to yield the maximum heat transport rate and the overall thermal resistance under steady-state conditions for miniature heat pipe with grooved wick structure. In their model, they considered the contact angle, the amount of initial liquid charge and the effects of liquid-vapor interfacial shear stress. They presented a new method called modified Shah Method for the effect of the liquid-vapor interfacial shear stress. Also, they conducted experimental work to obtain the maximum heat transport rate and the overall thermal resistance to verify their model. Additionally, a numerical model was performed for thermal optimization of the grooved wick structure with respect to the width and the groove height. As a result, they obtained the capillary radius distribution as well as the liquid and vapor pressure distributions along the heat pipe under steady- state operation. Also, the maximum heat transport rate of heat pipes with outer diameter of 3 and 4 mm with an optimized groove wick structure can be enhanced up to 48% and 73%, respectively and the total thermal resistance can be reduced up to 7% and 11%, respectively, from the existing configurations. A theoretical and experimental study of a copper heat pipe sintered with a copper powder wick was presented by Fadhil (2006) [33]. He considered in his 31
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theoretical simulation, a two –dimensional axisymmetric performance analysis for steady–state condition to identify the effect of each of the input heat flux, inclination angle, wick thickness, coolant temperature and absence of the adiabatic section on the heat pipe performance. The governing equations used in the analysis were, Navier–Stokes equations, energy equation in addition to the mass conservation equation. The numerical scheme was developed with a control volume approach. Pure water was used as a working fluid. The theoretical results show that the velocity of the liquid in the wick structure is very small in comparison with vapour velocity. The increase in the input heat flux leads to a clear increase in the heat pipe operating temperature. Moreover, the change in the heat pipe inclination angle from 90o to -90o has led to an insignificant increase in the heat pipe operating temperature. Also, the increase in wick thickness has improved the performance of the heat pipe. Finally, the absence of the adiabatic section has led to a significant decrease in the operating temperature of the heat pipe. In his analysis, the heat pipe in a horizontal position with a wick thickness of 1 mm and a coolant temperature 25 oC, the maximum heat transfer rate that can be transported by this pipe without the evaporator reaching the dry out state is approximately 3.8 kW/m2. The experimental results show that, at the same operating conditions, the heat pipe performance is better than the thermosyphon performance. Also, he shows that the optimum amount of the liquid charge was about twice the amount theoretically estimated for heat pipe with sintered copper powder wick. The heat pipe performance improved when the inlet coolant temperature was increased from 25 to 50 oC. The heat pipe thermal performance decreased when it was operating against gravity. The heat pipe operating temperature increases with the wick thickness increase. The absence of the adiabatic section led to a decrease in the heat pipe operating temperature and improvement in its performance. Finally,
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comparing the numerical results with those obtained from the experimental work showed that there was a good agreement. Gang et al. (2011) [34] designed and constructed a novel heat-pipe photovoltaic/thermal system (HP-PV/T), as in figure 2-8. Simultaneously, this system can supply electrical and thermal energy. Also, it can be used in cold regions without freezing. They developed a dynamic model to examine the dynamic performances of the HP-PV/T system and is validated by experimental results. The results show that the average heat gain per unit collecting area and the average electrical gain per unit PV area are 276.9 and 62.3 W/m2, respectively and the corresponding efficiencies are 41.9% and 9.4%, respectively. Also, second-law efficiency, based on the second law of thermodynamics, is provided to analyze the total efficiency of the HP-PV/T system, and the average total second-law efficiency of the system is 6.8%, in the test duration with an average solar radiation intensity of 661 W/m2. The simulation results, such as temperatures of the PV cells, base panel, heat pipe and water, agree well with the values in experimental results with a relative error of less than or equal to ±5.0%. Simulation values of the instantaneous electrical gain and heat gain as well as the instantaneous electrical efficiency and thermal efficiency match the experimental results approximately. The mean deviations are about 16.0%, and the average deviations are less than or equal to ±2.4% during the test. Analytical and experimental investigations were presented by Ling and Cao (2000) [35] for the radially rotating miniature high-temperature heat pipe, as in figure 2-9. The heat pipe used in this study was a wickless miniature heat pipe. They considered diameter in the range of 1.5-2 mm for the radially rotating miniature high-temperature heat pipe. The diffuse effects of non-condensable gases on temperature distribution along the heat pipe length are investigated. They obtained closed-form solutions for the temperature distribution along the heat pipe 33
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length and it showed good agreement with experimental data. The results showed that heat pipe with sodium as the working fluid has a very large heat transfer capability and a high effective thermal conductance that is 60-100 times higher than the thermal conductivity of copper. Moreover, they showed that the heat pipes can still work effectively and reliably, although the diffuse effects of the noncondensable gases would increase temperature drop along the heat pipe length. Mezaache (2005) [36], performed a numerical and experimental investigations for steady-state thermal performance of a gas-loaded heat pipe. The physical modeling was based on the simple conduction model for the vapour region and a two dimensional heat and mass transfer model for the gas region. The heat pipe system is designed, with 1.05m long and 0.0889m diameter, and variable heat input less than 800W. The experimental evaluation of the thermal performance is made with water as working fluid and 0.1588 moles of helium as non-condensable gas. Prediction of the wall temperature along the heat pipe, and the radial and axial field of temperature and gas concentration in the vapour-gas condenser region are obtained from the analysis. The measured results agree well with numerical predictions. The results showed that the mass diffusion reduced the thermal performances of the VCHP by reducing its isothermal region due to the accumulation of the non-condensable gas at vapour-liquid interface. Consequently a good thermal performance of the system cannot be obtained with the use of working fluid and non-condensable satisfying large values of the radial diffusion parameter, which defined as the ratio of the radial gas diffusion rate to the vapour condensation rate. However, the research showed that this choice is not the only criteria to consider, since in a VCHP, is necessary to take account also of the chemical compatibility between the wall, the non-condensable gas and the working fluid, and of the level of operating temperature that is imposed by the saturation pressure of the working fluid. 34
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Cleary et al. (2006) [37] proposed the replacement of the thermoelectric module (TEM) based approach with a variable conductance heat pipe (VCHP). In this study an existing theory was used to investigate the use of wicked and nonwicked reservoirs and the effect of reservoir volume on the sensitivity of the evaporator temperature to changes in both ambient temperature and heat load for both heated and unheated reservoirs. Also, the effectiveness of the use of a steel collar between the reservoir and the condenser for reducing the heat loss to ambient was investigated. They conclude the following: concave Theoretically with a variable heat load, complete passive control is possible for fixed ambient temperature. While, complete passive control for variable ambient temperature is not possible thus the reservoir temperature must be actively controlled. The evaporator temperature of VCHPs with large actively heated wicked reservoirs is very sensitive to small changes in reservoir temperature but by reducing the reservoir size it is possible to provide the necessary temperature control with a temperature range that is more practical to implement. For the same evaporator temperature control, a VCHP with an actively heated non-wicked reservoir requires a much larger reservoir than a VCHP with an actively heated wicked reservoir. A VCHP with a large non-wicked reservoir provides the necessary active length temperature control with the lowest power consumption, however, a VCHP with a small wicked reservoir can provide the same control but with increased power consumption. A TEM with an optimized heat sink subjected to a constant heat load of 10 W and an ambient temperature range of -5 oC to 65 oC consumes 3.1 W at the lowest ambient temperature compared to a power consumption of 0.176 W for a VCHP with a non-wicked reservoir and 2.63W for a VCHP with a 35
Chapter two
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wicked reservoir indicating that there is the potential for significant power consumption reduction by replacing a TEM with a VCHP. An analytical and experimental study was introduced by Leriche et al. (2012) [38] for a Variable Conductance Heat Pipe (VCHP) applied to vehicle thermal management, as in figure 2-10. The objective of their study was the reduction of engine energy consumption after a cold start by controlling – heating cooling cycle of oil. The performance of a copper/water VCHP using nitrogen as a noncondensable gas was theoretically modeled based on a nodal method and an experimental test bench. VCHP operated as a thermal switch, with a start-up temperature of 80 C. The present study comprised also, the effect of the air mass flow rate on the condenser and the effect of the inclination angle (i.e., adversegravity, horizontal position or gravity-aided) on the performance of the VCHP. The theoretical results obtained from their study are: The developed nodal model shows that using a VCHP to cool the engine oil in an insulated sump during a vehicle‟s cold start is appropriate. This model shows that a solid pipe, a heat pipe container or a standard heat pipe is not suitable to cool the system with control delay. This nodal model could be used to simulate the integration of the VCHP in the vehicle‟s general thermal model during a cold start, as well as to estimate the consumption and the amount of pollution produced, using an insulated oil sump connected to at least two VCHP. While, the results obtained from the experiments are: The inclination angle has a strong influence on the VCHP‟s efficiency. In fact, VCHP efficiency is strongly affected if the angle is negative and the temperature at the evaporator is high. In addition, for α= 0, it has been shown that the VCHP cools the system only for low power levels. For high power 36
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levels, the temperature at the evaporator is greatly increased. However, with positive angle, with the help of gravity, VCHP efficiency is improved because the gravity helps to generate the wick effect. The start-up of the heat pipe depends on the air velocity through the condenser fins. Whereas, the start-up for high velocities is more rapid than for low velocities. Also, they showed that, the VCHP is an interesting solution for the vehicle thermal management in order to reduce the engine energy consumption after a cold start by controlling heating-cooling cycle of oil. Saad et al. (2012) [39] presented a numerical and experimental investigation to evaluate the effect of non-condensable gases and axial conduction on the transient performance of a copper-water wicked heat pipe. The heat pipe had an outer diameter of 19.05 mm, wall thickness of 1.65 mm and a length of 355.6 mm. while, the wick structure was 4 layers of a woven copper wire screen mesh with wire diameter of 0.109 mm and 3937 strands per meter (100 strands/inch). The effect of non-condensable gases and axial conduction was incorporated to an existing transient wicked heat pipe network model. Consequently, the different components of the heat pipe were modeled using a large number of elements in both axial and radial directions to incorporate the axial heat conduction in the heat pipe wall and wick and introduce non-uniform boundary conditions. Also, a simple flat-front model for the non-condensable gases was incorporated in the model. Hence the predictions of the steady and transient response model of the heat pipe are in good agreement with the major features of the experimental results. Finally, the results show that the transient response was affected by the presence of noncondensable gases. Whereas, they causes the wall to be heated along the length of the heat pipe over time as the non-condensable gases was compressed. Also, the axial conduction lengthen the region over which this occurs, but haven‟t a great 37
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influence on the time response during this phase. Thus, similar to steady state results, the axial conduction affect the overall thermal resistance of the heat pipe. While during cooling phase, the cooling rate of the heat pipe was decreased once the non-condensable gases occupies much of the cooled region of the heat pipe. This results in a practical limit on the vapor temperature of the heat pipe during the cool-down phase. And, thus the axial conduction has a significant effect during this cooling period because it is the only heat transfer mode to the cold section in the heat pipe once the cooled section was occupied by the non-condensable gas.
2.2 Literature Related to Working Fluid with Nanoparticles 2.2.1 Theoretical Literature A two-dimensional analytical model was used by Shafahi et al. (2010) [40] to study the thermal performance of a cylindrical heat pipe utilizing nanofluids. Their analysis was based on a comprehensive analytical model proposed by Zhu and Vafai
[14]. The pure water base fluid with three of the most common
nanoparticles, namely Al2O3 , CuO and TiO2, with a range of 10, 20 and 40 nm diameters, are considered as the working fluid.The investigation comprise the heat pipe velocity, pressure, temperature, and maximum heat transfer limit for different nanoparticle concentration levels and sizes. Moreover, they explored the possibility of reducing the size of the cylindrical heat pipe by utilizing nanofluids. From the results under the same operational conditions, when the evaporator temperature was kept at 90 oC, the smallest particle size (10 nm) of CuO based nanofluid provide the largest reduction in the size of the heat pipe which reache up to 78% of the nominal size. Also the results show that using CuO nanofluid with 4% and 10nm concentration and diameter respectively, with heat load varied from 200 to 800 W reduce the thermal resistance of the cylindrical heat pipe up to 75% of its initial resistance. The influence of nanofluid concentration and the geometrical 38
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characteristics of the wick on the maximum heat transfer limit of the cylindrical heat pipe were investigated. Whereas, the optimum concentration levels in producing the maximum heat transfer were about 5%, 15% and 7% for Al 2O3, CuO and TiO2, respectively. Solomon et al (2014) [41] developed a two – dimensional transient numerical model to predict the wall temperature, liquid velocity, vapour velocity and vapour pressure in wicked heat pipe. In this model, the mass, momentum and energy equations are solved numerically for liquid and vapour regions. Then, the effect of Cu – water nanofluid on heat pipe thermal performance is studied and the transient profiles of liquid and vapour velocities in the wick region and the location of dry-out in the evaporator section are obtained. The obtained results from the model show that: The addition of Cu – nanoparticles reduce the wall temperature, operating pressure, vapour temperature and heat pipe overall thermal resistance; thereby, increasing the heat transfer of the heat pipe at the same heat load. The liquid and vapour velocities of the heat pipe with DI water is found to be 20% higher when compared with that of the heat pipe charged with 0.1 wt% of Cu – water nanofluid at the same operating conditions. The addition of nanoparticles increases the effective thermal conductivity of the wick structure, due to decreasing the pore size of the wick, which acts as a coating layer and enhances the heat transfer capability of the heat pipe.
2.2.2 Experimental Literature Investigating the effects of nanofluid on heat pipe thermal performance are carried out by Tsai et al. (2004) [42] using a circular meshed heat pipe with 170 mm length and 6 mm outer diameter. It was designed as a heat spreader for CPU in a notebook or a desktop PC. The nanofluid used in the study was an 39
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aqueous solution of various-sized gold nanoparticles. The measured results show that the thermal resistance of the heat pipe ranges from 0.17 to 0.215 oC/W with different nanoparticle solutions, which is lower than that with DI water. Whereas, the enhancement in the thermal resistance reach up to 37% when the nanoparticle size is 24 nm. Also, the results show that the thermal resistance of a vertical meshed heat pipe varies with the size of gold nanoparticles. Kang et al. (2006)[43] investigated the effects of silver nanofluid on the thermal performance of 211 µm wide x 217 µm deep grooved circular heat pipe with 200 mm length and 6 mm diameter. The nanofluid used in the experimental study is an aqueous solution of 10 and 35 nm diameter silver nanoparticles with concentrations ranged from 1 mg/l to 100 mg/l. The experiment was performed to measure the temperature distribution and to compare the heat pipe thermal resistance using nano-fluid and DI-water. The condenser section was cooled by water with 40 oC . The results show that at the same charge volume, the measured nanofluid filled heat pipe the temperature distribution demonstrate that the thermal resistance decreased 10–80% compared to DI-water at an input power of 30–60 W. Also, thermal resistance of grooved heat pipe appears to be dependent on the size of the nanoparticles, where the maximum reduction was 50% at 10 nm and 80% at 35 nm, respectively. Finally, they explained the reason for heat pipe thermal enhancement as follows. The nanoparticles can flatten the transverse temperature gradient of the fluid and reduce the boiling limit because of the increasing effective liquid conductance in heat pipes. Hence, for the same reason the thermal resistance of a heat pipe is reduced. As a result, using the nanofluids gives higher thermal performances than that of conventional pure water in grooved heat pipes. This finding makes nanofluids more attractive as a cooling fluid for devices with high energy density.
40
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The enhancement of heat pipe thermal efficiency with nanofluids was investigated by Naphon et al. (2008) [44]. A straight copper tube with outer diameter and length of 15, 600 mm, respectively was used to fabricate the heat pipe. The de-ionic water, alcohol, and nanofluids (alcohol and nanoparticles) are used as working fluid in the heat pipe testing. The titanium nanoparticles with diameter of 21 nm was used in the experiments where the mixtures of alcohol and nanoparticles are prepared using an ultrasonic homogenizer. Effects of working fluid volume, heat pipe tilt angle and nanoparticles concentrations on the thermal efficiency of heat pipe was investigated. The preliminary results for the working fluids show that the optimum condition are 60° tile angle and 66% charge amount for water and 45° tile angle and 66% charge amount for alcohol. The results also show that the enhancement of thermal efficiency of heat pipe was strongly affected by the nanoparticles concentration. The thermal efficiency of heat pipe with the nanofluids is compared with that the based fluid. Whereas, 0.10% nanoparticles volume concentration was enhanced the thermal efficiency by 10.60%. At the optimum condition, 45° tile angle and 66% charge amount for alcohol. Chiang (2009) [45] experimentally investigated the effect of silver (Ag) nanofluids on the screen wick heat pipe thermal performance. The outer diameter and length of the heat pipe used in the experiment were 6 mm and 200 mm, respectively. The nanoparticles used in the experiments were Ag particles with 35 nm in size and the base working fluid was pure-water. The nanofluids in this study was prepared using a two-step method with 15 and 50 PPM. The temperature distribution along the heat pipe was measured to calculate the thermal resistance by the following equation; (2-2)
41
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For same charge volume, the preliminary results show that there is a reduction in thermal resistance of heat pipe with nanofluid as compared with DI water. Whereas, the performance with 15 PPM Ag nanofluid was higher than 50 PPM. Thus, the reason for heat pipe thermal enhancement as follows. Using the existing heat pipe and nanofluid theories, particularly those related to the effective thermal conductivity of wick structure, and nanoparticles can flatten the transverse temperature gradient of the fluid and reduce the wick‟s thermal resistance because of increasing effective liquid conductance in heat pipes. Hence, the thermal resistance of a heat pipe is reduced for the same reason. Kang et al. (2009) [46] used a conventional 1 mm wick-thickness sintered circular heat pipe to investigate effects of an aqueous solution of 10 and 35 nm diameter silver nanoparticles and its
concentration on
heat pipe thermal
performance. The experiments were performed to measure the temperature distribution and compare the heat pipe temperature difference using nanofluid, with nanoparticle concentrations ranged from 1, 10 and 100 mg/l, and DI-water. The condenser section of the heat pipe was cooled by water supplied from a constant temperature bath maintained at 40 oC. The measured results show that for the same charge volume, the temperature distribution of the heat pipe with nanofluids demonstrated that the temperature difference decreased 0.56–0.65 oC compared to DI-water at an input power of 30–50 W. In addition, the heat transfer capacity of heat pipe increased from 50 W by using DI-water to 70 W by using nanofluid as a working fluid. The results also show that the effect of nanoparticle size on heat pipe thermal performance is slight, at the same concentration. Whereas for the nanofluid with 35 nm a lower temperature difference of heat pipe was noted. Nevertheless, it was closed to 10 nm. The obtained heat pipe thermal enhancement is due to that the nanoparticles can flatten the transverse temperature gradient of the fluid and reduce
42
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the boiling limit because of increasing effective liquid conductance in heat pipes. Hence, the thermal resistance of a heat pipe is reduced for the same reason. Do et al. (2010) [47] experimentally, investigated the effects of the waterbased Al2O3 nanofluids on the thermal performance of circular screen mesh wick heat pipes with the volume fraction of 1.0 and 3.0 Vol.%. Based on the experimental results it is shown that the utilization of the water- based Al2O3 nanofluids as the working fluid enhances the thermal performance of the heat pipe and the volume fraction of nanoparticles has a great effect on the reduction of the wall temperature at the evaporator section. The thermal resistance of the heat pipe using the water-based Al2O3 nanofluids with 3.0 Vol.% is significantly decreased up to about 40% at the evaporator-adiabatic section as compared with that of the DI water-based heat pipe. Also, it is shown that the maximum heat transfer rate of the heat pipes can be enhanced using the water-based Al2O3 nanofluids instead of DI water. This enhancement not imputed to the improvement of the working fluid properties only, but they also due to the observed thin porous coating layer formed by nanoparticles suspended in nanofluids at the evaporation region of the wick structures which in turn extend the evaporation surface and improve the surface wettability and capillary wicking performance. Senthilkumar et al. (2010) [48] experimentally, investigated the improvement of thermal performance of wire mesh heat pipe using copper nanofluid with aqueous solution of n-Butanol. The copper nanofluid which has a 40 nm size with a concentration of 100 mg/lit is kept in the suspension of the deionized (DI) water and an aqueous solution of n-Butanol, was used as a working fluid in the heat pipe. Besides the working fluid, the effect of heat pipe inclination and heat input on the thermal efficiency and thermal resistance are investigated. From the experimental results, they found that the thermal efficiency of copper nanofluid with aqueous solution of n-Butanol is higher than the base fluid 43
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DI water and copper nanofluid and the thermal resistance reduces to three fourth of base fluid. Also, the results show that the thermal performances of the heat pipe may be enhanced by adding a very small amount of long chain alcohol which gives better performance than the conventional working fluid and nanofluid. This may be due to the dilute aqueous solution of n-Butanol which have a positive surface tension gradient with temperature which gives rise to an increased value of the capillary limit and the boiling limit of the heat pipe along with the nanofluid. Mousa (2011) [49], presented an experimental study to investigate the effect of nanofluid on the performance of a circular heat pipe, as in figure 2-11. Pure water and Al2O3-water based nanofluid are used as working fluids. An experimental setup is designed and constructed to observe the effect of filling ratio, volume fraction of nanoparticles in the base fluid, and heat input rate on the thermal resistance of the heat pipe. The total thermal resistance of the heat pipe (R) for pure water and Al2O3-water based nanofluid is also predicted. The results show that the optimum filling ratio of charged fluid was about 0.45–0.50 for both pure water and Al2O3 water based nanofluid, respectively. Whereas the percentage enhancement in the total resistance reaches up to 62.6% at the heat applied and nanoparticls concentration equal to 60W and 1.2%, respectively. Also, the thermal performance of heat pipe can be decreased when the concentration of the nanofluid increased after reaching the maximum value. Finally, the obtained heat transfer data from the experiments was correlated as follow: [
]
(2-3)
Where: : Overall heat pipe thermal resistance. Dimensionless heat transfer rate (
)
44
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Filling atio (F )=
Literature review
charged liquid volume total evaporator volume
An experimental study was carried out by Liu and Zhu (2011) [50] to investigate the effect of nanofluid on thermal performance of a horizontal mesh heat pipe working at steady sub-atmospheric pressures. The nanofluid used in the experimental study is an aqueous solution of 50 nm average diameter CuO nanoparticles with mass concentrations ranged from 0.5 to 2 wt.%. The primary observation from the experimental results show that using of nanofluids enhance heat transfer coefficients of both evaporator and condenser. The maximum heat flux at the optimal mass concentration of nanoparticles (1.0 wt.%) corresponding to the maximum heat transfer enhancement, reached up to 42%. Also the results show the following: The average wall temperature distributions tend to be more uniform and lower than those for deionized water. The evaporating HTC can be increased nearly by 2.5 times when the mass concentration is 1.0 wt.% . Obviously, The average total heat resistance of the heat pipe decreases by 60% with the 1.0 wt.% CuO nanofluid for deionized water, at the pressure of 7.45 kPa. The HTC enhancement of the heat pipe using the nanofluid is affected by the operating pressure. Thus, the HTC enhancement effect increases significantly with the decrease of the pressure. Whereas, the pressure has no significant effect on the maximum heat flux enhancement, and hence it can be neglected. An experimental study was performed to investigate the thermal performance of an inclined miniature mesh heat pipe using water-based CuO nanofluid as the working fluid by Wang et al. (2012) [51]. The study focused mainly on the effects 45
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of the inclination angle and the operating temperature on the heat transfer performance of the heat pipe using the nanofluid with the mass concentration of CuO nanoparticles of 1.0 wt%. The experiment was performed at three steady operating temperatures of 40°C, 50°C and 60°C. The experimental results show that for water based nanofluid with 1.0 wt% CuO mass concentration, the evaporation and the condensation HTCs as well as the maximum heat removal capacity are significantly enhanced. Under the same operating temperature and the same inclination angle conditions, the total heat resistance of the nanofluid heat pipe can be lowered to about half of that using pure water, while the maximum heat removal capacity can increase up by 40 %. Also, they found that the inclination angle has a strong effect on the heat transfer performance of heat pipes using water or the nanofluid. Whereas, the average evaporation HTC and condensation HTC increase by about 22 % and 5 % compared with those of the horizontal pipe when the inclination angle is equal to 45°. However, the maximum heat flux increases gradually with the increase of the inclination angle, and it increase about by 30% when the inclination angle changes from 0° to 90°. An experimental investigation was presented by Solomon et al. (2012) [52] to study the thermal performance of a heat pipe operated with nanoparticle coated wick. Screen type wicks (100 mesh/inch) with and without deposition of nanoparticles are used in this study. Copper particles with average particle size of 80-90 nm are coated over the surface of the screen mesh by using a simple immersion technique which followed by drying to coat the wick with nanoparticles. Three different heat inputs are used to investigate the performance of the heat pipe. The results show that the coated wick reduces the wall temperature at the evaporator and condenser of the heat pipe, in turn the thermal resistance is reduced while heat transfer coefficient is increased in the evaporator relative to that of conventional one whereas the same are opposite in the condenser. However, 40 46
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Literature review
percent thermal resistance reduction and 40 percent heat transfer coefficient enhancement are observed at the evaporator section. Thus the total resistance of heat pipe operated with coated wick is lower than that of conventional one and it decreases by 19%, 15%, and 14% for 100,150 and 200 W respectively. The transient and steady state thermal performances of a medium-sized cylindrical stainless steel meshed heat pipe have been investigated experimentally by Hajian et al. (2012) [53], utilizing both DI-water and silver nanofluid, as working fluids. Thermal resistance and response time of the heat pipe are the characteristics of steady states and transient, respectively. The response time definition is based on the variation of the heat pipe surface temperature. The experiments have been performed under heat rates in the medium range, less than 500 W. Nanofluids were used with concentrations of 50, 200 and 600 ppm. By applying 50 ppm nanofluid, the thermal resistance and the response time of the heat pipe decreased by
30% and about 20%, respectively, compared to DI-water.
Such enhancements were attributed to improvements of both working fluid thermal conductivity and boiling heat transfer – in the evaporator section. Furthermore, for the steady state condition the performance of both DI-water and nanofluid were better at higher heat rates. When the 50 ppm nanofluid is used, as the working fluid, enhancement of the thermal performance of the heat pipe in comparison with DIwater was observed. For the nanofluids with more concentration (200 and 600 ppm) there is no enhancement in the thermal performance. Some possible reasons were presented that can justify the observation of reverse effects of nanofluid concentration on the heat pipe performance. Using no surfactant resulted in partial conglomeration and sedimentation and consequently, changing of the nanofluid concentration which caused the instability of the heat pipe operation.
47
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2.2.3 Theoretical and Experimental Literature From the available literature for cylindrical heat pipe with wire screen mesh, it is clear that the fundamental studies of nanofluids applied in heat pipes are experimental studies. Moreover, the research on application of nanofluids in heat pipes was firstly published in 2004. 2.3 Summary The previous literature review shows that there have been many studies focusing on some specific characteristics of the heat pipe and factors affecting the heat pipe performance, such as the effect of interfacial, capillary pressure and the capillary limit for specific heat pipes. Other studies concerning the effect of pressure in the vapour side of the heat pipe. Numerous studies concentrated on the effects of the working fluid amount and the inclination angle, as well as the non-condensable gases effect, on the thermal performance of the heat pipe. Also, longitudinal axial conduction as well as multiple heat source effects through the pipe wall on the heat pipe performance. In addition to these the energy saving in domestic sector, the enhancement of solar collector efficiency by using heat pipe as well as many other aspects have been the concern of other studies. Recently the working fluid types (using nanoparticles technique) are fetch the researches attention for heat pipe thermal performance enhancement. According to my best knowledge, there are no comprehensive studies investigating the effect of the nanofluid, as working fluid, on the cylindrical heat pipe performance. Moreover, there have been no previous studies using the nanofluid in variable conductance heat pipe. Also, there is no study used the latent heat and surface tension of nanofluid to calculate the capillary heat transfer limit. Therefore, this study tries to consider effect of these important parameters on the performance of heat pipe.
48
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Figure 2-1 Schematic view of the cylindrical heat pipe with multiple heat sources [19].
Figure 2-2 Schematic of the experiment setup [21]. 49
Chapter two
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Figure 2-3 schematic diagram of the woven-wired wick [22].
(a)
(b)
Figure 2-4 (a) A novel heat pipe-heat sink., (b) A new kind wick structure [27].
Figure 2-5 Block Diagram of the control system of PCHP [31]. 50
Chapter two
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Figure 2-6 Conventional VCHP operation [31].
Figure 2-7 Schematic of a variable conductance heat pipe with a non-wicked heated reservoir [31].
51
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Figure 2-8 The HP-PV/T solar collector [34].
Figure 2-9 Schematic of a radially rotating heat pipe with a tilt angle [35]. 52
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Figure 2-10 Variable conductance heat pipe in vehicle [38].
Figure 2-11 Schematic layout of the test rig [48]. 53
Chapter three
Theoretical work
Chapter Three Theoretical Work
3.1 Introduction In this chapter, a mathematical analysis of the governing partial differential equation (PDE) that describes the laminar flow of fluid and heat transfer is done. The governing (PDE) equations are based on the conservation of mass, momentum and energy. These equations have been solved using forward-backward (upwind) finite difference method.
3.2 The Physical Model Typically, the simple heat pipe consists of a sealed and evacuated pipe lined with an annular porous wicking material and a small amount of working fluid in liquid state filled the wick. The center core of the pipe is left open to permit vapor flow. The internal design and operation of the heat pipe is illustrated in figure 3-1. Specifications of the heat pipe under consideration for the analysis in this work are listed in table 3.1 and illustrated in figure 3-2. Table 3.1 Heat pipe specifications. ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Heat pipe container material copper Wall thickness 0.85mm Outer diameter 19.05mm Heat pipe length 555mm Evaporator length 150mm Condenser length 97mm Working fluid DI water Water based-Al2O3nanofluid Water based-CuO nanofluid Set temperature 100 oC ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ 54
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Theoretical work
Due to its compatibility with copper material (pipe container and wick structure) and acceptable for the operating temperatures below 200 oC [1], pure water was chosen as a working base fluid. Also, the thermal performance of the heat pipe is strongly affected by the thermophysical properties of working fluid. Therefore, the thermal physical properties of water for a range of saturation temperatures that can be expected in the present study as well as nanofluid properties are summarized in Appendix -A 3.3 Mathematical Formulation and Governing Equations of CCHP A number of physical assumptions are considered in the present analysis, which may be summarized in the following points. Uniform evaporation and condensation are considered around the circumferential direction. Therefore, the problem becomes axis-symmetric and all the derivatives with respect to the circumferential direction are zero. Thus the problem becomes two-dimensional in cylindrical coordinates. The heat pipe operates under steady-state conditions and contains only one fluid. The vapour and liquid flow are assumed laminar and incompressible. The wick is assumed isotropic and saturated with the working liquid. Regardless of variation in heat load or cooling temperature (sink temperature), the effective conductance of a CCHP is constant. Thus, the relationship between the heat transported by a CCHP, the evaporator temperature and the sink temperature is represented by the following equation [30, 37]: (
)
(3-1)
As Ur and Lc are constant for CCHPs it is clear from equation 3-1 that for a constant heat load a change in sink temperature results in an equal change in
55
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Theoretical work
evaporator temperature. Whilst for constant sink temperature a change in heat load results in a proportional change in the evaporator temperature. The maximum heat load that can be transporting by the CCHP is that at the set point temperature, which given by [37]: (
)
(3-2)
By dividing equation 3-1 by equation 3-2 gives:
(
)
(3-3)
The operating (saturation) temperature can be obtained after arranging the above equation, as follows:
(
)
(3-4)
For correct operation of heat pipe, the maximum capillary pumping pressure drop (ΔPc,max) must be greater than the total pressure drop in the pipe [1]. (3-5) If this condition is not met, the wick will dry out in the evaporator region and the heat pipe will not operate. The maximum allowable heat flux for which the above equation holds is referred to as the capillary limit. Typically, the capillary limit will determine the maximum heat flux (Qmax) over much of the operating range. The capillary driving pressure drop is given by [1]: (3-6) Also, it is useful to relate the liquid pressure drop and flow rate for a wick structure by using a form of Darcy’s law, as [1]: ̇
(3-7)
While, for laminar vapour flow the pressure drop can be written as [1]: 56
Chapter three
Theoretical work ̇
(3-8)
Since mass flow will vary in both the evaporator and the condenser regions, an effective length rather than the geometrical length must be used for these regions. Therefore replace the lengths of the evaporator le and the condenser lc by le /2 and lc /2. Therefore, the total effective length for fluid flow will then be leff where (3-9) The pressure difference, ΔPg, due to the hydrostatic head of liquid may be positive, negative or zero, depending on the relative positions of the condenser and evaporator. The pressure difference may be determined from [1]: (3-10) Thus equation 3-5, can be rewritten after substituting equations 3-6, 3-7, 3-8 and 310 as follows: ̇
̇
For horizontal heat pipe (
(3-11) ) and perfectly wetting system (
), the
pressure drop due to vapour flow can be neglected [2], thus the maximum flow rate may obtain from equation 3-11, as: ̇
*
+*
+* +
(3-12)
Finally, Tsat can be obtained after calculated Qmax from: ̇
(3-13)
3.3.1 Governing Equations Radially, the heat pipe consists of three main regions namely vapour, wick structure and wall region. Thus, the governing equations described according to these regions. Also, the described equations, due to the heat and mass flow along the interface, are solved as a conjugate problem. 57
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Theoretical work
3.3.1.1 Vapour Region The governing equations in vapor region are continuity, Navier-Stokes in x and r-directions and energy equations as follows, [54]: (
)
(3-14) *
+
* (
*
)
+
(3-15) +
*
+
(3-16) (3-17)
The boundary conditions for vapor region are the following: The radial velocities at liquid-vapor interface,(r = rv) [16]: (
)
(
)
(
)
(3-18)
The temperature at the vapor-liquid interface of the evaporator, adiabatic and condenser sections is calculated approximately using Clausius – Clapeyron equation, [16, 18, 33]. (
)
(
(3-19)
)
The boundary conditions at both end caps of the heat pipe, impermeable wall and no-slip condition, are: ( (
) )
( (
)
(
)
)
(
)
58
(3-20)
Chapter three
Theoretical work
The impermeable condition at the end cap can be justified by the fact that no evaporation is taking place at this end cap due to the lack of a wick structure there ( i.e., no liquid is accumulated there ) [33]. At pipe centerline (r = 0) the symmetry boundary conditions are: (
)
,
(
,
)
(3-21)
Pressure gradient along the vapour core is calculated from the momentum equation in x-direction, as: *
+
(3-22)
The shear rate of the vapour at the wick surface is calculated from the basic equation, as: (3-23) The governing equations transformed in terms of stream function and vorticity to assort with the numerical analysis, as follows: (3-24) (3-25) (3-26) Substituting equations 3-24 and 3-25 into equation 3-26 to obtain the vorticity equation in terms of stream function, as follows: (3-27) Also, differentiating equation 3-15 with respect to r-direction and equation 316 with respect to x-direction, and subtract the resulting equations to eliminate the pressure term. Substitute equations 3-24, 3-25 and 3-26 into the final equation to get the following equation:
59
Chapter three
Theoretical work
*
+
*
+
*
+
(3-28)
Finally, equations 3-24 and 3-25 can be substituted into equation 3-17 to obtain the following equation: *
+
*
+
(3-29)
For non-dimensional form of the governing equations and the boundary conditions the following dimensionless quantities can be used: ,
,
,
,
,
,
,
,
, (
)
,
, (
)
(
)
(3-30)
,
,
,
(
(
)
(
)
)
After substituting the above dimensionless quantities, the governing equation of motion transformed to the following form: (3-31) *
+ *
*
+
+ *
(3-32) +
60
(3-33)
Chapter three
Theoretical work
The corresponding boundary conditions of the heat pipe become: At both end caps, ( (
)
). (
,
)
(
,
)
(3-34) (
)
(
,
At the centerline, ( (
)
(
) ).
(
,
)
(
)
(
) )
(
,
At the vapor –wick interface, ( (
)
,
)
(3-35)
):
∫
(3-36) (3-37)
[
]*
(
[
)+
(3-38)
]
Also, the pressure gradient along the vapour core can be obtained after substituting the dimensionless quantities into equation 3-22. *
+
*
+
(3-39)
While, the shear rate of the vapour at the wick surface is: (3-40)
3.3.1.2 Wick Structure The conceptual model of the liquid flow in the wick structure is a porous medium. In porous media, volume –averaged of the Navier-Stokes equations are used where it is related to Darcy velocity, as [14, 18, 33]:
61
Chapter three
Theoretical work
Conservation of mass: (
)
(3-41)
Momentum equation in axial direction: (
*
)
+
| |
⁄
(3-42)
Momentum equation in the radial direction: (
*
) ⁄
+
| |
(3-43)
Energy equation: (
)
*
+
*
+
(3-44)
Where, F is a geometric function based on the porous wick structure and is calculated as follows, [14]: √
(3-45)
⁄
The effective thermal conductivity and heat capacity of wick structure, for screen wire mesh, are written as [40,55]:
(
)
[(
) (
)(
)]
[(
) (
)(
)]
(
)
(
)(
(3-46) )
(3-47)
Since the phase change phenomena was not included in current model, for modeling latent heat of vaporization and condensation a heat sink (Se) was employed in the evaporator section and a heat source (Sc) was used in the condenser section. The values of these terms are [18]:
62
Chapter three
Theoretical work ( (
(
))|
(
(
)
)
)
(3-48) ( (
(
))|
(
(
)
)
)
The boundary conditions for wick structure are as following: The temperature at the vapor-liquid interface of the evaporator, adiabatic and condenser sections is: (
)
(
(3-49)
)
The boundary conditions at both end caps of the heat pipe: ( (
)
(
)
(
)
(
)
)
(
)
(3-50)
The radial blowing and suction velocities at liquid-vapor interface [33]: (
)
(
)
(
)
(3-51)
At wick – wall interface: (3-52)
Pressure gradient along the wick region is calculated from the momentum equation in x-direction, as: *
+
(
) 63
⁄
| |
(3-53)
Chapter three
Theoretical work
Using the same procedure, as in vapour region section, the governing equations obtained in terms of vorticity and stream function are: (3-54) *
+ ⁄
*
*
+
*
*
+
(
+
(
)
)+
(3-55)
*
+
(3-56)
By using the dimensionless quantities defined by equation (3-30) the equation of motion transferred into the following: (3-57) *
(
+ (
) ⁄
*
*
*
+ (
(
+
)
)
*
)+
(3-58)
+
(3-59)
The corresponding boundary conditions for the wick structure are: At both end caps, ( (
)
) ,
(
)
,
(
)
(3-60) (
)
,
(
)
(
,
64
)
Chapter three
Theoretical work
At the wick –vapor interface, ( (
)
(
)
(
)
):
∫
(3-61) (3-62)
[
]*
(
At wick – wall interface (
[
)+
(3-63)
]
): (3-64)
The dimensionless liquid pressure gradient along the wick region is: (
) (
*
+
) ⁄
|
(
|
) (3-65)
3.3.1.3 Wall Region Only conduction heat transfer through the heat pipe wall exists. Thus, the corresponding governing equation is, [18, 33]: *
+
(3-66)
The boundary conditions in this region are as following: At both ends of heat pipe: (
)
(
)
(3-67)
At wall – wick interface: (3-68) At heat pipe external surface: 65
Chapter three
Theoretical work (
)
(3-69) (
)
The governing equations and the boundary conditions can be obtained in dimensionless form by substituting the dimensionless quantities defined in equation (3-30) into the above equations: Thus: *
+
(3-70)
The corresponding boundary conditions of the heat pipe are: At both ends of heat pipe, (
): (3-71)
At wall – wick interface (
): (3-72)
At the outer wall ( (
):
) (
)
(3-73)
3.4 Mathematical Formulation and Governing Equations of VCHP In VCHPs, the evaporator temperature may controlled by varying the heat pipe effective conductance in order to compensate for changes in both heat transfer rate and cooling (sink) temperature. 66
Chapter three
Theoretical work
The gas-loaded heat pipe is the most common type of VCHP [30, 37]. A Gas-loaded VCHP is charged with a non-condensable gas (such as nitrogen, argon or air as in the present study, figure 3-3). By varying the volume of gas in the heat pipe the active length and thus the effective conductivity of the gas-loaded VCHP can be varied. Thus, it is possible to control the evaporator temperature by changing the effective conductivity of the VCHP depending on the heat transfer rate and sink temperature. Low active length temperature and thus low active length pressure at low heat transfer rates or low sink temperatures causes the gas to expand into the condenser until equilibrium is reached whereby the total pressure throughout the condenser is constant where the gas filled region is referred to as the inactive condenser section. The non-condensable gas acts as a buffer preventing the vapor flow from entering the inactive region and condensing on the wall of the inactive condenser length and therefore no heat transferred in the inactive region of the condenser as the vapor cannot condense and release its latent heat of vaporization in the inactive region. Thus it is possible to control the effective thermal conductivity of the VCHP by varying the active length of the condenser. Finally, the evaporator temperature to be controlled with changes in heat transfer rate and sink temperature due to the change in the effective conductance. In this study the VCHP is modeled using the flat front model, but with axial conduction along the wall. Whereas, the flat front model makes the following assumptions [30]: 1. There is a flat front between the pure vapor in the active length and the noncondensable gas with vapor mixture in the inactive length of the condenser. 2. There is pure vapor in the active length. Thus the active length temperature is the saturation temperature corresponding to the active length pressure.
67
Chapter three
Theoretical work
3. The total pressure throughout the VCHP is uniform as such the sum of the vapor and non-condensable gas pressures is equal to the saturation vapor pressure in active condenser length. 4. Axial conduction along the wall and wick is assumed negligible so there is a step change in temperature across the vapor-gas interface as shown in figure 3-4. The mass of non-condensable gas (
) is calculated using the ideal gas
law as [30, 37]: *
(
Where (
)+
(
)
(3-74)
) is the volume of non-condensable gas in the condenser which can be
obtained from the following equation: (3-75) Substitute equation 3-75 into equation 3-74 and rearrangement gives an expression for the inactive length; *
(
(
)
(3-76)
)+
The active length of the condenser can be defined as, [37]. (3-77) Thus, by Substituting equation 3-76 into equation 3-77 an expression for (
) can
be found in form, *
(
)
(
(3-78)
)+
The heat removed by the VCHP is expressed as [37]. (
)
(3-79)
By substituting equation 3-78 into equation 3-79, the final form of the VCHP heat removed can be obtained as follows: 68
Chapter three
Theoretical work
(
)*
*
(
(
)
)+
+
(3-80)
The maximum heat transfer rate, whereby the entire condenser length is active is given by, [37]: (
)
(3-81)
Thus, dividing equation 3-80 by equation 3-81 gives [37]: (
)*
*
(
)
(
)+
+
(3-82)
Where; (3-83) The active length temperature (
) can be obtained from equation 3-82 after
calculating the maximum heat transfer rate as in CCHP modeling.
3.4.1 Governing Equations The governing equations and boundary conditions of VCHP are same as those used in CCHP with the following difference in final form:
3.4.1.1 Vapour Region The radial velocities at the liquid-vapor interface,(r = rv) [16]: (
)
(
)
(
)
At the vapor –wick interface, (
(3-84)
):
69
Chapter three
(
Theoretical work
) [
]*
(
(
)
)+
[
]
(3-85)
3.4.1.2 Wick Structure ( (
(
))|
(
(
)
)
)
(3-86) ( (
(
))|
(
(
)
)
)
The radial blowing and suction velocities at liquid-vapor interface: (
)
(
)
(
)
(3-87)
At the wick –vapor interface, ( (
):
) [
]*
(
(
)
)+
[
]
(3-88)
3.4.1.3 Wall Region At the outer wall ( (
):
) (
( (
)
(3-89)
) )
70
Chapter three
Theoretical work
3.5 Numerical Modeling: In the present study, a cylindrical heat pipe of 19.05 mm outer diameter with three types of working fluids (water, water based-Al2O3 and water based CuO nanofluids) is selected. The selected length of the evaporator, adiabatic and condenser section is same as the used length in the experimental work. The governing equations of the heat pipe, which are used in the three main regions (vapour region, wick structure and wall region), according to the physical domain of the problem, are discretized using a finite difference method and the resulting equations are solved using Forward – Backward upwind with collocated grid scheme as shown in Appendix – B and figure 3-5. The heat pipe dimensionless length is taken to be (L/ro). Whereas, the ⁄
increment in space coordinates are
and
. While, the domain
was discredited with structural homogenous meshes. The equations of vapor region, wick structure and wall region have been solved with various numbers of meshes and as shown in figure 3-6, 9881 nodes were sufficient to achieve results that were independent to mesh structure. The computation is done for a mesh number (241×41). A line-by-line iteration method in the axial and radial directions using Fortran PowerStation version 4.0 is used for the solution procedure of the discretized equations.
3.5.1 Convergence of Numerical Solution The monitor on the convergence of the numerical solution called "convergence criterion", which is applied in the present study is based on summation of the absolute value of the relative errors of any variable ( ), where relative error (Er) is defined as follows [16]: 71
Chapter three
∑
Theoretical work
|
|
(3-90)
Where superscript (n) refers to the previous iteration and ( For an exact solution, (
).
) must be zero to satisfy the Finite Difference
Equations (FDE), but for an inexact or nearly exact solution, there is sufficiently small relative error for all the variables solved everywhere in the field. The normalized relative error for different variables can be defined as: (3-91) Where ( ) is a convergence criterion. The value of ( ) adopted for the present study is typically equal to (10-5).
3.5.2 Numerical Procedure 1. Calculate saturation temperature for CCHP using equation (3-4) or active length temperature for VCHP using equation (3-82). 2. Calculate velocity and temperature boundary condition at the vapor-liquid interface using equations (3-18) and (3-38) for CCHP and equations (3-84) and (3-85) for VCHP. 3. Solve the equations of stream function and vorticity in vapour and liquid regions sequentially based on the velocities obtained in step 2 and the values of stream function and vorticity at the boundaries where the boundary conditions are applied. 4. Calculate the velocity components ( and ) by using the current values of stream function and the values at boundaries. 5. Solve the momentum equations in x-direction for vapour region and wick structure using the current values for velocities. 6. Solve the energy equations in vapour, liquid and wall regions sequentially by using the current values of stream function and the values at boundaries. 72
Chapter three
Theoretical work
7. Solve the shear rate equations at the wick surface using the current values for velocities. 8. Check convergence of the solution, if it is satisfied, calculations will be ended. Otherwise, replace (
) and return to step 2 and repeat the
above procedure until convergence is achieved. Figure 3-7 illustrates the flow chart for the current computer program in the present study.
Heat Input
Heat Output Liquid Flow in Wick
Evaporator Section
Adiabatic Section
Condenser Section
Figure 3-1 Schematic of typical Heat Pipe.
Qin
Qout
rv
rw
ro
Solid wall Wick Structure
Vapour Core r v u x x=0
Symmetry Axis x=Le
x=Le+ La
x=Le+ La+ Lc
Figure 3-2 Physical domain and coordinates of the system. 73
Chapter three
Theoretical work
Heat Output
Heat Input Liquid Flow in Wick
Vapour+Non Condensable gas
Evaporator Section
Adiabatic Section
Inactive Active Condenser Condenser Section Section
Figure 3-3 Schematic of a variable conductance heat pipe.
Figure 3-4 Temperature and vapor pressure profiles assumed by the flat front model for different VCHP configurations, [37]. 74
Chapter three
Theoretical work
jn=jn-1+∆r
∆x
∆r
j2=j1+∆r
j1=0 i1=0
i2=i1+∆x
im=im-1+∆x
Wall Temperature (oC)
Figure 3-5 The discretized domain.
Heat Pipe Length (m)
Figure 3-6 Checking for grid independency.
75
Chapter three
Theoretical work
Start Input Data Calculate the thermophysical properties of the working fluid at Tset Calculate the ̇
at Tset from equation 3-12
Calculate the
at Tset from equation 3-13 Calculate Tsat or Tal
Calculate the thermophysical properties of the working fluid at Tsat Calculate the ̇
at Tsat from equation 3-12
Calculate the
at Tsat from equation 3-13 Grid Generation
Start Field Iteration Sweep Calculate Ve and Vc from equation 3-18 Solve equations 3-31 and 3-36 for ѱ and 𝜔 in vapour region Solve equations 3-57 and 3-61 for ѱ and 𝜔 in liquid region Solve equations 3-24 and 3-25 for 𝑢 and 𝑣 velocities 2
1 76
Chapter three
Theoretical work
1
2 Solve equations 3-39, 3-65 for 𝑃
in vapour region and wick structure
Solve equations 3-33, 3-59 and 3-70 for 𝜃 in vapour, wick and wall region Solve equation 3-40 for 𝜏
for vapour at wick surface
IF
No
Yes No
IF ϵ ≤ 10-5 Yes Print Final Values End
Figure 3-7 Flow chart for the current computer program.
77
Chapter Four
Experimental work
Chapter Four Experimental Work
4.1 Introduction The main objective of the experimental work is to study the effect of some parameters on the heat pipe performance in the steady-state conditions, and to verify the numerical results. The studied parameters are input heat flux, coolant temperature, working fluid type and the mass of the non-condensable gas. The experimental rig involves the following major elements: Heat pipe. Water cooling system. Power supply system. Measuring instruments. Schematic and pictorial views of the experimental rig are illustrated in figures 4-1 and 4-2, respectively.
4.1.1 Heat Pipe The three basic components of the heat pipe (container, working fluid and wick structure are described below) determine its operational characteristics. One of the most important considerations in choosing the material for the heat pipe container and wick is its compatibility with the working fluid. Degradation of the container or wick and contamination of the working fluid due to chemical reaction can seriously impair heat pipe performance. For example, non-condensable gas created during a chemical reaction eventually can accumulate near the end of the 78
Chapter Four
Experimental work
condenser, decreasing the condensation surface area. This reduces the ability of the heat pipe to transfer heat to the external heat sink, [56].
4.1.1.1 The Container and End Caps The isolation of the working fluid from the outside environment is the basic function of the container. It has, therefore, to be leak-proof, to maintain the pressure differential across its walls and to enable the transfer of heat to take place into and from the working fluid. Selection of the container material including the end caps and filling tube depends on several factors. These are as follows [1]: Compatibility (both with working fluid and the external environment). Strength-to-weight ratio. A high strength-to-weight ratio is more important in spacecraft applications. Thermal conductivity. A high thermal conductivity ensures minimum temperature drop between the heat source and the wick. Ease of fabrication, including weldability, machineability and ductility. Porosity (the material should be non-porous to prevent the diffusion of gas into the heat pipe). Wettability. Copper is the most common wall material for low temperature heat pipes, due to its compatibility with water and other low temperature working fluids as well as having a high thermal conductivity. This was confirmed by several previous works which used copper heat pipe containers and no any complaints were recorded. Therefore, copper is selected as heat pipe containers in the present work. Standard copper pipe of 19.05 mm external diameter, 0.85 mm thickness and 55.5 cm length has been selected. Two pipes are fabricated for the tests of water and two types of nanofluids, the two pipes have the same dimensions. 79
Chapter Four
Experimental work
The heat pipe ends are sealed by the end caps which are fabricated from brass material and consist of two parts, the first is flange with 63 mm outer diameter and 19.1 mm diameter concentric hole for pipe insertion. The flange was welded to the pipe outer diameter. While the other part is 8 mm thick disk linked with the flange by four M10 bolts distributed along the circumference. These caps can be opened if changing of working fluid or wick structure is desired. Also, rubber O-rings are used between the flange and disk at the pipe ends to prevent any leakage. The condenser end cap is drilled concentrically to provide the necessary access for evacuating or charging the heat pipe. The evacuating or charging tube, is made of a 1/4 in (6.35 mm) copper tube, inserted in the concentric hole and welded to the end cap. The welding process type is oxyacetylene welding using special welding wire under low temperature to reduce the parts contamination. After completing the container and its accessories the following cleaning processes were followed: Cleaning the end caps with a rough sand paper. Cleaning the end caps and the outer pipe surface with a sand paper type zero. Flushing with reverse osmosis (RO) water carefully. Drying with a blower. Re-cleaning with acetone and a soft cloth. Re-flushing with RO water thoroughly. Drying with hot air from hair Straightener.
4.1.1.2 The Working Fluid Another critical element for proper heat pipe operation is the suitable working fluid for a given application, which in turn identify the operating vapour temperature range. Within the approximate temperature range several possible working fluids may exist, and a variety of characteristics must be examined in 80
Chapter Four
Experimental work
order to determine the most acceptable of these fluids for the application being considered. The main requirements are: Compatibility with wick and wall materials Good thermal stability Wettability of wick and wall materials The operational temperature range has to lie between the triple point and the critical point for liquid to exist in the wicking material. Vapour pressures not too high or low over the operating temperature range High latent heat High thermal conductivity Low liquid and vapour viscosities High surface tension Acceptable freezing or pour point. The selection of the working fluid must also be based on thermodynamic considerations which are concerned with the various limitations to heat flow occurring within the heat pipe, such as the viscous, sonic, capillary, entrainment and nucleate boiling limitations. A convenient means for quickly comparing working fluids is provided by a dimensional fluid property group named the Merit number (M) defined as [1]: (4-1) It is clear from the above equation that the Merit number has the dimensions of heat flux (W/m2) and depends on the working fluid properties only. With reference to the capillary limit, that if vapour pressure loss and gravitational head can be neglected then the properties of the working fluid which determine the maximum heat transport can be combined to form a figure of merit (M).
81
Chapter Four
Experimental work
Finally, the selection of the working fluid besides the factors listed above also based on cost, availability and high Merit number. Therefore, at the low and moderate temperature range, many working fluids are available for heat pipes operation such as water, ammonia, acetone, ethanol and methanol. Also, refrigerants such as R-11, R-12, R-113, R-123, R-134a and many other fluids are used. In current investigation, sterilized (distilled) water was used in the experiments. It was manufactured by PARENTERAL DRUGS LIMITED (INDIA) and supplied by the Ministry of Health. The water was supplied in 5 ml containers with total dissolved solids (TDS) ranging from 4 to 7 ppm. Also, two types of nanofluid, Al2O3 – water based and CuO – water based are prepared (as in Appendix – C) and used in this investigation.
4.1.1.3 The Wick Structure For a heat pipe, the selection of the wick depends on many factors, several of which are closely linked to the properties of the working fluid. Obviously the prime purpose of the wick is to generate capillary pressure to transport the working fluid from the condenser to the evaporator. It must also be able to distribute the liquid around the evaporator section to any area where heat is likely to be received by the heat pipe. Heat pipe wicks can be classified as either homogeneous wicks or composite wicks. Homogeneous wicks are composed of a single material and configuration. The most common types of homogeneous wicks include wrapped screen, sintered metal, axial groove, annular, crescent, and arterial. Composite wicks are composed of two or more materials and configurations. The most common types of composite wicks include variable screen mesh, screen-covered groove, screen slab with grooves, and screen tunnel with grooves. 82
Chapter Four
Experimental work
Regardless of the wick configuration, the desired material properties and structural characteristics of heat pipe wick structures are a high thermal conductivity, high wick porosity, small capillary radius, and high wick permeability, [1, 56]. In the present work, a copper wire screen mesh was selected to form the wick structure, as shown in figure 4-3. The copper mesh was supplied by TWP Inc., USA with the following specification: Table 4.1 wire screen mesh specification.
material mesh/inch
Copper
145
mesh/m wire diameter (mm)
aperture
(N)
(dw)
(mm)
5708.66
0.05588
0.1016
source
USA
The porosity and permeability of the existing wire screen mesh (wick) are calculated from the following equations, [2]: (4-2)
(
(4-3)
)
From the information of table 4.1 and the above equations the calculated porosity and permeability of the wick are 0.737 and 1.4813E-10 respectively. A sheet of wire screen mesh with 32.7 cm length and 55.5 cm width was wrapped around 1/2 in copper tube with 75 cm length to make wick structure as six layers of the screen mesh. The copper tube with the mesh layers is inserted into the container and released to line the internal wall of the container, while the copper pipe removed carefully. The pictorial view of the wick inside the container is illustrated in figure 4-3. 83
Chapter Four
Experimental work
The end caps then linkage and the heat pipe must be evacuated to remove materials that may subsequently appear as unwanted non-condensables, or that chemically react with the working fluid forming undesirable corrosive products. The non-condensables are due to not only the free gas in the pipe but also to the molecules absorbed on the metal surface. Removal of free gases in the pipe can be done simply by pumping down with a vacuum pump. Removal of absorbed gas requires the evacuation of the pipe at elevated temperatures. A general rule is to evacuate the pipe at a temperature not less than the heat pipe operating temperature [33]. To ensure the heat pipe without any leakages, it kept under vacuum for three days. Then it was injected with a small amount of working fluid and re-evacuated under wall temperature of (35-40 oC) to a vacuum pressure of 755 mm Hg for 18 hour. The vacuum process is achieved by two stage vacuum pump (Prodit, 150 L/min.; Model 6174/0000/000; Italy). Finally, when the evacuation process is completed, the heat pipe becomes ready for charging. Many researchers depend on Chi, cited by [33], relationship for liquid inventory calculation as: (4- 4) Where, m is the fluid inventory. Av, Aw are the vapour and wick cross –sectional areas respectively. L is the total heat pipe length. ε is the wick porosity. ρv, ρl are the vapour and liquid densities respectively at the heat pipe operating temperature. The researchers ignored the mass of vapour in their calculation and considered only the amount of working fluid which is completely saturated the 84
Chapter Four
Experimental work
wick. In this investigation, the amount of working fluid that is charged into heat pipe is determined experimentally and found to be equal to 240% of the amount that is completely saturated the wick. When the optimal amount of charging fluid is supplied to the heat pipe for best thermal performance, the charging valve is closed and the heat pipe is then prepared for the experimental tests. Seven thermocouples Type “T” are fixed at the outer surface of the heat pipe wall as shown in figure 4-4. Each thermocouple at the evaporation section is covered with one layer of thermal plaster followed by one layer of glass wool insulation and one layer of thermal sleeve and finally all fixed with three layers of thermal plaster. The thermocouples at the adiabatic section are covered with four layers of thermal plaster. While the thermocouples at the condenser section are covered with three layers of thermal plaster followed by two layers of thermal sleeve and finally all fixed with five layers of thermal plaster. Rubber coated wire heater with about 60 W maximum heat transfer rate was wrapped around the heat pipe to make the evaporator section, as shown in figure 4-5. A thermally controlled cooling jacket, for the condenser cooling, which consists of inlet and outlet ports for cooling water, is fabricated using a 63 mm PVC pipe as in figure 4-6. The cooling water enters the jacket from the bottom side and leaves from the upper opposite side through ¼ in copper tubes. each copper tube was fabricated with a port for cooling water temperature sensor. To minimize the heat losses to the environment, the evaporator and adiabatic sections are wrapped by 22 mm thick glass wool insulation and then all length of the heat pipe wrapped by 12 mm thick glass wool insulation.
85
Chapter Four
Experimental work
4.1.2 Water Cooling System The heat pipe condenser jacket was provided by circulating cooling water from a temperature controlled bath which is fabricated locally. A plastic and PVC tubes are used to circulate the cooling water between the water bath and the condenser jacket by pipeline booster pump (15 L/min. maximum capacity and 17 m maximum head, made in China). The used cooling water is R.O. water with 30 ppm as TDS to reduce the dirt and salt precipitation on the condenser surface. The cooling water from the water bath, which consists of two parts hot and cold, enters the lower side of the condenser jacket and leaves the jacket at the upper opposite side to return to the water bath as shown previously in figure 4-1. The bulk temperature of the cooling water, which called sink temperature (Ts), is taken as the arithmetic mean of inlet and outlet temperatures of the condenser jacket [14]. Prior to water bath, the water temperature in the bath was controlled by NTC10K standard sensor mounted inside the bath and connected to LTR-5CSRE controller supplied by (lea electronic, Italy). According to signed signal from NTC sensor, which calibrated as in Appendix – D, to LTR-5, it will switched to on/off a 500 W bath copper heater.
4.1.3 Power Supply System The power supply system in this investigation consists of the following two main components:
4.1.3.1 AC Automatic Voltage Regulator To overcome the instability of the main power supply the voltage regulator (REESHANY) type SVC – R2000VA is used.
86
Chapter Four
Experimental work
4.1.3.2 Variable AC Transformer (Variac) For supply power to the electrical heater on the heat pipe evaporator section, a variable AC transformer (Variac) type (HSN) with an output voltage ranging from 0 to 250 V is used.
4.1.4 Measuring Instruments 4.1.4.1 Power Measuring Instrument The voltage, current and as a results the power used by the heating element are determined by digital AC Power Meter type (GWINSTEK GPM-8212) which supplied by (Good Will Instrument Co., Ltd., Taiwan). The readings are displayed with four digits and the AC Power Meter has the following measuring ranges: For Current (160.0 mA to 20.48 A) with accuracy of (±0.1% of reading±0.1% of range) at (23 oC±5 oC). For Voltage (5.000 V to 640.0 V) with accuracy of (±0.1% of reading±0.1% of range) at (23 oC±5 oC). For Power (800.0 mW to 13.10 kW) with accuracy of (±0.2% of reading±0.2% of range) at (23 oC±5 oC). The heat received by the heat pipe evaporator (Qe) is calculated as follows: ∑
(4-5)
Where; is the power input which taken directly from AC Power Meter or calculated by multiplying the current passing through the heating element by the voltage across its terminals. ∑
is the summation of the convection and radiation losses from the outer
surface of the heat pipe insulation as illustrated in Appendix – E.
87
Chapter Four
Experimental work
4.1.4.2 Temperature Measuring System In this investigation, T-type thermocouple was used for temperature measurement with the range of -150 oC ~ 400 oC. The temperature measuring system consists of 12 thermocouples type “T” , each with 0.8 mm probe, distributed at various locations on the heat pipe wall as shown in figure 4-4, and three additional thermocouples; two of them are used to measure the ambient temperature and the third is mounted in the water bath, hot part, to measure the water temperature. The thermocouple wires are fixed carefully at the appropriate positions on the heat pipe surface. Therefore, each thermocouple bead was placed in its proper place and well insulated with multiple layers of a water-proof plaster in condenser section to prevent the direct contact between the thermocouple bead and the condenser cooling water, while in the evaporator section the thermocouple bead insulated with a layer of sleeve and glass wool and multiple layers of thermal plaster to prevent the direct contact between the thermocouple bead and the heating element. The thermocouples used to measure the condenser cooling water temperature are placed at the center core of the condenser water jacket input and output tubes. The temperature of the outer surface of the heat pipe insulating materials is measured by three thermocouples, one for each section. Each thermocouple bead was fixed by thermal plaster and covered with thin layer of glass wool. All thermocouples are connected to Multi-channel Temperature Meter type (AT4564) with 64 channel supplied by (Applent Instruments, Inc., China). The thermocouples and the Multi-channel Temperature Meter are used for first time for measurement in this investigation. Therefore, calibrations of the thermocouples in the range of -100 oC to 400 oC with basic accuracy of ±0.2% of reading which provided by the manufacturer are considered.
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4.1.4.3 Cooling Water Flow Rate Measuring Instrument The volume flow rate of the cooling water in the condenser was measured by using floating type rotameter (CRYOTEX srl model 10C, Italy) with range of 0.3 to 3.2 L/min of water at 20 oC. The rotameter is calibrated after mounted in the experimental rig and before tests are performed using a measuring cylinder and stop watch, the details of calibration as in Appendix – F. Determination of the heat transfer rate to the cooling water in the condenser section is calculated as: The heat transferred to the cooling water was determined by the following relation; ̇
(4-6)
Where; is the rate of heat transfer in (W), ̇ is the mass flow rate of the cooling water in (kg/s), is the specific heat at constant pressure in (J/kg.oC) ∆T is the water temperature difference across the condenser in (oC).
4.2 Accuracy and Uncertainty of Measurements For the measured power, temperature and coolant flow rate, the results for the elemental accuracy and uncertainty are summarized in table 4.2. Nominal values of 25 W and 26 oC as sink temperature in VCHP with 1.5 mg of air are chosen as the representative of the largest experimental values. Table 4.2 accuracy and uncertainty of measurements. Parameter Power (W) Average evaporator-condenser temperature difference (oC) Flow rate (g/s)
Nominal value 21.53
Accuracy (%) Uncertainty 0.4 ±0.0861
32.816
0.2
±0.0656
8.334
0.3
±0.025
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The uncertainty of each measured parameter causes error in all calculated parameters. The propagation of error for „n‟ calculated parameters, X i , in a particular objective function, R, can be determined using the Root-Sum-Squares (RSS) uncertainty method: √∑
(
Where
)
(4-7)
is represents the uncertainty of the variable Xi in the objective
function R. Thus, the uncertainty in the total resistance of the heat pipe was determined depending on the definition; ̅
̅
(
(4-8)
)
And for the maximum value of Rth which occurred in VCHP at (Q=5 W, Ts=18.3 oC, ( ̅
̅ )=27.116 oC and mngs=1.5 mg), the results are summarized in
table 4.3. Table 4.3 accuracy and uncertainty of measurements. Parameter Power (W) Average evaporator-condenser temperature difference (oC) Thermal resistance (oC/W)
Nominal value 4.83
Accuracy (%) Uncertainty 0.4 ±0.0193
27.116
0.2
±0.0542
5.614
0.447
±0.025
4.3 Experimental Heat Pipes Specification As mentioned previously, two heat pipes were fabricated with the same dimensions. One used for constant and variable conductance operations with water as working fluid. After that it is used for constant and variable conductance operations of Al2O3-water based nano-working fluid with different concentration. While, the other is used for constant and variable conductance operations of CuOwater based nano-working fluid with different concentration. After a complete set 90
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of experiments for each nanoparticles concentration tests, the wick is replaced carefully by new one for the next set of tests. Thus, the specifications of the heat pipe are listed in table 4.4. Table 4.4 heat pipe specifications. Symbol (Unit)
Value
Container outer diameter
(Do) mm
19.05
Evaporator length
(Le) mm
150
Adiabatic length
(La) mm
308
Condenser length
(Lc) mm
97
Wall thickness
(twall) mm
0.85
Wick thickness
(tw) mm
0.67
Wick effective pore radius
(rc) mm
0.0875
N
6
(VL) m3
3.47*10-5
Name
Number of screen mesh layers Volume of working fluid
water, water based-Al2O3 and
Working fluids
water based-CuO nanofluids
Non-Condensable gas
air
4.4 Experimental Procedures First of all, the heat pipe is tested for different working fluid volume ranging from 75% to 275% of that required to saturate the wick, which is defined as the working fluid filling ratio. All tests are performed under the same cooling flow rate and the data recorded after the heat pipe reaches steady state. After specifying the optimal working fluid filling ratio, the heat pipe tests are performed with the following procedure for CCHP and VCHP: 91
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4.4.1 Experimental Procedure of CCHP Testing In all the thermal performance tests of the heat pipes, the heat pipe is fixed horizontally, and all its terminals are connected to their proper measuring instruments. Then, the following steps are considered: 1. The cooling water pump is switched on and the volume flow rate is adjusted at 0.5 L/min. throughout the experiments and its temperature is controlled at 18.3 oC , 22 oC and 26 oC. While, the waiting time was required for steady temperature distribution along the heat pipe wall. 2. Initially, the heat pipe is operated for (5-7) minutes at 10 W as a thermal load and 22 oC as cooling water temperature and then the power and the cooling pump were switched off. At this time, a small amount of the noncondensable gases may be collected at the condenser end. Thus, after 10 minutes the heat pipe is re-evacuated for (5-7) minutes and a small amount of the working fluid nearly 6 to 8% of the filling ratio was drawn from the heat pipe through the evacuation process. Therefore, the filling ratio increased by 8%. 3. After this operation, the heat pipe returns to the operation under the different thermal load of 5, 15 and 25 W. For each power level setting, the power is set and then the heat pipe allowed to reach steady state conditions, which defined as the state when the temperature at all the thermocouple locations approximately does not change with time. The heat pipe reaches the steady state condition within 17-20 minutes, the power inputs and the temperature at the various locations are all recorded after 22 minutes. 4. Once a change is made in the thermal load with the same cooling temperature, steady state is typically achieved within a few minutes, and the all data are recorded. The same procedure is repeated at each power input.
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5. Then after increasing the water cooling temperature by 4 oC, steps 3 and 4 are repeated and the data are recorded. The above procedure is repeated for the working fluid of 0, 1, 3 and 5% concentration for Al2O3 and CuO nanoparticles respectively. The time require to reaches the steady state condition for the heat pipe with nano-working fluids reduced by 17-21% of that required for distilled (DI) water.
4.4.2 Experimental Procedure of VCHP Testing When the constant conductance heat pipe (CCHP) charged with small amount of non-condensable gas, such as air in this work, it is converted to variable conductance heat pipe (VCHP). All steps followed in CCHP testing are applied in VCHP testing with one difference. The difference is represented by charging the heat pipe with small amount of air (0.5, 1.1 and 1.5 mg) as non-condensable gas. This process is done after completing step 2, and then the same previous steps 3, 4 and 5 are achieved. Finally, for completing each experimental set of test data nearly 1-2 hours for CCHP and 1.5-2.5 hours for VCHP are required for all working fluids.
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Thermocouples Heating Element
Heat Pipe
Condenser
Rotameter
By-bass Water Line
Water Bath
Water Circulating Pump
Copper Heater
Temperature Controller
Temperature Meter
AC-Multimeter
Variac
Automatic Voltage Regulator
Figure 4-1: Schematic diagram of experimental rig components.
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4
1
10
5 9
6
11 7
8 13
15
14 3
12
2 Figure 4-2 Pictorial view of the test rig. 1- Heat Pipe
2- Water Bath
3- Water Circulating Pump
4- Water Bath Temperature Controller 5- Water Circulating Pump Switch 6- Water Bath Heater Switch
7- Rotameter
8- Water Circulating Adjusting Valve
9- Vacuum Indication Gage
10- Vacuum Valve
11- Evacuating-Charging Valve
12- Automatic Voltage Regulator
13- Variac
15- Temperature Data Logger
95
14- AC-Multimeter
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Experimental work
Figure 4-3 Copper wire screen mesh.
Heat Pipe Surface
Insulation
Zero Position
1
12
11
10
2
3
4
9 5
7
6
8
Evaporator Section
Condenser Section
Adiabatic Section
Thermocouple No.
1
2
3
4
5
6
7
Position (cm)
2
6
12
20
30.5
48
53
8
9
Water Water input output
Figure 4-4 Heat pipes thermocouple locations.
96
10
11
12
7.5
30.4
50.6
Chapter Four
Experimental work
Figure 4-5 Rubber coated wire heater.
Figure 4-6 condenser cooling jacket.
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Chapter Five Results and Discussion
5.1 Introduction The results of numerical model for constant conductance heat pipe (CCHP) and variable conductance heat pipe (VCHP) are presented and discussed in this chapter. Whereas, Sixty three different cases for CCHP and One hundred and eighty nine different cases for VCHP are studied to determine the thermal behavior of CCHP and VCHP with wire screen mesh wick structure. All of these cases are chosen to show the effect of the parameters that control the performance of the heat pipe such as heat flux, heat sink temperature, working fluid type, nanoparticles concentration and the mass of non-condensable gas (air). Also, the results of the experimental work for CCHP and VCHP are discussed when the variation in the heat flux, heat sink temperature, working fluid type, nanoparticles concentration and the mass of non-condensable gas (air) are considered.
5.2 Validation of the Present Model To verify the current model, results of the heat pipes (CCHP and VCHP) with conventional or nanofluid, as a working fluid, must be compared with the other researchers results.
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5.2.1 CCHP A- Heat pipe with conventional working fluid The results of the present model are compared with the results of Saad et al. [39] as shown in figure 5-1. Their results at constant heat input (Qin= 100 W), wall thermal conductivity (kw=394 W/m oC), wick porosity (ε=0.645), outer radius of heat pipe (ro=0.009525 m), heat pipe length (L=0.355 m). The relative error, for the evaporator-condenser temperature difference, between the present work and the work of Saad et al. [39] is 9%. Figure 5-2 shows the comparison of the results of the present model with the results of Mahjoub and Mahtabroshan [18] at constant heat transfer rate (Qin =10, 30 and 50 W), wall thermal conductivity (kw=394 W/m oC), wick porosity (ε=0.75), outer radius of heat pipe (ro=0.00445 m) and heat pipe length (L=0.2 m). The maximum relative error, for the liquid pressure drop, between the present model and the model of Mahjoub and Mahtabroshan [18] is 2%. B- Heat pipe with nano-working fluid Figure 5-3 shows the comparison of the results of the present model with the experimental results of Do et al. [47]. Their results at heat transfer rate (Qin =3 W), wall thermal conductivity (kw=394 W/m oC), wick porosity (ε=0.6557), outer radius of heat pipe (ro=0.002 m) and heat pipe length (L=0.3 m). They used Al2O3 – water based nanofluid with nanoparticles concentration of 1 and 3 Vol. % as working fluid. The maximum relative error between the experimental results of Do et al. [47] and the present theoretical work is 3.5%.
99
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5.2.2 VCHP The present results have been compared with the results of Saad et al. [39] as shown in figure 5-4. Their results are performed at constant heat input (Qin= 100 W), wall thermal conductivity (kw=394 W/m oC), wick porosity (ε=0.645), outer radius of heat pipe (ro=0.009525 m), heat pipe length (L=0.355 m) and mass of non-condensable gas (Mncg=14.5*10-7 kg). The comparison shows a good agreement with the results of the present work, and the relative error for the evaporator-condenser temperature difference is 9.3%.
5.3 Numerical Results 5.3.1 CCHP Sixty three computational runs (as summarized in table 5.1) are performed for the three different values of the parameters such as input heat flux, nanoparticles concentration and heat sink temperature, for three different working fluids. The effects of variation of theses parameters on temperature distribution, vapour flow, liquid flow, axial conduction, the maximum heat transport capillary limit, thermal resistance and heat pipe thermal performance enhancement are investigated.
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Table (5.1) Summery of cases studied. Case Number
Ts (oC)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26
φ (Vol.%)
Working fluid
0
Water
q (W/m2)
1 Al2O3 – water based Nanofluid
3
5
556.97
1 CuO – water based Nanofluid
3
5
0
Water
1 Al2O3 – water based Nanofluid
3
5
1670.91
1 CuO – water based Nanofluid
3
5
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Table (5.1) Continued. Case Number
Ts (oC)
43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26
φ (Vol.%)
Working fluid
0
Water
q (W/m2)
1 Al2O3 – water based Nanofluid
3
5
2784.86
1 CuO – water based Nanofluid
3
5
5.3.1.1 Temperature Distribution The variation of temperature along the heat pipe depends on several parameters. Some of these parameters are:
Input heat flux.
Coolant temperature.
Working fluid type.
Nanoparticles concentration within the working fluid. Figures 5-5 to 5-7 show the temperature contours for cases No. 1, 22 and 43,
respectively. These figures show the effect of variation of input heat flux on the temperature distribution for pure water and for the same coolant temperature.
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Figures 5-5, 5-8 and 5-9 show the temperature contours for cases No. 1, 2 and 3, respectively. All these figures show the effect of variation of coolant temperature on temperature distribution for pure water and the same input heat flux. As shown from all above figures, the temperature along heat pipe increases as input heat flux or coolant temperature increases due to increasing of the working fluid evaporation rate. Figure 5-10 to 5-12 show the temperature contours for cases No. 4, 7 and 10, respectively. These figures show the effect of variation of nanoparticles concentration (NPC) on temperature distribution for Al2O3 – water based nanofluid and the other parameters are kept constant. Figure 5-13 to 5-15 show the temperature contour for cases No. 13, 16 and 19, respectively. These figures show the effect of variation of nanoparticles concentration (NPC) on temperature distribution for CuO – water based nanofluid and the other parameters are kept constants. It is clear from the figures 5-10 to 515, that the temperature along heat pipe decreases as NPC increases. This behavior is due to decreasing the velocity and increasing the thermal conductivity of the working fluid with increasing of NPC. It is obvious from the above figures that because of the axial conduction in the pipe wall, the region of the adiabatic section near the evaporator acts as part of the evaporator; likewise, the region adjacent to the condenser acts as part of the condenser.
5.3.1.2 Vapour Flow Figures 5-16 to 5-18 show the distribution of the vapour velocity, at the heat pipe centerline along the vapour core. Figure 5-16 shows the effect of variation of input heat flux on vapour velocity for cases No. 1, 22 and 43 for water for coolant temperature of 18.3 oC. Figure 5-17 shows the effect of variation of input heat flux 103
Chapter Five
Results and Discussion
on vapour velocity for cases No. 8, 29 and 50 for 3 Vol.% of Al2O3 – water based nanofluid for coolant temperature of 22 oC. Figure 5-18 shows the effect of variation of input heat flux on vapour velocity for cases No. and 21, 42 and 63 for 5 Vol. % of CuO – water based nanofluid for coolant temperature of 26 oC. As shown from each figure separately 5-16, 5-17 and 5-18; the vapour velocity increases when the input heat flux increases. This is due to increasing of the working fluid evaporation rate with increasing of the input heat flux. It is clear from the figures 5-16 to 5-18, the vapour velocity, when the input heat flux is varied and the other parameters are kept constants, has the same behavior (it is worth to mention that same trend can be seen when different cases study are used for water, 1 and 5 Vol.% of Al2O3 – water based nanofluid and 1 and 3 Vol.% of CuO – water based nanofluid at coolant temperature of 18.3, 22 and 26 o
C with visible shifting in velocity value ). Thus, we select and discuss some cases
from table 5.1 to show the effect of variation of the main parameters on the operation of the heat pipe. Figure 5-19 shows the distribution of the vapour velocity, at the heat pipe centerline along the vapour core, for cases No. 22, 23 and 24 for constant input heat flux and pure water and the only variable is the coolant temperature. As shown in the figure, increasing the coolant temperature will decrease the vapour velocity due to increasing the vapour density [33]. Figure 5-20 shows the distribution of the vapour velocity, at the vapour core centerline, for cases No. 23, 26 and 35. In these cases, the working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid and the other parameters are kept constants. The behavior of the figure shows that the vapoure velocity decreases when the nanofluid is used. This is due to increasing the density of the working fluid in the presence of nanoparticles.
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Figure 5-21 shows the distribution of the vapour velocity, at the heat pipe centerline along the vapour core, for cases No. 57, 60 and 63 for constant heat flux and coolant temperature. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid. From the figure, the vapoure velocity decreases with increasing of the nanoparticles concentration and that is due to increasing of the density of the nanofluid. At the same time increasing of the nanoparticles concentration lead to decrease the operation temperature so the saturation pressure will decrease. Figure 5-22 shows the distribution of the radial vapour velocity of pure water, at the wick-vapour interface, for cases No. 1, 22 and 43 for various input heat flux. As shown in the figure, the radial vapour velocity at the wick-vapour interface in evaporator and condenser sections increases with increasing of the input heat flux due to increasing of the evaporation rate of the working fluid. Figure 5-23 shows the distribution of the radial vapour velocity, at the wickvapour interface, for cases No. 22, 23 and 24 for pure water, constant input heat flux and various coolant temperatures. This increase in the coolant temperature leads to decrease the radial vapour velocity in the evaporator and condenser sections. This behavior is due to increasing of vapour density with the coolant temperature increase. Figure 5-24 shows the distribution of the radial vapour velocity, at the wickvapour interface, for cases No. 23, 26 and 35 for constant heat flux and coolant temperature. In these cases, the working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid. As shown in the figure, the vapour velocity decreases when the nanofluid is used. This is due to increasing of the latent heat of vaporization and the density of the nanofluid as compared with the water.
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Figure 5-25 shows the distribution of the radial vapour velocity, at the wickvapour interface, for cases No. 57, 60 and 63 where both the heat flux and coolant temperature are kept constants. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid.
From the figure, the vapoure velocity at the
evaporator and condenser sections decrease with increasing of the nanoparticles concentration due to increasing the latent heat of vaporization and the vapour density. Figure 5-26 shows the variation of the shear rate with the input heat flux along the heat pipe, at the wick-vapour interface, for cases No. 1, 22 and 43 for pure water, constant coolant temperature. As shown in the figure, the shear rate increases when the input heat flux increases. This is due to increasing of the vapour velocity. Figure 5-27 shows the variation of the shear rate with the coolant temperature along the heat pipe, at the wick-vapour interface, for cases No. 22, 23 and 24 for pure water, constant input heat flux. The figure shows that the shear rate decreases when the coolant temperature increases. This is due to decreasing of the vapour velocity. Figure 5-28 shows the variation of the shear rate along the heat pipe, at the wick-vapour interface, for cases No. 23, 26 and 35 for constant heat flux and coolant temperature. In these cases, the working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid. From the figure it is clear that the shear rate decreases when the nanoflued is used. This is due to decreasing of the vapour velocity in the presence of nanoparticles. Figure 5-29 shows the variation of the shear rate along the heat pipe, at the wick-vapour interface, for cases No. 57, 60 and 63 where both the heat flux and coolant temperature are kept constants. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid. As shown in the figure, the shear rate decreases 106
Chapter Five
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with increasing of the nanoparticles concentration. This is due to decreasing of the nanofuid velocity with increasing of NPC.
5.3.1.3 Liquid Flow Figure 5-30 shows the distribution of the liquid velocity, at the midpoint along the wick structure, for cases No. 1, 22 and 43. This figure shows the effect of variation of input heat flux on liquid velocity for coolant temperature of 18.3 oC for water. The behavior in the figure shows that with increasing of the input heat flux the liquid velocity will increase, this is due to increasing of the mass flow rate of evaporation of the working fluid. Figure 5-31 shows the distribution of the liquid velocity, at the midpoint along the wick structure, for cases No. 22, 23 and 24 for pure water and constant input heat flux and the only variable is the coolant temperature. From the figure, when the coolant temperature increases there is a very small increment in the liquid velocity especially at the adiabatic section. Figure 5-32 shows the distribution of the liquid velocity along the wick structure, for cases No. 23, 26 and 35. The working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid and the other parameters are kept constants. From the figure, it is clear that when using the nanofluid the liquid velocity will decrease. This is due to increasing of the working fluid density. Figure 5-33 shows the distribution of the liquid velocity, at the midpoint along the wick structure, for cases No. 57, 60 and 63 for constant heat flux and coolant temperature. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid. As seen in the figure, the liquid velocity decreases with increasing of the nanoparticles concentration. This behavior is due to increasing of the liquid density. 107
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Figure 5-34 shows the distribution of the liquid pressure drop, at the midpoint along the wick structure, for cases No. 1, 22 and 43 for pure water, constant coolant temperature and various input heat flux. It is clear from the figure, the liquid pressure drop increases with increasing of the input heat flux due to increasing of the liquid velocity. Figure 5-35 shows the distribution of the liquid pressure drop along the wick structure, for cases No. 22, 23 and 24 for pure water, constant input heat flux and various coolant temperatures. The figure shows that the liquid pressure drop decreases with increasing of the coolant temperature due to decreasing of the liquid viscosity. Figure 5-36 shows the distribution of the liquid pressure drop, at the midpoint along the wick structure, for cases No. 23, 26 and 35 for constant heat flux and coolant temperature. The working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid. As shown in the figure, liquid pressure drop decreases when the nanofluid is used. This is due to increasing of the liquid density which reduces the liquid velocity and in turn results in low shear stresses. Figure 5-37 shows the distribution of the liquid pressure drop, at the midpoint along the wick structure, for cases No. 57, 60 and 63 where both the heat flux and coolant temperature are kept constants. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid. From the figure it can be seen that the liquid pressure drop decreases with increasing of the nanoparticles concentration within the nanofluid. This is due to increasing of the liquid density which in turn led to decreasing of the liquid velocity.
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5.3.1.4 Axial Conduction During steady state operation of the heat pipe a specified value of the input heat flux transferred axially through the heat pipe wall which is called axial heat flux (axial conduction) and calculated at the end of the adiabatic section. Figure 5-38 shows the variation of the axial heat flux with input heat flux at constant coolant temperature for cases No. 1, 22 and 43 for water, 4, 25 and 46 for 1Vol. % of Al2O3 – water based nanofluid and 13, 34 and 55 for 1Vol. % of CuO – water based nanofluid. As shown from the figure, the axial heat flux increases when the input heat flux increase. Also, at the same input heat flux the axial heat flux decreases when the nanofluis are used due to increasing of the thermophysical properties of the working fluid. Figure 5-39 shows the axial to input heat flux ratio variation with sink temperature at constant input heat flux for cases No. 22, 23 and 24 for water, 25, 26 and 27 for 1Vol. % of Al2O3 – water based nanofluid and 34, 35 and 36 for 1Vol. % of CuO – water based nanofluid for input heat flux of 1670.91 W/m2. The figure shows that the axial to input heat flux ratio decreases when the sink temperature increases. Also, at the same sink temperature, the heat ratio decreases when the nanofluids are used due to increasing of the thermal properties of the working fluid. Figure 5-40 shows the axial to input heat flux ratio variation with NPC for constant input heat flux and sink temperature for cases No. 48, 51 and 54 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 57, 60 and 63 for 1, 3 and 5 Vol. % of CuO – water based nanofluid. It is clear from the figure that the axial to input heat flux ratio decreases with increasing of nanoparticles concentration within the working fluid. This means that the axial conduction decreases with the nanoparticles concentration. This behavior is attributed to the enhancement of the working fluid thermal conductivity, and increases its ability for
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heat absorbing from evaporator inner surface and transporting it to the condenser section.
5.3.1.5 The Maximum Heat Transport Capillary Limit Figure 5-41 shows the variation of the maximum heat transfer calculated using equation 3-13 with the operating temperature for constant coolant temperature for cases No. 1, 22 and 43 for water, 4, 25 and 46 for 1Vol. % of Al2O3 and 13, 34 and 55 for 1Vol. % of CuO – water based nanofluid. As seen in the figure, the maximum heat transfer limit increases with increasing of the operating temperature due to increase of the mass flow rate of the working fluid. This behavior is similar for water or nanofluid. While, the increasing in the maximum heat transfer limit when the nanofluid was used instead of water is attributed to the increasing in the maximum mass flow rate and enhancing the latent heat of vaporization. Figure 5-42 shows variation of the maximum heat transfer limit with the coolant temperature for constant input heat flux for cases No. 22, 23 and 24 for water, 25, 26 and 27 for 1Vol. % of Al2O3 and 34, 35 and 36 for 1Vol. % of CuO – water based nanofluid. It is clear from the figure, the maximum heat transfer limit increases with the increase of the coolant temperature due to increasing the operating temperature of the heat pipe which led to enhance the maximum mass flow. This behavior is similar for water or nanofluid. While, for nanofluid the increasing in the maximum heat transfer limit is due to the increasing of both the maximum mass flow rate and the latent heat of vaporization. Figure 5-43 shows the variation of the maximum heat transfer limit with NPC at constant input heat flux and coolant temperature for cases No. 48, 51 and 54 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 57, 60 and 63 for 1, 3 and 5 Vol. % of CuO – water based nanofluid. From the figure, when 110
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Results and Discussion
the nanoparticles increases the maximum heat transfer limit increases. This is due to the increasing in both the maximum mass flow rate and the latent heat of vaporization. Figure 5-44 shows the variation of the maximum capillary pressure of the wick structure with the operating temperature for constant coolant temperature for cases No. 1, 22 and 43 for water, 4, 25 and 46 for 1Vol. % of Al2O3 – water based nanofluid and 13, 34 and 55 for 1Vol. % of CuO – water based nanofluid. As seen in the figure, the maximum capillary pressure decreases with increasing of the operating temperature due to decreasing the surface tension of the working fluid. This behavior is similar for water and nanofluids. While, the increasing in the maximum capillary pressure when the nanofluid was used is attributes to the higher surface tension of the nanofluid. Figure 5-45 shows the variation of the maximum capillary pressure of the wick structure with the coolant temperature at constant input heat flux for cases No. 22, 23 and 24 for water, 25, 26 and 27 for 1Vol. % of Al2O3 – water based nanofluid and 34, 35 and 36 for 1Vol. % of CuO – water based nanofluid. The figure shows that the maximum capillary pressure decreases with increasing of the coolant temperature due to increasing in operating temperature which in turn leads to decreasing in the surface tension of the working fluid. This behavior is similar for water and nanofluids. While, with the nanoparticles in the base fluid the capillary pressure increased due to enhancing the surface tension of the nanofluid. Figure 5-46 shows the variation of maximum capillary pressure of the wick structure with NPC for constant input heat flux and coolant temperature for cases No. 48, 51 and 54 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 57, 60 and 63 for 1, 3 and 5 Vol. % of CuO – water based nanofluid. From the figure, it is clear that the maximum capillary pressure increases when the
111
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nanoparticles concentration increases. This behavior is attributed to the nanofluid surface tension enhancement due to the presence of the nanoparticles.
5.3.1.6 Thermal Resistance Figure 5-47 shows the variation of the thermal resistance of the heat pipe with the heat flux for cases No. 1, 22 and 43 for water, 4, 25 and 46 for 1Vol. % of Al2O3 – water based nanofluid and 13, 34 and 55 for 1Vol. % of CuO – water based nanofluid for constant coolant temperature. As seen in the figure, there is no significant variation in the thermal resistance with increasing the input heat flux. This behavior is similar for water and nanofluids. While, the decreasing in the thermal resistance when the nanofluid was used instead of water is attributed to the enhancing of the working fluid thermal properties which increases the ability for heat transporting along the heat pipe. Figure 5-48 shows the variation of the thermal resistance of the heat pipe with the coolant temperature for cases No. 22, 23 and 24 for water, 25, 26 and 27 for 1Vol. % of Al2O3 – water based nanofluid and 34, 35 and 36 for 1Vol. % of CuO – water based nanofluid for constant input heat flux. The figure shows an insignificant variation in the thermal resistance with the coolant temperature increase. This behavior is similar for water and nanofluids. Figure 5-49 shows the variation of the thermal resistance of the heat pipe with NPC for cases No. 48, 51 and 54 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 57, 60 and 63 for 1, 3 and 5 Vol. % of CuO – water based nanofluid where both the input heat flux and coolant temperature are kept constants. The figure shows that the thermal resistance decreases when the nanoparticles concentration increases. This behavior is due to enhancing the working fluid thermal properties in the presence of more nanoparticles.
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5.3.1.7 Heat Pipe Thermal Performance Enhancement Utilization of nanoparticles with specified concentration within the base fluid (water) enhanced several thermophysical properties such as; density, viscosity, surface tension, thermal conductivity and the latent heat of vaporization. Therefore, enhancing the above properties will increase the ability of the heat pipe for heat transporting and, hence, the heat pipe thermal performance can be enhanced. The enhancement of the heat pipe thermal performance implies reduction of the thermal resistance between evaporator and condenser. The improvement in the thermal resistance, when the nanofluid was used, can be obtained from the following equation: (5-1) The reduction obtained in the thermal resistance of the heat pipe for the present study ranging from 6.4 to 31.49% for Al2O3 – water based nanofluid and 6.517 to 34.04% for CuO – water based nanofluid. However, the highest reduction in the thermal resistance of CCHP occurred nearly at coolant temperature of 26 oC. Thus, figure 5-50 shows the thermal resistance improvement of the heat pipe for cases No. 6, 9, 12, 27, 30, 33, 48, 51 and 54 for Al2O3 – water based nanofluid and figure 5-51 shows the thermal resistance improvement of the heat pipe for cases No. 15, 18, 21, 36, 39, 42, 57, 60 and 63 for CuO – water based nanofluid. These figures show that the thermal resistance improvement increases with the increase in both nanoparticles concentration and input heat flux to reach up to about 31.49% and 34.04% for the nanofluid with 5 Vol.% of Al2O3 and CuO NPC respectively, at 2784.86 W/m2. This behavior is attributed to enhancing the thermal properties of the working fluid which causes to increase the heat pipe ability for heat transfer from source to sink.
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5.3.2 VCHP One hundred and eighty nine computational runs (as summarized in table 5.2) are performed at three different values for each of the following parameters; input heat flux, nanoparticles concentration, mass of non-condensable gas (air) and heat sink temperature for three different working fluids, to show the effect of variation of these parameters on temperature distribution, vapour flow, liquid flow, axial conduction, the maximum heat transport capillary limit, thermal resistance, condenser active length and heat pipe thermal performance enhancement.
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Table (5.2) Summery of cases studied. Case Number
Ts (oC)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26
Working fluid
φ (Vol.%)
Water
0
q (W/m2)
Mass of air (mg)
1 Al2O3 – water based Nanofluid
3
5
556.97
1 CuO – water based Nanofluid
3
5 0.5 Water
0
1 Al2O3 – water based Nanofluid
3
5
1 CuO – water based Nanofluid
3
5
115
1670.91
Chapter Five
Results and Discussion
Table (5.2) Continued. Case Number
Ts (oC)
43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26
Working fluid
φ (Vol.%)
Water
0
q (W/m2)
Mass of air (mg)
2784.86
0.5
556.97
1.1
1 Al2O3 – water based Nanofluid
3
5
1 CuO – water based Nanofluid
3
5
Water
0
1 Al2O3 – water based Nanofluid
3
5
1 CuO – water based Nanofluid
3
5
116
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Table (5.2) Continued. Case Number
Ts (oC)
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26
Working fluid
φ (Vol.%)
Water
0
q (W/m2)
Mass of air (mg)
1 Al2O3 – water based Nanofluid
3
5
1670.91
1 CuO – water based Nanofluid
3
5 1.1 Water
0
1 Al2O3 – water based Nanofluid
3
5
1 CuO – water based Nanofluid
3
5
117
2784.86
Chapter Five
Results and Discussion
Table (5.2) Continued. Case Number
Ts (oC)
127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168
18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26
Working fluid
φ (Vol.%)
Water
0
q (W/m2)
Mass of air (mg)
1 Al2O3 – water based Nanofluid
3
5
556.97
1 CuO – water based Nanofluid
3
5 1.5 Water
0
1 Al2O3 – water based Nanofluid
3
5
1 CuO – water based Nanofluid
3
5
118
1670.91
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Results and Discussion
Table (5.2) Continued. Case Number
Ts (oC)
169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189
18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26 18.3 22 26
Working fluid
φ (Vol.%)
Water
0
Q (W)
Mass of air (mg)
2784.86
1.5
1 Al2O3 – water based Nanofluid
3
5
1 CuO – water based Nanofluid
3
5
5.3.2.1 Temperature Distribution The variation of temperature along the heat pipe in VCHP depends on the same parameters as in CCHP beside another important parameter which is called mass of the non-condensable gas. This parameter is strongly used to control the evaporator temperature. As in CCHP, some cases from table 5.2 are chosen and discussed to show the effect of variation of the parameters that control the heat pipe operation. Figures 5-52 to 5-54 show the temperature contours for cases No. 1, 22 and 43, respectively. These figures show the effect of variation of input heat flux on temperature distribution for pure water for the same constant coolant temperature and the mass of non-condensable gas (air). 119
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Figures 5-52, 5-55 and 5-56 show the temperature contours for cases No. 1, 2 and 3, respectively. All these figures show the effect of variation of coolant temperature on temperature distribution for pure water while the other parameters are kept constants. As shown from these figures, the temperature along heat pipe increases as input heat flux or coolant temperature increases due to increasing of the working fluid evaporation rate. Figure 5-57 to 5-59 show the temperature contours for cases No. 4, 7 and 10, respectively. These figures show the effect of variation of nanoparticles concentration (NPC) on the temperature distribution for Al2O3 – water based nanofluid while the other parameters are kept constants. Figure 5-60 to 5-62 show the temperature contours for cases No. 13, 16 and 19 respectively. These figures show the effect of variation of nanoparticles concentration (NPC) on the temperature distribution for CuO – water based nanofluid and the other parameters are kept constants. From the above figures for nanofluid, there is a small decrease in the temperature along heat pipe as NPC increases. This behavior is due to decreasing the velocity and increasing the thermal conductivity of the working fluid with increasing of NPC. The significant change in the contour temperature distribution shown in these figures is due to presence of the non-condensable gas. Figure 5-63 to 5-65 show the temperature contours for cases No. 9, 72 and 135 respectively. These figures show the effect of variation of mass of noncondensable gas (air) on temperature distribution for Al2O3 – water based nanofluid and the other parameters are kept constants. As shown in the figures, the temperature increases along heat pipe as air mass increases. This is due to increasing of the inactive length of the condenser which causes to increase the operating temperature.
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5.3.2.2 Vapour Flow Figure 5-66 shows the distribution of the vapour velocity, at the heat pipe centerline along the vapour core, for cases No. 1, 22 and 43 for water. This figure shows the effect of variation of the input heat flux on vapour velocity for coolant temperature of 18.3 oC and mass of non-condensable gas (air) of 0.5 mg. It can be seen from the figure that the vapour velocity increases when the input heat flux increases. This is due to the increasing of working fluid evaporation rate and decreasing of the condenser inactive length, which means decreasing the volume of non-condensable gas in condenser zone, with increasing the input heat flux. The main difference between this figure and figure 5-16 is the shift down of the vapour velocity profile due to missing a part of condenser which is occupied by air. Figure 5-67 shows the distribution of the vapour velocity, at the heat pipe centerline, for cases No. 22, 23 and 24 for variable coolant temperature and the other parameters are kept constants. The figure shows that the vapour velocity decreases with the increase of coolant temperature, although the condenser active length increases slightly. This behavior is due to increasing of the vapour density, with the coolant temperature increase. Hence, the presence of non-condensable gas in the condenser zone reduces the vapour velocity than that of figure 5-19. Figure 5-68 shows the distribution of the vapour velocity, at the vapour core centerline, for cases No. 23, 26 and 35. In these cases, the working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid. It is clear from the figure that the vapoure velocity decreases when the nanofluid is used as working fluid. This behavior is due to increasing of the thermal properties of the working fluid and increasing the condenser inactive length when the nanofluid is used. The difference between this figure and figure 5-20 is the significant reduction in the vapour velocity of the pure water due to the
121
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presence of non-condensable gas, while the nanofluids velocities nearly equal in these figures. Figure 5-69 shows the distribution of the vapour velocity, at the heat pipe centerline, for cases No. 57, 60 and 63 for constant heat flux, coolant temperature and mass of air. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid. As seen in the figure, the vapoure velocity decreases with increasing of the NPC. This is due to increasing in the density and latent heat of vaporization (hfg) of the nanofluid and the condenser inactive length in the presence of more NPC. Thus, this figure differs from figure 5-21 only by the small reduction in the vapour velocity due to the existence of air in the condenser section. Figure 5-70 shows the distribution of the vapour velocity, at the heat pipe centerline, for cases No. 44, 107 and 170 for variable mass of air and the other parameters are kept constants. As shown in this figure, the vapour velocity decreases as the mass of non-condensable gas (Mncg) increases. This behavior is due to increasing of the condenser inactive length as the volume and the pressure of the mass of non-condensable gas (Mncg) increase. Figure 5-71 shows the distribution of the radial vapour velocity along the heat pipe, at the wick-vapour interface, for cases No. 1, 22 and 43 for pure water for various input heat flux and other parameters are kept constants. From the figure, the radial vapour velocity at the wick-vapour interface in the evaporator section increases with increasing of the input heat flux, while this behaviour is opposite in the condenser section. This is because of the increase in the evaporation rate of the working fluid and the decrease in the condenser inactive length as the input heat flux increase. The results, of radial velocity at the condenser section, in this figure there is different shape than the results in figure 5-22. Besides the reduction which is in the values of the vapour velocities at the evaporator section. All these are due to the effect of presence of non-condensable gas. 122
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Figure 5-72 shows the distribution of the radial vapour velocity along the heat pipe, at the wick-vapour interface, for cases No. 22, 23 and 24 for pure water for various coolant temperature and the other parameters are kept constants. As seen in the figure, the increase in the coolant temperature led to decrease the radial vapour velocity in evaporator and condenser sections due to increasing in the vapour density, even with the slight increase in the condenser active length, with the coolant temperature increase. It can be observed the change of results between this figure and figure 5-23 which is represented by the reduction of the vapour velocities values at the evaporator section and increasing it at the condenser section. This is due to the existing of air in the condenser section which causes a reduction in the flow area. Figure 5-73 shows the distribution of the radial vapour velocity along the heat pipe, at the wick-vapour interface, for cases No. 23, 26 and 35 for constant heat flux, coolant temperature and air mass. In these cases, the working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid. As shown in the figure, the vapour velocity decreases when the nanofluid is used. This is due to increasing in the thermal properties of the working fluid and increasing the condenser inactive length as the nanofluid is used. Thus, the difference between this figure and figure 5-24 is the reduction of the vapour velocities values at the evaporator section and increasing of it at the condenser section because of unused a part of the condenser section due to the existing of air. Figure 5-74 shows the distribution of the radial vapour velocity along the heat pipe, at the wick-vapour interface, for cases No. 57, 60 and 63 where the heat flux, coolant temperature and air mass are kept constants. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid. The figure shows that the vapoure velocity at the evaporator and condenser sections decreases when the NPC increases. This is due to the increasing in the vapour density of the nanofluid and 123
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the condenser inactive length with the increase of NPC. It is obvious that the results in this figure and figure 5-25 show different behaviour of the vapour velocities in the condenser section, whereas their values increased in the presence of noncondensable gas. Figure 5-75 shows the distribution of the radial vapour velocity along the heat pipe, at the wick-vapour interface, for cases No. 58, 121 and 184 where the heat flux, coolant temperature and NPC of CuO – water based nanofluid are kept constants and the only variable is the mass of non-condensable gas. As seen in the figure, the vapour velocity at the evaporator section has nearly the same values with small variation for all cases. While at the condenser section the increasing is clear in the vapour velocity with the mass of non-condensable gas (Mncg) increasing. This behavior is due to increasing in the condenser inactive length which leads to decrease the flow area of vapour.
5.3.2.3 Liquid Flow Figure 5-76 shows the distribution of the liquid velocity for pure water, at the midpoint along the wick structure, for cases No. 1, 22 and 43. This figure shows the effect of variation of input heat flux on liquid velocity where the other parameters are kept constants. As shown in the figure, the liquid velocity increases when the input heat flux increases. This is due to increasing of the mass flow rate of the working fluid and decreasing the condenser inactive length with increasing of input heat flux. Figure 5-77 shows the distribution of the liquid velocity, at the midpoint along the wick structure, for cases No. 22, 23 and 24 for pure water, constant input heat flux and mass of air and the only variable is the coolant temperature. It is clear from the figure that there is an insignificant effect of the coolant temperature on the liquid velocity. 124
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Figure 5-78 shows the distribution of the liquid velocity, at the midpoint along the wick structure, for cases No. 23, 26 and 35 for constant heat flux, coolant temperature and air mass. The working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid. The figure shows that when using the nanofluid, the liquid velocity will decrease. This behavior is due to the increasing in working fluid density and the capillary pressure as the nanofluid is used. Figure 5-79 shows the distribution of the liquid velocity, at the midpoint along the wick structure, for cases No. 57, 60 and 63 where the heat flux, coolant temperature and air mass are kept constants. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid. As seen in the figure, the liquid velocity decreases with the increasing of the nanoparticles concentration. This is due to the increasing in liquid density and the capillary pressure in the presence of more NPC. Figure 5-80 shows the distribution of the liquid velocity, at the midpoint along the wick structure, for cases No. 58, 121 and 184 where the heat flux, coolant temperature and NPC of CuO – water based nanofluid are kept constants and various mass of non-condensable gas. As seen in the figure, the liquid velocity decreases as the mass of non-condensable gas (Mncg) increases. This behavior is due to the increasing in the condenser inactive length which leads to decreasing in the heat pipe effective length. Figure 5-81 shows the distribution of the liquid pressure drop, at the midpoint along the wick structure, for cases No. 1, 22 and 43 for pure water, constant coolant temperature and air mass and various input heat flux. It is clear from the figure that the liquid pressure drop increases with increasing of the input heat flux due to increasing in the liquid velocity and the condenser active length. Figure 5-82 shows the distribution of the liquid pressure drop, at the midpoint along the wick structure, for cases No. 22, 23 and 24 for pure water, 125
Chapter Five
Results and Discussion
constant input heat flux and air mass and various coolant temperatures. From the figure, it is clear that the liquid pressure drop decreases with the increasing in coolant temperature due to the decreasing of the liquid viscosity. Figure 5-83 shows the distribution of the liquid pressure drop, at the midpoint along the wick structure, for cases No. 23, 26 and 35 for constant heat flux, coolant temperature and air mass. The working fluids used are water, 1 Vol. % of Al2O3 – water based nanofluid and 1 Vol. % of CuO – water based nanofluid. As seen in the figure, liquid pressure drop decreases when the nanofluid is used. This is due to the decreasing in the liquid velocity because of the presence of the nanoparticles in the base fluid (water). Figure 5-84 shows the distribution of the liquid pressure drop, at the midpoint along the wick structure, for cases No. 57, 60 and 63 where the heat flux, coolant temperature and air mass are kept constants. The working fluids used are 1, 3 and 5 Vol. % of CuO – water based nanofluid. It can be seen from the figure that the liquid pressure drop decreases as the NPC increases. This is because of the decreasing of liquid velocity due to increasing in the density in the presence of more NPC. Figure 5-85 shows the distribution of the liquid pressure drop along the wick structure, for cases No. 58, 121 and 184 where the heat flux, coolant temperature and NPC of CuO – water based nanofluid are kept constants and various mass of non-condensable gas. As seen in the figure, the liquid pressure drop decreases when the mass of non-condensable gas (Mncg) increases. This behavior is due to the decreasing in the liquid velocity because of the increasing in the condenser inactive length which leads to decreasing the heat pipe effective length. In this section, the difference between the above figures when compared with the figures in CCHP is the very small reduction in the liquid velocity and the
126
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significant reduction in the liquid pressure drop due to the presence of the noncondensable gas which causes the reduction in the heat pipe effective length.
5.3.2.4 Axial Conduction Figure 5-86 shows the variation of the axial heat flux with input heat flux for cases No. 64, 85 and 106 for water, 67, 88 and 109 for 1Vol. % of Al2O3 – water based nanofluid and 76, 97 and 118 for 1Vol. % of CuO– water based nanofluid for constant coolant temperature and air mass. As seen in the figure, the axial heat flux decreases when the input heat flux reaches the minimum value at 1670.91W and then increases when the input heat flux increases, for all used types of working fluids. At the same value of heat input, the axial heat flux increases when the nanofluids are used. The change of the results between this figure and figure 5-38 is the reduction in the axial conduction values due to the presence of non-condensable gas. Whereas, increasing the input heat flux decreases the condenser inactive length, and at the same time it increases when the nanofluid is used. Figure 5-87 shows the variation of the axial to input heat flux ratio with heat sink temperature for cases No. 85, 86 and 87 for water, 88, 89 and 90 for 1Vol. % of Al2O3 – water based nanofluid and 97, 98 and 99 for 1Vol. % of CuO – water based nanofluid for constant input heat flux and air mass. The behavior in the figure shows that the heat ratio decreases when the sink temperature increases. For the same fixed sink temperature, the heat ratio increases when the nanofluids are used. This behavior is opposite to that found in figure 5-39 which is due to the effect of non-condensable gas, whereas the sink temperature decreases the condenser inactive length while using the nanofluid increases it. Figure 5-88 shows the variation of the axial to input heat flux ratio with NPC for cases No. 48, 51 and 54 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 57, 60 and 63 for 1, 3 and 5 Vol. % of CuO – water based nanofluid 127
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where input heat flux, coolant temperature and air mass are kept constant. The figure shows that the heat ratio increases when the NPC increases for both Al2O3 and CuO – water based nanofluids. Contrarily, this behavior differs than that found in figure 5-40 because of increasing the condenser inactive length with more NPC, in the presence of non-condensable gas in condenser section. Figure 5-89 shows the variation of the axial to input heat flux ratio with mass of non-condensable gas for cases No. 49, 112 and 175 for 3 Vol. % of Al2O3 – water based nanofluid and cases No. 58, 121 and 184 for 3 Vol. % of CuO – water based nanofluid for constant input heat flux, coolant temperature. As shown in the figure, the axial to input heat flux ratio increase when the mass of non-condensable gas increase. This is due to increasing in the volume of the non-condensable gas in the condenser zone which leads to decreasing of the heat pipe effective length.
5.3.2.5 The Maximum Heat Transport Capillary Limit Figure 5-90 shows the variation of the maximum heat transfer limit that can be transported by the heat pipe with active length temperature calculated by equation 3-82 for cases No. 64, 85 and 106 for water, 67, 88 and 109 for 1Vol. % of Al2O3 – water based nanofluid and 76, 97 and 118 for 1Vol. % of CuO – water based nanofluid for constant coolant temperature and air mass and various input heat flux. As seen from the figure, for all types of the working fluid the maximum heat transfer limit increases with the active length temperature which is due to the increasing of the maximum mass flow rate of the working fluid. For the same fixed value of active length temperature, the maximum heat transfer limit increases when the nanofluid is used which is due to increasing of the maximum mass flow rate and the latent heat of vaporization. Figure 5-91 shows the variation of the maximum heat transfer limit of the heat pipe with coolant temperature for cases No. 85, 86 and 87 for water, 88, 89 128
Chapter Five
Results and Discussion
and 90 for 1Vol. % of Al2O3 – water based nanofluid and 97, 98 and 99 for 1Vol. % of CuO – water based nanofluid for constant input heat flux and air mass. It is clear from the figure that the maximum heat transfer limit increases with the increase of the coolant temperature due to increasing in the heat pipe active length temperature which leads to increase the maximum mass flow rate. This behavior is similar for water or nanofluid. While, for nanofluid the increasing in the maximum heat transfer limit is due to the increasing in both the maximum mass flow rate and the latent heat of vaporization. Figure 5-92 shows the variation of the maximum heat transfer limit of the heat pipe with NPC for cases No. 111, 114 and 117 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 120, 123 and 126 for 1, 3 and 5 Vol. % of CuO – water based nanofluid where the input heat flux, coolant temperature and air mass are kept constants. The behavior in the figure shows that when the nanoparticles concentration increases the maximum heat transfer limit increases. This is due to the increasing in both the maximum mass flow rate and the latent heat of vaporization. For maximum heat transfer limit, the difference between the above figures and the figures in CCHP is the increase in the values of maximum heat transfer limit due to the existing of the non-condensable gas which causes the reduction in the heat pipe effective length and increases maximum mass flow rate. Figure 5-93 shows the variation of the maximum heat transfer limit of the heat pipe with the mass of non-condensable gas for cases No. 49, 112 and 175 for 3 Vol. % of Al2O3 – water based nanofluid and cases No. 58, 121 and 184 for 3 Vol. % of CuO – water based nanofluid for constant input heat flux, coolant temperature. It is clear from the figure that the maximum heat transfer limit increases when the mass of non-condensable gas increases. This behavior is attributed to increasing the pressure inside the heat pipe due to increasing the 129
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volume of the non-condensable gas. This leads to decrease the effective length and thus increases the maximum mass flow rate of the working fluid. Figure 5-94 shows the variation of the maximum capillary pressure of the wick structure with the active length temperature for cases No. 64, 85 and 106 for water, 67, 88 and 109 for 1Vol. % of Al2O3 – water based nanofluid and 76, 97 and 118 for 1Vol. % of CuO – water based nanofluid for constant coolant temperature and air mass. As seen in the figure, the maximum capillary pressure decrease with the active length temperature increases due to decreasing the surface tension of the working fluid. This behavior is similar for water or nanofluid. At the same active length temperature, the maximum capillary pressure for water and nonofluids nearly equal. Figure 5-95 shows the variation of the maximum capillary pressure of the wick structure with the coolant temperature for cases No. 85, 86 and 87 for water, 88, 89 and 90 for 1Vol. % of Al2O3 – water based nanofluid and 97, 98 and 99 for 1Vol. % of CuO – water based nanofluid for constant input heat flux and air mass. The figure shows that the maximum capillary pressure decreases when the coolant temperature increases. This is due to increasing in the active length temperature which in turn leads to decrease the surface tension of the working fluid. This behavior is similar for water or nanofluid. While, with the presence of the nanoparticles in the base fluid the capillary pressure increased, at the same fixed sink temperature, due to the enhancing in the surface tension of the working fluid. Figure 5-96 shows the variation of the maximum capillary pressure of the wick structure for cases No. 111, 114 and 117 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 120, 123 and 126 for 1, 3 and 5 Vol. % of CuO – water based nanofluid where the input heat flux, coolant temperature and air mass are kept constants. As seen in the figure the maximum capillary pressure increases when the nanoparticles concentration increases. This behavior is 130
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Results and Discussion
attributed to the nanofluid surface tension enhancement due to the increase of the concentration. For maximum capillary pressure, the difference between the above figures and the figures in CCHP is the reduction in the values of maximum capillary pressure due to the existing of the non-condensable gas which causes the increase in the active length temperature which in turn leads to decrease the surface tension of the working fluid. Figure 5-97 shows the variation of the maximum capillary pressure of the wick structure with the mass of non-condensable gas for cases No. 49, 112 and 175 for 3 Vol. % of Al2O3 – water based nanofluid and cases No. 58, 121 and 184 for 3 Vol. % of CuO – water based nanofluid for constant input heat flux, coolant temperature. As seen in the figure, the maximum capillary pressure decrease with the mass of non-condensable gas increase due to increasing the operating pressure inside the heat pipe which leads to decreasing the surface tension of the working fluid.
5.3.2.6 Thermal Resistance Figure 5-98 shows the variation of the thermal resistance of the heat pipe for cases No. 64, 85 and 106 for water, 67, 88 and 109 for 1Vol. % of Al2O3 – water based nanofluid and 76, 97 and 118 for 1Vol. % of CuO – water based nanofluid for constant coolant temperature and air mass and various input heat flux. From the figure, it is clear that the thermal resistance of heat pipe is relatively high at low heat input and decreases when the heat input increases. This behavior is similar for water or nanofluid. At the same input heat flux, the insignificant difference in the thermal resistance when the nanofluid was used attributed to the presence of the non-condensable gas.
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Figure 5-99 shows the variation of the thermal resistance of the heat pipe for cases No. 85, 86 and 87 for water, 88, 89 and 90 for 1Vol. % of Al2O3 – water based nanofluid and 97, 98 and 99 for 1Vol. % of CuO – water based nanofluid for constant input heat flux and air mass and various coolant temperature. As shown in the figure, the thermal resistance decreases when the coolant temperature increases due to the increasing in active length temperature and thus increases the thermal conductivity of the working fluid. This behavior is similar for water or nanofluid. The decreasing in the thermal resistance, at the same coolant temperature, when the nanofluid was used attributed to the enhancing of the working fluid thermal properties. Figure 5-100 shows the variation of the thermal resistance of the heat pipe for cases No. 111, 114 and 117 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 120, 123 and 126 for 1, 3 and 5 Vol. % of CuO – water based nanofluid where the input heat flux, coolant temperature and air mass are kept constants. As seen in the figure, the thermal resistance decreases with the increase of NPC. This behavior is attributed to the increasing in the thermal conductivity of the working fluid. The difference between this figure and figure 549 is the increase in the thermal resistance values which is attributed to the existing of non-condensable gas. Figure 5-101 shows the variation of the thermal resistance of the heat pipe for cases No. 49, 112 and 175 for Al2O3 – water based nanofluid and cases No. 58, 121 and 184 for CuO – water based nanofluid for constant input heat flux, coolant temperature and NPC and various mass of non-condensable gas. As seen in the figure, the thermal resistance increases as the mass of non-condensable gas increases. This behavior is attributed to the increasing of the condenser inactive length which is in turn increases the temperature difference between the evaporator and condenser with the presence of more mass of non-condensable gas. 132
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5.3.2.7 Condenser Active Length Figure 5-102 shows the variation of the condenser active length with the input heat flux for cases No. 64, 85 and 106 for water, 67, 88 and 109 for 1Vol. % of Al2O3 – water based nanofluid and 76, 97 and 118 for 1Vol. % of CuO – water based nanofluid for constant coolant temperature and air mass. As seen in the figure, the condenser active length increases with the input heat flux increases, for both water and nanofluid. This behavior is due to the increasing in vapour pressure which compresses the non-condensable gas in the condenser section when the input heat flux increases. Figure 5-103 shows the variation of the condenser active length with the coolant temperature for cases No. 85, 86 and 87 for water, 88, 89 and 90 for 1Vol. % of Al2O3 – water based nanofluid and 97, 98 and 99 for 1Vol. % of CuO – water based nanofluid for constant input heat flux and air mass. It is clear from the figure that there is small increment in the condenser active length when the coolant temperature increases, for both water and nanofluid. This is due to increasing in the vapour density which leads to increase the pressure of the working fluid when the coolant temperature increases. Figure 5-104 shows the variation of the condenser active length for cases No. 111, 114 and 117 for 1, 3 and 5 Vol. % of Al2O3 – water based nanofluid and cases No. 120, 123 and 126 for 1, 3 and 5 Vol. % of CuO – water based nanofluid where the input heat flux, coolant temperature and air mass are kept constants. As shown in the figure, the condenser active length decreases when NPC increases. This behavior is attributed to the decreasing in the pressure of the working fluid in the presence of more NPC, which allows the volume of non-condensable gas to expand and hence, the condenser inactive length is increased. Figure 5-105 shows the variation of the condenser active length with air mass for cases No. 49, 112 and 175 for Al2O3 – water based nanofluid and cases 133
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No. 58, 121 and 184 for CuO – water based nanofluid for constant input heat flux, coolant temperature and NPC. The behavior in the figure shows that the condenser active length decreases with the increasing of mass of non-condensable gas. This is due to increasing of the volume and pressure of the non-condensable gas within the heat pipe.
5.3.2.8 Heat Pipe Thermal Performance Enhancement Enhancement of the heat pipe thermal performance which is represented by the improvement of the thermal resistance is discussed previously in CCHP. While in VCHP the difference is the presence of three different amounts (0.5, 1.1 and 1.5) of non-condensable gas (air). The reduction obtained in the thermal resistance of VCHP for the present study ranging from 0.005 to 4.07% for Al2O3 – water based nanofluid and 0.018 to 4.17% for CuO – water based nanofluid. The highest reduction obtained in the thermal resistance for VCHP occurred at coolant temperature of 26 oC and mass of non-condensable gas of 0.5mg. Thus, figure 5-106 shows the thermal resistance improvement of the heat pipe for cases No. 6, 9, 12, 27, 30, 33, 48, 51and 54 for Al2O3 – water based nanofluid and figure 5-107 shows the thermal resistance improvement of the heat pipe for cases No. 15, 18, 21, 36, 39, 42, 57, 60 and 63 for CuO – water based nanofluid. These figures show that the thermal performance improvement increases with the increasing of both nanoparticles concentration and input heat flux to reach about 4.07% and 4.17% for the nanofluid with 5 Vol.% of Al2O3 and CuO NPC respectively, at 2784.86 W/m2. This behavior is attributed to the enhancing of the thermal properties of the working fluid which increases the heat pipe ability for heat transfer from source to sink.
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5.4 Experimental Results In this section, the experimental tests are performed at the same conditions and parameters of those used in the theoretical measurements.
5.4.1 CCHP 5.4.1.1 Effect of Liquid Inventory on Heat Pipe Thermal Behavior Figures 5-108 to 5-110 show typical plots of the wall temperature profiles along the tested heat pipe for various Filling Ratio (FR). While, figure 5-111 shows the heat pipe thermal resistance variation with filling ratio. The horizontal heat pipe was used at a heat flux of 556.97, 1670.91 and 2784.86 W/m2. During the tests, the coolant (sink) temperature at the condenser was maintained constant at 18.3 oC. Ten fill charges of 10.9, 14.5, 18, 21.7, 25.3, 28.9, 32.5, 34.7, 36.2 and 39.8 grams are tested which represented by 75%, 100%, 125%, 150%, 175%, 200%, 225%, 240%, 250% and 275% respectively, of the theoretical charge that saturates the wick. One of the performance evaluation criteria of the heat pipe is the evaporator wall temperature, where the lower wall temperature at a certain heat flux indicates best thermal performance, similar observation was stated by [33]. Another criterion which represented the overall heat pipe is the thermal resistance. Whereas, the lower thermal resistance is refers to the best heat pipe thermal performance. The results of figures 5-108 to 5-111 show that the heat pipe with inventory charge of 240% has the best performance over the other charges. Practically, when the inventory was increased more than 240% then the excessive amount of the inventory charge might cause the blocking of the condenser or increase in the thermal resistance at the evaporator. Then, the inventory charge of 240% was used for all heat pipe tests with water or nanofluid as working fluid.
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5.4.1.2 Effect of Heat Transfer Rate on Heat Pipe Thermal Behavior The effect of input heat flux variation on heat pipe behavior was represented by number of figures. Figures 5-112 and 5-113 show the axial wall temperature distribution for three different values of heat flux for water and 5 Vol.% of Al2O3 – water based nanofluid respectively. Whereas, with increasing of the input heat flux the working fluid mass flow rate increases so that the saturation pressure increases, all this lead to increase the wall temperature along the heat pipe. Figure 5-114 shows the overall thermal resistance of the heat pipe at the different input heat flux for water and 5 Vol.% of Al2O3 – water based nanofluid respectively. These figures show that there is a small decreasing in the thermal resistance with increasing in the input heat flux. All these figures are plotted for cases No. 1, 22 and 43 for water and cases No. 10, 31 and 52 for 5 Vol.% of Al2O3 – water based nanofluid. The coolant temperature for all these cases was kept constant at 18.3 oC. While, for nanofluid with different concentration the wall temperature distribution and overall thermal resistance have the same behavior as in water.
5.4.1.3 Effect of Coolant Temperature on Heat Pipe Thermal Behavior To investigate the thermal behaviour of the heat pipe for different sink temperatures, all experiments are accomplished for three cooling water temperatures at the heat pipe condenser section. Figures 5-115 and 5-116 show the influence of sink temperature (Ts) on axial wall temperature distribution of the heat pipe for cases No. 43, 44 and 45 for water and cases No. 52, 53 and 54 for 5 Vol.% of Al2O3 – water based nanofluid for constant input heat flux. It can be noticed that the wall temperature increases as the sink temperature increases. This is due to the increasing of the working fluid density which leads to increase the operation temperature. In addition, there is small decreasing in the heat pipe thermal resistance when the coolant temperature 136
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increases as shown in figure 5-117 for water and 5 Vol.% of Al2O3 – water based nanofluid respectively.
5.4.1.4 Effect of Nanoparticles Concentration on Heat Pipe Thermal Behavior Two types of nanoparticles and three concentrations for each type are prepared and used as a working fluid besides water to get knowledge of the effect of the working fluid type (especially the nanoparticles concentration) on the heat pipe thermal behaviour. Figure 5-118 shows the effect of nanoparticles concentration (NPC) on axial wall temperature distribution of the heat pipe for cases No. 45, 48, 51 and 54 for Al2O3 – water based nanofluid. Also, figure 5-119 shows the effect of nanoparticles concentration (NPC) on axial wall temperature distribution of the heat pipe for cases No. 45, 57, 60 and 63 for CuO – water based nanofluid. It can be shown from these figures that the axial wall temperature decreases when the NPC increases. This behavior is attributed to decreasing in the velocities and the increasing of the thermal conductivity of the working fluid in the presence of more NPC which in turn decreases the operating temperature for Al2O3 and CuO – water based nanofluids. Figure 5-120 shows the effect of nanoparticles concentration (NPC) on the heat pipe thermal resistance for cases No. 45, 48, 51 and 54 for Al2O3 – water based nanofluid and cases No. 45, 57, 60 and 63 for CuO – water based nanofluid. These figures show that the thermal resistance decreases with the increase of NPC. This is due to the increasing in the thermal properties of the working fluid in the presence of nanoparticles which makes the heat pipe efficient for heat transporting from evaporator to condenser section. All these figures are plotted for constant input heat flux and coolant temperature.
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The experiments show that the nanoparticles concentration (NPC) has significant effect on the heat pipe thermal resistance, this is discussed previously through their effect on the heat pipe thermal performance enhancement. The reduction in thermal resistance of the heat pipe which is obtained in this study is ranging from 9.07 to 44.4% for Al2O3 – water based nanofluid and 10.2 to 48.6% for CuO – water based nanofluid. However, Figures 5-121 and 5-122 show the highest thermal resistance improvement obtained for Al2O3 and CuO – water based nanofluids respectively, at coolant temperature equals to 26 oC and heat flux equals to 2784.86 W/m2. As shown from the figures, the thermal resistance improvement for Al2O3 – water based nanofluid reaches up to 44.4%, while 48.6% for CuO – water based nanofluid at NPC of 5 Vol.%. The difference between the theoretical and experimental results for the thermal resistance improvement when the nanofluids are used essentially is attributed to the formation of a thin porous coating layer by nanoparticles on the wick surface in the evaporation region. The enhancement of the heat pipe thermal performance is due to the deposition of the nanoparticles on the wick surface was verified experimentally by [47, 52] and confirmed by [57,58]. They stated that the coating layer formed by nanoparticles improves the surface wettability by reducing the contact angle and increasing the surface roughness which in turn increases the critical heat flux. This improves the maximum heat transporting rate and reduces the thermal resistance of the heat pipe using nanofluids.
5.4.1.5 Comparison between Numerical Predictions and Experimental Results The temperature distribution along the heat pipe wall which is predicted by the present numerical model is compared with that measured from the experiments for some cases No. 1, 3, 45, 48, 54 and 63, where figures 5-123 to 5-128 show the comparison results. Figures 5-129 and 5-131 show the comparison results of the 138
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Results and Discussion
predicted heat pipe thermal resistance with that measured from the experiments for cases No. 2, 23 and 44 for water, 11, 32 and 53 for 5 Vol.% of Al2O3 – water based nanofluid and 20, 41 and 62 for 5 Vol.% of CuO – water based nanofluid respectively. It is clear from these figures that both experimental and numerical results have the same behavior and the maximum relative error, of the evaporatorcondenser temperature difference, is 8.2% for pure water and 25% for nanofluids. The high relative error value, when the nanofluids are used, is due to the effect of nanoparticles deposition on the wick surface at the evaporating zone, which is cannot be included within the theoretical model.
5.4.2 VCHP 5.4.2.1 Effect of Liquid Inventory on Heat Pipe Thermal Behavior The same optimal filling ratio which is obtained for CCHP (240% of that saturates the wick) is also obtained and used for VCHP as shown in figures 5-132 and 5-133.
5.4.2.2 Effect of Heat Transfer Rate on Heat Pipe Thermal Behavior The effect of input heat flux variation on heat pipe thermal behavior was implemented with three different masses of non-condensable gas. Figures 5-134 and 5-135 show the axial temperature distribution for cases No. 127, 148 and 169 for water and cases No. 142, 163 and 184 for 3 Vol.% of CuO – water based nanofluid respectively, for coolant temperature of 18.3 oC and 1.5mg of air as noncondensable gas. These figures show that with increasing of the input heat flux the wall temperature along the heat pipe increases. This is due to increasing of the working fluid evaporation rate so that the inside pressure will increase. Figure 5136 shows the overall thermal resistance of the heat pipe at the different input heat flux for water and 3 Vol.% of CuO – water based nanofluid. This figure shows that 139
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Results and Discussion
the thermal resistance decreases with increasing of the heat flux. This is due to the increasing in the condenser active length which leads to reduce the evaporatorcondenser temperature difference. Also, the increasing of the input heat flux increases the working fluid thermal properties. Unlike CCHP, there is a clear decrease in the thermal resistance of VCHP due to the effect of the noncondensable gas.
5.4.2.3 Effect of Coolant Temperature on Heat Pipe Thermal Behavior Figures 5-137 and 5-138 show the influence of sink temperature (Ts) on axial wall temperature distribution of the heat pipe for cases No. 169, 170 and 171 for pure water and cases No. 184, 185 and 186 for 3 Vol.% of CuO – water based nanofluid respectively, for input heat flux of 2784.86 W/m2 and air mass of 1.5 mg. It can be noticed that the wall temperature increases as the sink temperature increases. This is due to the increasing of the working fluid density which leads to increase the operation temperature, even with the increase in the condenser active length. In addition the heat pipe thermal resistance decreases when the coolant temperature increases as shown in figure 5-139 for water and nanofluid. This trend of behavior is attributed to the increasing in the condenser active length and the thermal conductivity of the working fluid with increasing of the operating temperature.
5.4.2.4 Effect of Mass of Non-Condensable Gas on Heat Pipe Thermal Behavior To investigate the effect of non-condensable gas (Mncg) on the heat pipe thermal behaviour, three masses of air 0.5, 1.1 and 1.5mg are used. Figures 5-140 and 5-141 respectively, show the axial wall temperature distribution for cases No. 44, 107, 170 for pure water and cases No. 56, 119, 182 for 1 Vol.% CuO – water 140
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Results and Discussion
based nanofluid for input heat flux of 2784.86 W/m2 and coolant temperature of 22 o
C. As shown in these figures, the axial wall temperature increases as the air mass
increases. This is due to the decreasing of the condenser active length which leads to the increasing in the active length temperature. Also, it can be noticed from figure 5-142 that the heat pipe thermal resistance increases when the air mass increases. This is due to the increasing of the condenser inactive length which causes the increase in the temperature difference between the evaporator and condenser sections in the presence of more non-condensable gas.
5.4.2.5 Effect of Nanoparticles Concentration on Heat Pipe Thermal Behavior As in CCHP, the same nanofluids are used as working fluid besides water to investigate the effect of the working fluid type, with different nanoparticles concentration, on the heat pipe thermal behaviour. Figures 5-143 and 5-144 show the effect of nanoparticles concentration (NPC) on axial wall temperature distribution of the heat pipe for cases No. 45, 48, 51 and 54 for Al2O3 – water based nanofluid and cases No. 45, 57, 60 and 63 for CuO – water based nanofluid for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5mg. It can be noticed from these figures that the wall temperature decreases as the NPC increases. This is due to the decreasing of the velocities and the increasing of the thermal properties of the working fluid and thus decreases the operation temperature in the presence of more NPC. Although, increasing of NPC leads to increasing in the condenser inactive length and the operation temperature. Figure 5-145 shows the effect of nanoparticles concentration (NPC) on the heat pipe thermal resistance for cases No. 45, 48, 51 and 54 for Al2O3 and cases No. 45, 57, 60 and 63 for CuO – water based nanofluid. These figures show that the thermal resistance decreases as the NPC increases. This is due to the increasing of
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the thermal conductivity of the working fluid, and that is true even with the reverse effect of increasing the condenser inactive length in the presence of more NPC. As in CCHP, the experiments show that the nanoparticles concentration (NPC) also has significant effect on the VCHP thermal performance. Whereas, the reduction in thermal resistance of the heat pipe which is obtained in this study ranging from 0.441 to 9.88% for Al2O3 and 0.48 to 10.48% for CuO – water based nanofluid. Thus, figures 5-146 and 5-147 show the highest thermal resistance improvement obtained for Al2O3 and CuO – water based nanofluid respectively, at 26 oC as coolant temperature, 2784.86 W/m2 as input heat flux and 0.5mg as mass of non-condensible gas (air). As shown from the figures, the thermal resistance improvement for Al2O3 – water based nanofluid reaches up to 9.88%, while 10.48% for CuO – water based nanofluid at nanoparticles concentration of 5 Vol.%.
5.4.2.6 Comparison between Numerical Predictions and Experimental Results The axial temperature distribution along the heat pipe wall which is predicted by the present numerical model is compared with that measured from the experiments for some cases No. 1, 45, 54, 63, 64 and 127, where figures 5-148 to 5-153 show the comparison results. Figures 5-154 and 5-156 show the comparison results of the predicted heat pipe thermal resistance with that measured from the experiments for cases No. 2, 23 and 44 for water, 11, 32 and 53 for 5 Vol.% of Al2O3 – water based nanofluid and 20, 41 and 62 for 5 Vol.% of CuO – water based nanofluid respectively. It is clear from these figures that both experimental and numerical results have the same behavior and the maximum relative error is 4.5% for pure water and 19% for nanofluids respectively. As in CCHP, the high relative error value, when the nanofluids are used, is due to the same reason. 142
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Wall temperature (oC)
50 45
Q=100 W Present work
40
Q=100 W-Saad [39]
35 30 25 20 15 10 5 0 0
0.1
0.2
0.3
0.4
Heat pipe length (m)
Figure 5-1 Wall temperature distribution along heat pipe as compared with the results of Ref. [39].
0
0.05
Heat pipe length (m) 0.1 0.15
0.2
0.25
Liquid pressure drop (Pa)
0
-500
-1000 Q=10W - Mahjoub [18] Q=30W - Mahjoub [18]
-1500
Q=50W - Mahjoub [18] Q=10W-Present work Q=30W-Present work
-2000
Q=50W-Present work
-2500
Figure 5-2 Liquid pressure drop variation along the heat pipe for various heat transfer rates as compared with the results of Ref. [18]. 143
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50 Q=3W , NPC=0.01-Present work
45
Q=3W , NPC=0.03-Present work
Wall Temperature (oC)
40
Q=3W , NPC=0.01-Do et al [47]
35
Q=3W , NPC=0.03-Do et al [47]
30 25 20 15 10 5 0 0
0.05
0.1
0.15 0.2 Heat Pipe Length (m)
0.25
0.3
0.35
Figure 5-3 Heat pipe wall temperature distribution at various nanoparticles concentrations as compared with the results of Ref. [47]. 70
Wall Temperature (oC)
60 50 40 30 20 Q=100W Experimental results of Saad [39] Q=100W Numerical results of Saad [39]
10
Q=100W Present work
0 0
0.1
0.2
0.3
0.4
Heat Pipe Length (m)
Figure 5-4 Heat pipe wall temperature distribution for VCHP as compared with the results of Ref. [39]. 144
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Figure 5-5 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and coolant temperature of 18.3 oC.
Figure 5-6 Temperature distribution contour for the heat pipe, at input heat flux of 1670.91 W/m2 and coolant temperature of 18.3 oC.
Figure 5-7 Temperature distribution contour for the heat pipe, at input heat flux of 2784.86 W/m2 and coolant temperature of 18.3 oC. 145
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Figure 5-8 Temperature distribution contour for the heat pipe, at coolant temperature of 22 oC and input heat flux of 556.97 W/m2.
Figure 5-9 Temperature distribution contour for the heat pipe, at coolant temperature of 26 oC and input heat flux of 556.97 W/m2.
Figure 5-10 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and Al2O3 NPC of 1 Vol.%. 146
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Figure 5-11 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and Al2O3 NPC of 3 Vol.%.
Figure 5-12 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and Al2O3 NPC of 5 Vol.%.
Figure 5-13 Temperature distribution contour for the heat pipe at input heat flux of 556.97 W/m2 and CuO NPC of 1 Vol.%.
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Figure 5-14 Temperature distribution contour for the heat pipe at input heat flux of 556.97 W/m2 and CuO NPC of 3 Vol.%.
Figure 5-15 Temperature distribution contour for the heat pipe at input heat flux of 556.97 W/m2 and CuO NPC of 5 Vol.%.
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1.80E-01
Vapour Velocity (m/s)
1.60E-01
1.40E-01 1.20E-01 1.00E-01 8.00E-02 6.00E-02 q = 556.97 W/m2
4.00E-02
q = 1670.91 W/m2
2.00E-02
q = 2784.86 W/m2
0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-16 Vapour velocity variation of pure water at the heat pipe centerline for coolant temperature of 18.3 oC.
3.50E-05
Vapour Velocity (m/s)
3.00E-05 2.50E-05 2.00E-05 1.50E-05
q = 556.97 W/m2 q = 1670.91 W/m2
1.00E-05
q = 2784.86 W/m2
5.00E-06 0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-17 Vapour velocity variation at the heat pipe centerline for 3Vol. % of Al2O3 – water based nanofluid, at different input heat flux and coolant temperature of 22 oC. 149
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1.00E-05
Vapour Velocity (m/s)
9.00E-06 8.00E-06 7.00E-06 6.00E-06 5.00E-06 q = 556.97 W/m2
4.00E-06
q =1670.91 W/m2
3.00E-06
q =2784.86 W/m2
2.00E-06 1.00E-06 0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-18 Vapour velocity variation at the heat pipe centerline for 5Vol. % of CuO – water based nanofluid for different input heat flux and coolant temperature of 26 oC.
1.60E-01
Vapour Velocity (m/s)
1.40E-01
1.20E-01 1.00E-01 8.00E-02 6.00E-02 Ts = 18.3 oC
4.00E-02
Ts = 22 oC
2.00E-02
Ts = 26 oC
0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-19 Vapour velocity variation of pure water at the heat pipe centerline for different coolant temperature and input heat flux of 1670.91 W/m2. 150
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Vapour Velocity (m/s)
1.20E-01 water 1% Al2O3 1% CuO
1.00E-01 8.00E-02 6.00E-02 4.00E-02
2.00E-02 0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-20 Vapour velocity variation at the heat pipe centerline for input heat flux of 1670.91 W/m2 and coolant temperature of 22 oC.
7.00E-05
Vapour Velocity (m/s)
6.00E-05 5.00E-05
1% CuO 3% CuO
4.00E-05
5% CuO
3.00E-05 2.00E-05 1.00E-05 0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-21 Vapour velocity variation at the heat pipe centerline for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 151
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8.00E-02
Vapour Velocity (m/s)
6.00E-02 4.00E-02 2.00E-02 0.00E+00 q= 556.97 W/m2
-2.00E-02
q = 1670.91 W/m2
-4.00E-02
q = 2784.86 W/m2
-6.00E-02 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-22 Vapour velocity variation of pure water at the wick-vapour interface for coolant temperature of 18.3 oC.
8.00E-02
Vapour Velocity (m/s)
6.00E-02 4.00E-02 2.00E-02 0.00E+00 Ts = 18.3 oC
-2.00E-02
Ts = 22 oC
-4.00E-02
Ts = 26 oC
-6.00E-02 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-23 Vapour velocity variation of pure water at the wick-vapour interface for input heat flux of 1670.91 W/m2. 152
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Vapour Velocity (m/s)
6.00E-02
4.00E-02
2.00E-02
0.00E+00 water 1% Al2O3
-2.00E-02
1% CuO
-4.00E-02 0
0.1
0.2
0.3 0.4 Axial Distance (m)
0.5
0.6
Figure 5-24 Vapour velocity variation at the wick-vapour interface for input heat flux of 1670.91 W/m2 and coolant temperature of 22 oC.
3.00E-05 2.50E-05
Vapour Velocity (m/s)
2.00E-05 1.50E-05 1.00E-05 5.00E-06
0.00E+00 -5.00E-06
1% CuO
-1.00E-05
3% CuO
-1.50E-05
5% CuO
-2.00E-05 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-25 Vapour velocity variation at the wick-vapour interface for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 153
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.00E+00
Shear Rate (N/m2)
-1.00E-06 -2.00E-06 -3.00E-06 q = 556.97 W/m2
-4.00E-06
q = 1670.91 W/m2 q = 2784.86 W/m2
-5.00E-06 -6.00E-06 -7.00E-06 -8.00E-06
Figure 5-26 Shear rate variation of pure water at the wick-vapour interface for coolant temperature of 18.3 oC.
Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
0.00E+00 Ts = 18.3 oC
-1.00E-06 Shear Rate (N/m2)
Ts = 22 oC
-2.00E-06
Ts = 26 oC
-3.00E-06 -4.00E-06 -5.00E-06 -6.00E-06 -7.00E-06
Figure 5-27 Shear rate variation of pure water at the wick-vapour interface for input heat flux of 1670.91 W/m2. 154
Chapter Five
Results and Discussion Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
0.00E+00
Shear Rate (N/m2)
-1.00E-06
-2.00E-06
-3.00E-06 water 1% Al2O3 1% CuO
-4.00E-06
-5.00E-06
Figure 5-28 Shear rate variation at the wick-vapour interface for input heat flux of 1670.91 W/m2 and coolant temperature of 22 oC. Axial Distance (m)
0
0.1
0.2
0.3
0.4
0.5
0.6
Shear Rate (N/m2)
0.00E+00 -5.00E-10 -1.00E-09 1% CuO
-1.50E-09
3% CuO 5% CuO
-2.00E-09 -2.50E-09 -3.00E-09
Figure 5-29 Shear rate variation at the wick-vapour interface for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 155
Chapter Five
Results and Discussion
Axial Distance (m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.00E+00
Liquid Velocity (m/s)
-1.00E-03 -2.00E-03 -3.00E-03 -4.00E-03
q = 556.97 W/m2 q = 1670.91 W/m2
-5.00E-03
q = 2784.86 W/m2
-6.00E-03
Figure 5-30 Liquid velocity distribution along the wick structure for different input heat flux and coolant temperature of 18.3 oC.
0
0.1
Axial Distance (m) 0.2 0.3 0.4
0.5
0.6
0.00E+00
Liquid velocity (m/s)
-5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 Ts = 18.3 oC
-2.50E-03
Ts = 22 oC Ts = 26 oC
-3.00E-03
-3.50E-03 -4.00E-03
Figure 5-31 Liquid velocity distribution along the wick structure for different coolant temperature and input heat flux of 1670.91 W/m2. 156
Chapter Five
Results and Discussion Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
0.00E+00
Liquid Velocity (m/s)
-5.00E-04
water 1% Al2O3
-1.00E-03
1% CuO
-1.50E-03
-2.00E-03 -2.50E-03 -3.00E-03 -3.50E-03 -4.00E-03
Figure 5-32 Liquid velocity distribution along the wick structure for input heat flux of 1670.91 W/m2 and coolant temperature of 22 oC.
Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
0.00E+00 -5.00E-04 Liquid Velocity (m/s)
1% CuO
-1.00E-03 -1.50E-03
3% CuO 5% CuO
-2.00E-03 -2.50E-03 -3.00E-03 -3.50E-03 -4.00E-03 -4.50E-03 -5.00E-03
Figure 5-33 Liquid velocity distribution along the wick structure for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 157
Chapter Five
Results and Discussion Axial Distance (m)
0
0.1
0.2
0.3
0.4
0.5
0.6
Liquid Pressure Drop (Pa)
0.00E+00 -2.00E+02 -4.00E+02 -6.00E+02 q = 556.97 W/m2
-8.00E+02
q = 1670.91 W/m2
-1.00E+03
q = 2784.86 W/m2
-1.20E+03 -1.40E+03
Figure 5-34 Liquid pressure drop distribution along the wick structure for different input heat flux and coolant temperature of 18.3 oC.
Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
Liquid Pressure Drop (Pa)
0.00E+00 -1.00E+02 -2.00E+02 -3.00E+02 -4.00E+02 -5.00E+02 -6.00E+02
Ts = 18.3 oC
-7.00E+02
Ts = 22 oC
-8.00E+02
Ts = 26 oC
-9.00E+02 -1.00E+03
Figure 5-35 Liquid pressure drop distribution along the wick structure for different coolant temperature and input heat flux of 1670.91 W/m2. 158
Chapter Five
Results and Discussion Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
Liquid Pressure Drop (Pa)
0.00E+00 -1.00E+02 -2.00E+02 -3.00E+02 -4.00E+02
water
-5.00E+02
1% Al2O3
-6.00E+02
1% CuO
-7.00E+02 -8.00E+02 -9.00E+02
Figure 5-36 Liquid pressure drop distribution along the wick structure for input heat flux of 1670.91 W/m2 and coolant temperature of 22 oC.
Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
Liquid Pressure Drop (Pa)
0.00E+00 -2.00E+02 -4.00E+02 1% CuO
-6.00E+02
3% CuO 5% CuO
-8.00E+02 -1.00E+03 -1.20E+03
Figure 5-37 Liquid pressure drop distribution along the wick structure for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 159
Chapter Five
Results and Discussion
10000
Axial Heat Flux (W/m2)
9000 8000 7000 6000 5000 4000 3000
water
2000
1% Al2O3
1000
1%CuO
0 0
500
1000 1500 2000 Input Heat Flux (W/m2)
2500
3000
Figure 5-38 Axial heat conduction variation with the input heat flux for coolant temperature of 18.3 oC.
Axial Heat Flux/Input Heat Flux
3.1 Water
3.05
1% Al2O3
3
1% CuO
2.95 2.9 2.85 2.8 2.75 2.7 2.65 17
19
21
23
25
27
Sink Temperature (oC)
Figure 5-39 Axial to input heat flux ratio variation with the sink temperatre for input heat flux of 1670.91 W/m2. 160
Chapter Five
Results and Discussion
3.5
Axial heat flux/Input heat flux
3 2.5 2 1.5 1
Al2O3 Nanofluid CuO Nanofluid
0.5 0 0
1
2 3 Nanoparticles concentration %
4
5
Figure 5-40 Axial to input heat flux ratio variation with NPC for input heat flux of 1670.91 W/m2 and coolant temperature of 26 oC.
70
Qmax (W)
65 60 55 water 1% Al2O3
50
1%CuO
45
20
22
24 26 28 o Operating Temperature ( C)
30
32
Figure 5-41 Variation of the maximum heat transfer limit of the heat pipe with the operating temperature for coolant temperature of 18.3 oC. 161
Chapter Five
Results and Discussion
75
Qmax (W)
70
65
60 Water
55
1% Al2O3 1% CuO
50 17
19
21 23 Sink Temperature (oC)
25
27
Figure 5-42 Variation of the maximum heat transfer limit of the heat pipe with the sink temperature for input heat flux of 1670.91 W/m2.
120 110
Qmax (W)
100 90 80 Al2O3 Nanofluid
70
CuO Nanofluid
60 0
1
2
3
4
5
6
Nanoparticles concentration %
Figure 5-43 Variation of the maximum heat transfer limit of the heat pipe with NPC for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 162
Chapter Five
Results and Discussion
1740
water
1720
1% Al2O3 1%CuO
Pc (Pa)
1700
1680 1660 1640 1620 1600 20
22
24 26 28 Operating Temperature (oC)
30
32
Figure 5-44 Variation of capillary pressure of the wick structure with operating temperature for coolant temperature of 18.3 oC.
1700 Water
1690
1% Al2O3
1680
1% CuO
1670 Pc (Pa)
1660 1650 1640 1630 1620
1610 1600 17
19
21
23
25
27
Sink Temperature (oC)
Figure 5-45 Variation of the capillary pressure of the wick structure with sink temperature for input heat flux of 1670.91 W/m2. 163
Chapter Five
Results and Discussion
1900 1850 1800
Pc (Pa)
1750 1700 1650 1600 Al2O3 Nanofluid
1550
CuO nanofluid
1500 0
1
2
3
4
5
6
Nanoparticles concentration %
Figure 5-46 Capillary pressure of the wick structure for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC.
Rth ( oC/W)
1 0.9
water
0.8
1% Al2O3
0.7
1%CuO
0.6 0.5 0.4
0.3 0.2 0.1 0 5000
10000
15000 20000 Input Heat Flux (W/m2)
25000
Figure 5-47 Thermal resistance of the heat pipe for coolant temperature of 18.3 oC. 164
Chapter Five
Results and Discussion
Rth (oC/W)
1 0.9
Water
0.8
1% Al2O3
0.7
1% CuO
0.6 0.5 0.4 0.3 0.2 0.1 0 17
19
21
23
25
27
Sink Temperature (oC)
Figure 5-48 Thermal resistance of the heat pipe for input heat flux of 1670.91 W/m2.
1 0.9 0.8
Al2O3 Nanofluid
Rth (oC/W)
0.7
CuO Nanofluid
0.6
0.5 0.4 0.3
0.2 0.1 0 0
1
2 3 4 Nanoparticles concentration %
5
6
Figure 5-49 Thermal resistance of the heat pipe for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 165
Chapter Five
Results and Discussion
35
Improvement %
30 25 20 1% Al2O3
15
3% Al2O3
10
5% Al2O3
5 0 0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-50 Improvement of the heat pipe thermal resistance with input heat flux for Al2O3 – water based nanofluid, at coolant temperature of 26 oC. 40
35 1% CuO
Improvement %
30
3% CuO
25
5% CuO
20 15 10 5 0 0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-51 Improvement of the heat pipe thermal resistance with input heat flux for CuO – water based nanofluid, at coolant temperature of 26 oC. 166
Chapter Five
Results and Discussion
Figure 5-52 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2, coolant temperature of 18.3 oC and air mass of 0.5 mg.
Figure 5-53 Temperature distribution contour for the heat pipe, at input heat flux of 1670.91 W/m2, coolant temperature of 18.3 oC and air mass of 0.5 mg.
Figure 5- 54 Temperature distribution contour for the heat pipe, at input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and air mass of 0.5 mg. 167
Chapter Five
Results and Discussion
Figure 5- 55 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2, coolant temperature of 22 oC and air mass of 0.5 mg.
Figure 5-56 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2, coolant temperature of 26 oC and air mass of 0.5 mg.
Figure 5-57 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and Al2O3 NPC of 1 Vol.%.
168
Chapter Five
Results and Discussion
Figure 5-58 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and Al2O3 NPC of 3 Vol.%.
Figure 5-59 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and Al2O3 NPC of 5 Vol.%.
Figure 5-60 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and CuO NPC of 1 Vol.%.
169
Chapter Five
Results and Discussion
Figure 5-61 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and CuO NPC of 3 Vol.%.
Figure 5-62 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2 and CuO NPC of 5 Vol.%.
Figure 5-63 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2, Al2O3 NPC of 3 Vol.%, coolant temperature of 26 oC and air mass of 0.5 mg.
170
Chapter Five
Results and Discussion
Figure 5-64 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2, Al2O3 NPC of 3 Vol.%, coolant temperature of 26 oC and air mass of 1.1 mg.
Figure 5-65 Temperature distribution contour for the heat pipe, at input heat flux of 556.97 W/m2, Al2O3 NPC of 3 Vol.%, coolant temperature of 26 oC and air mass of 1.5 mg.
171
Chapter Five
Results and Discussion
1.20E-01
Vapour Velocity (m/s)
1.00E-01 8.00E-02 6.00E-02 4.00E-02 q = 556.97 W/m2
2.00E-02
q = 1670.91 W/m2 q = 2784.86 W/m2
0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-66 Vapour velocity variation at the heat pipe centerline for pure water, coolant temperature of 18.3 oC and air mass of 0.5 mg. 8.00E-02
Vapour velocity (m/s)
7.00E-02 6.00E-02 5.00E-02 4.00E-02 3.00E-02 Ts = 18.3 oC
2.00E-02
Ts = 22 oC
1.00E-02
Ts = 26 oC
0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-67 Vapour velocity variation at the heat pipe centerline for pure water, input heat flux of 1670.91 W/m2 and air mass of 0.5 mg. 172
Chapter Five
Results and Discussion
Vapour Velocity (m/s)
6.00E-02
water 1% Al2O3 1% CuO
4.00E-02
2.00E-02
0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-68 Vapour velocity variation at the heat pipe centerline for input heat flux of 1670.91 W/m2, coolant temperature of 22 oC and air mass of 0.5 mg. 7.00E-05
Vapour velocity (m/s)
6.00E-05 5.00E-05 1% CuO
4.00E-05
3% CuO
5% CuO
3.00E-05 2.00E-05 1.00E-05 0.00E+00 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-69 Vapour velocity variation at the heat pipe centerline for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and mass of air of 0.5mg. 173
Chapter Five
Results and Discussion
1.00E-01
Vapour Velocity (m/s)
9.00E-02 8.00E-02 7.00E-02 6.00E-02 5.00E-02 4.00E-02 Mncg = 0.5mg
3.00E-02
Mncg = 1.1mg
2.00E-02
Mncg = 1.5mg
1.00E-02 0.00E+00 0
0.1
0.2
0.3 0.4 Axial Distance (m)
0.5
0.6
Figure 5-70 Vapour velocity variation at the heat pipe centerline for pure water, input heat flux of 1670.91 W/m2 and coolant temperature of 22 oC.
1.00E-01
Vapour Velocity (m/s)
8.00E-02 6.00E-02 4.00E-02 2.00E-02 0.00E+00 q = 556.97 W/m2
-2.00E-02
q = 1670.91 W/m2 q = 2784.86 W/m2
-4.00E-02 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-71 Vapour velocity variation at the wick-vapour interface for pure water, coolant temperature of 18.3 oC and air mass of 0.5 mg.
174
Chapter Five
Results and Discussion
8.00E-02
Vapour Velocity (m/s)
6.00E-02 4.00E-02 2.00E-02 0.00E+00 Ts = 18.3 oC
-2.00E-02
Ts = 22 oC Ts = 26 oC
-4.00E-02 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-72 Vapour velocity variation at the wick-vapour interface for pure water, input heat flux of 1670.91 W/m2 and air mass of 0.5 mg. 8.00E-02
Vapour Velocity (m/s)
6.00E-02 4.00E-02 2.00E-02 0.00E+00 water
-2.00E-02
1% Al2O3 1% CuO
-4.00E-02
0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-73 Vapour velocity variation at the wick-vapour interface for input heat flux of 1670.91 W/m2, coolant temperature of 22 oC and air mass of 0.5 mg. 175
Chapter Five
Results and Discussion
5.00E-05
Vapour velocity (m/s)
4.00E-05 3.00E-05 2.00E-05 1.00E-05 0.00E+00 1% CuO
-1.00E-05
3% CuO 5% CuO
-2.00E-05 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-74 Vapour velocity variation at the wick-vapour interface for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5 mg. 3.50E-05 3.00E-05
Vapour Velocity (m/s)
2.50E-05 2.00E-05 1.50E-05
Mncg = 0.5mg
1.00E-05
Mncg = 1.1mg Mncg = 1.5mg
5.00E-06 0.00E+00 -5.00E-06 -1.00E-05 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-75 Vapour velocity variation at the wick-vapour interface for input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and CuO NPC of 3Vol. %. 176
Chapter Five
Results and Discussion
Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
1.00E-03
Liquid Velocity (m/s)
0.00E+00 -1.00E-03
-2.00E-03 -3.00E-03 q = 556.97 W/m2
-4.00E-03
q = 1670.91 W/m2 -5.00E-03
q = 2784.86 W/m2
-6.00E-03
Figure 5-76 Distribution of the liquid velocity along the wick structure for different input heat flux, coolant temperature of 18.3 oC and air mass of 0.5 mg.
0
0.1
Axial Distance (m) 0.2 0.3
0.4
0.5
0.6
5.00E-04
Liquid velocity (m/s)
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03
Ts = 18.3 oC
-2.50E-03
Ts = 26 oC Ts = 22 oC
-3.00E-03 -3.50E-03 -4.00E-03
Figure 5-77 Distribution of the liquid velocity along the wick structure for different coolant temperature, input heat flux of 1670.91 W/m2 and air mass of 0.5 mg.
177
Chapter Five
Results and Discussion Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
5.00E-04
Liquid Velocity (m/s)
0.00E+00 water
-5.00E-04
1% Al2O3
-1.00E-03
1% CuO
-1.50E-03 -2.00E-03 -2.50E-03 -3.00E-03 -3.50E-03
Figure 5-78 Distribution of the liquid velocity at the midpoint along the wick structure for input heat flux of 1670.91 W/m2, coolant temperature of 22 oC and air mass of 0.5 mg. Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
5.00E-04
Liquid Velocity (m/s)
0.00E+00 -5.00E-04
1% CuO
-1.00E-03
3% CuO
-1.50E-03
5% CuO
-2.00E-03 -2.50E-03 -3.00E-03
-3.50E-03 -4.00E-03 -4.50E-03 -5.00E-03
Figure 5-79 Distribution of the liquid velocity at the midpoint along the wick structure for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5 mg. 178
Chapter Five
Results and Discussion Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
5.00E-04
Liquid Velocity (m/s)
0.00E+00 -5.00E-04 Mncg = 0.5mg
-1.00E-03
Mncg = 1.1mg
-1.50E-03
Mncg = 1.5mg
-2.00E-03 -2.50E-03 -3.00E-03 -3.50E-03 -4.00E-03
Figure 5-80 Distribution of the liquid velocity at the midpoint along the wick structure for input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and CuO NPC of 3Vol. %.
Axial Distance (m)
0
0.1
0.2
0.3
0.4
0.5
0.6
Liquid Pressure Drop (Pa)
0.00E+00 -2.00E+02 -4.00E+02 -6.00E+02 -8.00E+02
q = 556.97 W/m2 q = 1670.91 W/m2
-1.00E+03
q = 2784.86 W/m2
-1.20E+03
Figure 5-81 Distribution of the liquid pressure drop at the midpoint along the wick structure for different input heat flux, coolant temperature of 18.3 oC and air mass of 0.5 mg. 179
Chapter Five
Results and Discussion Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
Liquid Pressure Drop (Pa)
0.00E+00 -1.00E+02 -2.00E+02 -3.00E+02 -4.00E+02 Ts = 18.3 oC
-5.00E+02
Ts = 22 oC
-6.00E+02
Ts = 26 oC
-7.00E+02
Figure 5-82 Distribution of the liquid pressure drop at the midpoint along the wick structure for different coolant temperature, input heat flux of 1670.91 W/m2 and air mass of 0.5 mg. Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
0.00E+00 Liquid Pressure Drop (Pa)
-1.00E+02 -2.00E+02 -3.00E+02 -4.00E+02 -5.00E+02 -6.00E+02
water
-7.00E+02
1% Al2O3
-8.00E+02
1% CuO
-9.00E+02
Figure 5-83 Distribution of the liquid pressure drop at the midpoint along the wick structure for input heat flux of 1670.91 W/m2, coolant temperature of 22 oC and air mass of 0.5 mg. 180
Chapter Five
Results and Discussion Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
Liquid Pressure Drop (Pa)
0.00E+00 -1.00E+02 -2.00E+02 -3.00E+02 -4.00E+02 -5.00E+02 -6.00E+02 1% CuO
-7.00E+02
3% CuO
-8.00E+02
5% CuO
-9.00E+02
Figure 5-84 Distribution of the liquid pressure drop at the midpoint along the wick structure for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5 mg. Axial Distance (m) 0
0.1
0.2
0.3
0.4
0.5
0.6
0.00E+00
Liquid Pressure Drop (Pa)
-1.00E+02 -2.00E+02
-3.00E+02 -4.00E+02 -5.00E+02 Mncg = 0.5mg
-6.00E+02
Mncg = 1.1mg
-7.00E+02
Mncg = 1.5mg
-8.00E+02
Figure 5-85 Distribution of the liquid pressure drop at the midpoint along the wick structure for input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and CuO NPC of 3Vol. %. 181
Chapter Five
Results and Discussion
Axial Heat Flux (W/m2)
20000
15000 water 1% Al2O3 1%CuO
10000 0
500
1000 1500 2000 Input Heat Flux (W/m2)
2500
3000
Figure 5-86 Variation of the axial heat conduction with the input heat flux for coolant temperature of 18.3 oC and air mass of 1.1 mg.
Axial Heat Flux/Input Heat Flux
9.5 9 8.5 8 7.5 7 6.5
Water
6
1% Al2O3 1% CuO
5.5 5 17
19
21
23
25
27
Sink Temperature (oC)
Figure 5-87 Axial to input heat ratio variation with the sink temperature for input heat flux of 1670.91 W/m2 and air mass of 1.1 mg.
182
Chapter Five
Results and Discussion
4.74 Axial heat flux/Input heat flux
4.73 4.72 4.71 4.7 4.69 4.68 4.67
Al2O3 Nanofluid
4.66
CuO Nanofluid
4.65 0
1
2
3
4
5
6
Nanoparticles concentration %
Figure 5-88 Axial to input heat ratio variation with NPC for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5 mg. 8
Axial heat flux/Input heat flux
7.5 7 6.5 6 5.5 5 4.5 Al2O3 Nanofluid
4
CuO Nanofluid
3.5 3 0.25
0.75 1.25 Mass of non-condensable gas (mg)
1.75
Figure 5-89 Axial to input heat ratio variation with Mncg for input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and NPC of 3 Vol.%. 183
Chapter Five
Results and Discussion
100
Qmax (W)
95 90 85 80 water
75
1% Al2O3 1%CuO
70 38
40
42 44 46 o Active Length Temperature ( C)
48
Figure 5-90 Variation of the maximum heat transfer limit of the heat pipe with the active length temperature for coolant temperature of 18.3 oC and air mass of 1.1 mg. 100 95 90 Qmax (W)
85 80 75 Water
70
1% Al2O3
65
1% CuO
60 17
19
21
23
25
27
Sink Temperature (oC)
Figure 5-91 Variation of the maximum heat transfer limit of the heat pipe with the sink temperature for input heat flux of 1670.91 W/m2 and air mass of 1.1 mg.
184
Chapter Five
Results and Discussion
170 160 150
Qmax (W)
140 130
120 110 100 Al2O3 Nanofluid
90
CuO Nanofluid
80 70 0
1
2
3
4
5
6
Nanoparticles concentration %
Figure 5-92 Variation of the maximum heat transfer limit of the heat pipe with NPC for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 1.1 mg. 140 130
Qmax (W)
120 110 100
90 Al2O3 Nanofluid
80
CuO Nanofluid
70 0
0.5
1 1.5 Mass of non-condensable gas (mg)
2
Figure 5-93 Variation of the maximum heat transfer limit of the heat pipe with Mncg for input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and NPC of 3 Vol.%. 185
Chapter Five
Results and Discussion
1590 water
1585
1% Al2O3
Pc (Pa)
1580
1%CuO
1575 1570 1565 1560 1555 38
40
42 44 46 Active Length Temperature (oC)
48
Figure 5-94 Variation of the maximum capillary pressure of the wick structure with the active length temperature for coolant temperature of 18.3 oC and air mass of 1.1 mg. 1576 Water
1574
1% Al2O3
1572
1% CuO
Pc (Pa)
1570 1568 1566 1564 1562 1560 1558 17
19
21
23
25
27
Sink Temperature (oC)
Figure 5-95 Variation of the maximum capillary pressure of the wick structure with the sink temperature for input heat flux of 1670.91 W/m2 and air mass of 1.1 mg.
186
Chapter Five
Results and Discussion
1565 1560
Pc (Pa)
1555 1550 Al2O3 Nanofluid
1545
CuO Nanofluid
1540 0
1
2
3
4
5
6
Nanoparticles concentration %
Figure 5-96 Variation of the maximum capillary pressure of the wick structure with NPC for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 1.1 mg. 1610 Al2O3 Nanofluid
1600
CuO Nanofluid
Pc(Pa)
1590 1580 1570 1560
1550 0
0.5
1
1.5
2
Mass of non-condensable gas (mg)
Figure 5-97 Variation of the maximum capillary pressure of the wick structure with Mncg for input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and CuO NPC of 3 Vol.%. 187
Chapter Five
Results and Discussion
5.4 water
4.9
1% Al2O3
Rth ( oC/W)
4.4
1%CuO
3.9 3.4 2.9 2.4 1.9 1.4 0
500
1000
1500
2000
2500
3000
Input heat flux (W/m2)
Figure 5-98 Variation of the thermal resistance of the heat pipe with the input heat flux for coolant temperature of 18.3 oC and air mass of 1.1 mg. 2.15 Water 1% Al2O3
2.1
Rth (oC/W)
1% CuO
2.05
2
1.95
1.9
17
19
21
23
25
27
Sink Temperature (oC)
Figure 5-99 Variation of the thermal resistance of the heat pipe with the sink temperature for input heat flux of 1670.91 W/m2 and air mass of 1.1 mg. 188
Chapter Five
Results and Discussion
1.39 1.38
Al2O3 Nanofluid
1.37
CuO Nanofluid
Rth (oC/W)
1.36 1.35 1.34 1.33 1.32 1.31 1.3 0
1
2
3
4
5
6
Nanoparticles concentration %
Figure 5-100 Variation of the thermal resistance of the heat pipe with NPC for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 1.1 mg. 1.8 1.7 1.6 Rth (oC/W)
1.5 1.4 1.3 1.2
Al2O3 Nanofluid CuO Nanofluid
1.1 1 0
0.5
1
1.5
2
Mass of non-condensable gas (mg)
Figure 5-101 Variation of the thermal resistance of the heat pipe with Mncg for input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and NPC of 3 Vol.%. 189
Chapter Five
Results and Discussion
0.045 0.04
0.035 Lca (m)
0.03 0.025 0.02 water
0.015
1% Al2O3
0.01
1%CuO
0.005 0 0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-102 Condenser active length variation with the input heat flux for coolant temperature of 18.3 oC and air mass of 1.1 mg. 0.03
Lca (m)
0.025
0.02
0.015 Water 1% Al2O3
0.01
1% CuO
0.005
17
19
21
23
25
27
Sink temperature (oC)
Figure 5-103 Condenser active length variation with the sink temperature for input heat flux of 1670.91 W/m2 and air mass of 1.1 mg. 190
Chapter Five
Results and Discussion
0.05 Al2O3 Nanofluid
0.045
CuO Nanofluid
Lca (m)
0.04 0.035 0.03 0.025 0.02 0
1
2
3
4
5
6
Nanoparticles concentration %
Figure 5-104 Condenser active length variation with NPC for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 1.1 mg. 0.045 Al2O3 Nanofluid
0.04
CuO Nanofluid
Lca (m)
0.035 0.03 0.025 0.02 0.015 0
0.5
1
1.5
2
Mass of non-condensable gas (mg)
Figure 5-105 Condenser active length variation with Mncg for input heat flux of 2784.86 W/m2, coolant temperature of 18.3 oC and NPC of 3 Vol.%. 191
Chapter Five
Results and Discussion
4.5 4
Improvement %
3.5 3 2.5 1% Al2O3
2
3% Al2O3
1.5
5% Al2O3
1 0.5 0
0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-106 Improvement of the heat pipe thermal resistance with input heat flux for for Al2O3 – water based nanofluid, coolant temperature of 26 oC and air mass of 0.5 mg. 4.5 4 Improvement %
3.5 3 2.5 2 1.5 1% CuO
1
3% CuO
0.5
5% CuO
0 0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-107 Improvement of the heat pipe thermal resistance with input heat flux for for CuO – water based nanofluid, coolant temperature of 26 oC and air mass of 0.5 mg. 192
Chapter Five
Results and Discussion
40 FR = 75%
FR = 100%
FR = 125%
FR = 150%
FR = 175%
FR = 200%
FR = 225%
FR = 240%
0.2
0.3
Wall temperature ( oC)
35 30 25 20 15 0
0.1
0.4
0.5
0.6
Axial distance (m)
Figure 5-108 Effect of filling ratio on the heat pipe wall temperature distribution for input heat flux of 556.97 W/m2 and the coolant temperature of 18.3 oC.
60 55
FR = 75%
FR = 100%
FR = 125%
FR = 150%
FR = 175%
FR = 200%
FR = 225%
FR = 240%
Wall temperature ( C)
50 45 40 35 30 25
20 15 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-109 Effect of filling ratio on the heat pipe wall temperature distribution for input heat flux of 1113.94 W/m2 and the coolant temperature of 18.3 oC. 193
Chapter Five
Results and Discussion
85
Wall temperature ( C)
75
FR = 75%
FR = 100%
FR = 125%
FR = 150%
FR = 175%
FR = 200%
FR = 225%
FR = 240%
0.3
0.4
65 55 45 35 25 15 0
0.1
0.2
0.5
0.6
Axial distance (m)
Figure 5-110 Effect of filling ratio on the heat pipe wall temperature distribution for input heat flux of 1670.91 W/m2 and the coolant temperature of 18.3 oC.
5 Rth-556.97 W/m2
4
Rth-1113.94 W/m2
Rth (oC/W)
Rth-1670.91 W/m2
3
2
1
0 50%
100%
150%
200%
250%
300%
Filling ratio
Figure 5-111 Effect of filling ratio on the heat pipe thermal resistance at coolant temperature of 18.3 oC. 194
Chapter Five
Results and Discussion 50
45 Wall temperature (oC)
40 35 30 25 20 15
q = 556.97 W/m2
10
q = 1670.91 W/m2
5
q = 2784.86 W/m2
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-112 Effect of input heat flux on the heat pipe wall temperature distribution for pure water and the coolant temperature of 18.3 oC.
35
Wall temperature (oC)
30 25
20 15 10
q = 556.97 W/m2 q = 1670.91 W/m2
5
q = 2784.86 W/m2
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-113 Effect of input heat flux on the heat pipe wall temperature distribution for 5 Vol.% of Al2O3 – water based nanofluid and the coolant temperature of 18.3 oC. 195
Chapter Five
Results and Discussion 1
0.9
Water
0.8
Al2O3 Nanofluid
Rth (oC/W)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
500
1000
1500
2000
2500
3000
Heat flux (W/m2)
Figure 5-114 Effect of input heat flux on the heat pipe thermal resistance for pure water and 5 Vol.% of Al2O3 – water based nanofluid for coolant temperature of 18.3 oC.
50 45 Wall temperature (oC)
40 35 30 25 20 15
Ts = 18.3 ( oC)
10
Ts = 22 ( oC)
5
Ts = 26 ( oC)
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-115 Effect of sink Temperature on the heat pipe wall temperature distribution for pure water and input heat flux of 2784.86 W/m2. 196
Chapter Five
Results and Discussion 50
45 Wall temperature (oC)
40 35 30 25 20 15
Ts = 18.3 ( oC)
10
Ts = 22 ( oC) Ts = 26 ( oC)
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-116 Effect of sink Temperature on the heat pipe wall temperature distribution for 5 Vol.% of Al2O3 – water based nanofluid and input heat flux of 2784.86 W/m2. 1 0.9
Water
0.8
Al2O3 Nanofluid
Rth (oC/W)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 17
19
21
23
25
27
Sink temperature (oC)
Figure 5-117 Effect of sink Temperature on the heat pipe thermal resistance for pure water and 5 Vol.% of Al2O3 – water based nanofluid for input heat flux of 2784.86 W/m2. 197
Chapter Five
Results and Discussion 45
Wall temperature (oC)
40 35 30 NPC = 0%
25
NPC = 1% NPC = 3%
20
NPC = 5%
15 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-118 Effect of Al2O3 NPC on the heat pipe wall temperature distribution for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC.
45 NPC = 0% NPC = 1%
Wall temperature (oC)
40
NPC = 3%
35
NPC = 5%
30 25
20 15 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-119 Effect of CuO NPC on the heat pipe wall temperature distribution for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 198
Chapter Five
Results and Discussion 0.5 Al2O3 Nanofluid
0.45
CuO Nanofluid
Rth (oC/W)
0.4 0.35 0.3 0.25 0.2 0
0.01
0.02
0.03
0.04
0.05
0.06
NPC
Figure 5-120 Effect of NPC on the heat pipe thermal resistance for input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC.
Improvement %
100 90
1% Al2O3
80
3% Al2O3 5% Al2O3
70 60 50 40 30
20 10 0 0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-121 Improvement of the heat pipe thermal resistance with input heat flux for coolant temperature of 26 oC. 199
Chapter Five
Results and Discussion
100 1% CuO
90
3% CuO
Improvement %
80
5% CuO
70 60 50 40 30 20 10 0 0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-122 Improvement of the heat pipe thermal resistance with input heat flux for coolant temperature of 26 oC.
25
Wall temperature (oC)
20
15
10
Experimental results
5
Numerical prediction
0 0
0.1
0.2
0.3 0.4 Axial distance (m)
0.5
0.6
Figure 5-123 Comparison of predicted and experimental wall temperature for water, input heat flux of 556.97 W/m2 and coolant temperature of 18.3 oC. 200
Chapter Five
Results and Discussion
35
Wall temperature (oC)
30 25 20 15 10 Experimental results Numerical prediction
5 0 0
0.1
0.2 0.3 Axial distance (m)
0.4
0.5
0.6
Figure 5-124 Comparison of predicted and experimental wall temperature for water, input heat flux of 556.97 W/m2 and coolant temperature of 26 oC. 50 45 Wall temperature (oC)
40 35 30 25 20 15 Experimental results
10
Numerical prediction
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-125 Comparison of predicted and experimental wall temperature for water, input heat flux of 2784.86 W/m2 and coolant temperature of 26 oC. 201
Chapter Five
Results and Discussion
45 40 Wall temperature (oC)
35 30
25 20 15 10
Experimental results
5
Numerical prediction
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-126 Comparison of predicted and experimental wall temperature for Al2O3 – water based nanofluid, input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and NPC of 1Vol. %. 45 40 Wall temperature (oC)
35 30 25 20 15 Experimental results
10
Numerical prediction
5 0 0
0.1
0.2 0.3 Axial distance (m)
0.4
0.5
0.6
Figure 5-127 Comparison of predicted and experimental wall temperature for Al2O3 – water based nanofluid , input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and NPC of 5Vol. %. 202
Chapter Five
Results and Discussion
40 35
Wall temperature (oC)
30 25 20 15 10 Experimental results
5
Numerical prediction
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-128 Comparison of predicted and experimental wall temperature for CuO – water based nanofluid – nanofluid , input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and NPC of 5Vol. %.
0.6 0.5
Rth
(oC/W)
0.4 0.3 0.2 Numerical Prediction
0.1
Experimental results
0 0
500
1000
1500
2000
2500
3000
Heat flux (W/m2)
Figure 5-129 Comparison of predicted and experimental thermal resistance for water for coolant temperature of 22 oC. 203
Chapter Five
Results and Discussion 0.4
0.35
Rth (oC/W)
0.3 0.25 0.2
0.15 0.1 Numerical Prediction
0.05
Experimental results
0 0
500
1000
1500
2000
2500
3000
Heat flux (W/m2)
Figure 5-130 Comparison of predicted and experimental thermal resistance for 5Vol. % of Al2O3 – water based nanofluid for coolant temperature of 22 oC.
0.4 0.35
Rth (oC/W)
0.3 0.25 0.2 0.15 0.1 Numerical Prediction
0.05
Experimental results
0 0
500
1000
1500
2000
2500
3000
Heat flux (W/m2)
Figure 5-131 Comparison of predicted and experimental thermal resistance for 5Vol. % of CuO – water based nanofluid for coolant temperature of 22 oC. 204
Chapter Five
Results and Discussion
105
FR = 75% FR = 175% FR = 250%
95
FR = 100% FR = 200% FR = 275%
FR = 125% FR = 225%
FR = 150% FR = 240%
Wall temperature (oC)
85 75 65 55 45
35 25 15 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Rth (oC/W)
Figure 5-132 Effect of filling ratio on heat pipe wall temperature distribution for input heat flux of 556.97 W/m2, coolant temperature of 18.3 oC and air mass of 1.1mg. 16 15 14 13 12 11 10 9 8 7 6 5 4 3 50%
100%
150%
200%
250%
300%
Filling ratio
Figure 5-133 Effect of filling ratio on heat pipe thermal resistance for coolant temperature of 18.3 oC and air mass of 1.1mg. 205
Chapter Five
Results and Discussion 70 q = 556.97 W/m2
Wall temperature (oC)
60
q = 1670.9 W/m2 q = 2784.86 W/m2
50 40 30 20 10 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-134 Effect of input heat flux on heat pipe wall temperature distribution for pure water, coolant temperature of 18.3 oC and air mass of 1.5 mg.
60 q = 556.97 W/m2
Wall temperature (oC)
50
q = 1670.9 W/m2 q = 2784.86 W/m2
40 30 20 10 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-135 Effect of input heat flux on heat pipe wall temperature distribution for 3 Vol.% CuO – water based nanofluid, coolant temperature of 18.3 oC and air mass of 1.5 mg. 206
Chapter Five
Results and Discussion 6
5.5
Water
5
CuO nanofluid
Rth (oC/W)
4.5 4 3.5 3 2.5 2 1.5 0
500
1000
1500
2000
2500
3000
Heat flux (W/m2)
Figure 5-136 Effect of input heat flux on heat pipe thermal resistance for pure water and 3 Vol.% CuO – water based nanofluid for coolant temperature of 18.3 oC and air mass of 1.5 mg.
70 Ts = 18.3 ( oC)
Wall temperature (oC)
60
Ts = 22 ( oC) Ts = 26 ( oC)
50 40 30 20 10 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-137 Effect of sink temperature on heat pipe wall temperature distribution for pure water, input heat flux of 2784.86 W/m2 and air mass of 1.5 mg. 207
Chapter Five
Results and Discussion 70 Ts = 18.3 ( oC)
Wall temperature (oC)
60
Ts = 22 ( oC) Ts = 26 ( oC)
50 40 30 20 10 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-138 Effect of sink temperature on heat pipe wall temperature distribution for 3 Vol.% of CuO – water based nanofluid, input heat flux of 2784.86 W/m2 and air mass of 1.5 mg. 1.8 1.7
Rth (oC/W)
1.6 1.5 1.4 Water
1.3
CuO nanofluid
1.2 17
19
21
23
25
27
Sink temperature (oC)
Figure 5-139 Effect of sink Temperature on heat pipe thermal resistance for pure water and 3 Vol.% of CuO – water based nanofluid for input heat flux of 2784.86 W/m2 and air mass of 1.5 mg. 208
Chapter Five
Results and Discussion 75 Mncg = 0.5 mg
Wall temperature (oC)
65
Mncg = 1.1 mg ’Mncg = 1.5 mg
55 45 35 25 15 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-140 Effect of mass of non-condensable gas on heat pipe wall temperature distribution for pure water, input heat flux of 2784.86 W/m2 and coolant temperature of 22 oC.
Wall temperature (oC)
65 60
Mncg = 0.5 mg
55
Mncg = 1.1 mg
50
’Mncg = 1.5 mg
45 40 35 30 25 20 15 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-141 Effect of mass of non-condensable gas on heat pipe wall temperature distribution for 1 Vol.% CuO – water based nanofluid, input heat flux of 2784.86 W/m2 and coolant temperature of 22 oC. 209
Chapter Five
Results and Discussion 1.7
Rth (oC/W)
1.5 1.3 1.1 Water
0.9
CuO nanofluid
0.7 0
0.5
1
1.5
2
Mncg (mg)
Figure 5-142 Effect of mass of non-condensable gas on heat pipe thermal resistance for pure water and 1 Vol.% CuO – water based nanofluid for input heat flux of 2784.86 W/m2 and coolant temperature of 22 oC. 60 NPC = 0%
Wall temperature (oC)
55
NPC = 1%
50
NPC = 3%
45
NPC = 5%
40 35 30 25 20 15 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-143 Effect of nanoparticles concentration (NPC) on heat pipe wall temperature distribution for Al2O3 – water based nanofluid, input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5mg. 210
Chapter Five
Results and Discussion 60 NPC = 0%
Wall temperature (oC)
55
NPC = 1%
50
NPC = 3%
45
NPC = 5%
40 35 30 25 20 15 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial distance (m)
Figure 5-144 Effect of nanoparticles concentration (NPC) on heat pipe wall temperature distribution for CuO – water based nanofluid, input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5mg. 1.02 1
Al2O3 Nanofluid CuO Nanofluid
Rth (oC/W)
0.98 0.96
0.94 0.92 0.9 0.88 0
0.01
0.02
0.03
0.04
0.05
0.06
NPC
Figure 5-145 Effect of nanoparticles concentration (NPC) on heat pipe thermal resistance for Al2O3 and CuO – water based nanofluid for input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5mg. 211
Chapter Five
Results and Discussion
12
Improvement %
10 8 6 4 1% Al2O3
2
3% Al2O3 5% Al2O3
0 0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-146 Improvement of heat pipe thermal resistance with input heat flux for Al2O3 – water based nanofluid, coolant temperature of 26 oC and air mass of 0.5 mg.
12
Improvement %
10 8 6 4 1% CuO
3% CuO
2
5% CuO
0 0
500
1000 1500 2000 Input heat flux (W/m2)
2500
3000
Figure 5-147 Improvement of heat pipe thermal resistance with input heat flux for CuO – water based nanofluid, coolant temperature of 26 oC and air mass of 0.5 mg. 212
Chapter Five
Results and Discussion
40
Wall Temperature (oC)
35 30 25 20 15 Experimental results
10
Numerical prediction
5 0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-148 Comparison of predicted and experimental wall temperature for water, input heat flux of 556.97 W/m2, coolant temperature of 18.3 oC and air mass of 0.5 mg. 60
Wall Temperature (oC)
50 40 30 20 Experimental results
10
Numerical prediction
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-149 Comparison of predicted and experimental wall temperature for water, input heat flux of 2784.86 W/m2, coolant temperature of 26 oC and air mass of 0.5 mg. 213
Chapter Five
Results and Discussion
60
Wall Temperature (oC)
50 40 30 20 10
Experimental results Numerical prediction
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-150 Comparison of predicted and experimental wall temperature for Al2O3 – water based nanofluid, input heat flux of 2784.86 W/m2, coolant temperature of 26 oC, NPC of 5Vol. % and air mass of 0.5 mg. 60
Wall Temperature
(oC)
50 40 30 20 Experimental results
10
Numerical prediction
0 0
0.1
0.2
0.3 0.4 Axial Distance (m)
0.5
0.6
Figure 5-151 Comparison of predicted and experimental wall temperature for CuO – water based nanofluid, input heat flux of 2784.86 W/m2, coolant temperature of 26 oC, NPC of 5Vol. % and air mass of 0.5 mg. 214
Chapter Five
Results and Discussion
50 45
Wall Temperature (oC)
40 35 30 25
20 15 10
Experimental results
5
Numerical prediction
0 0
0.1
0.2 0.3 Axial Distance (m)
0.4
0.5
0.6
Figure 5-152 Comparison of predicted and experimental wall temperature for water, input heat flux of 556.97 W/m2, coolant temperature of 18.3 oC and air mass of 1.1 mg. 50 45 Wall Temperature (oC)
40 35 30 25 20 15 10
Experimental results
5
Numerical prediction
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Axial Distance (m)
Figure 5-153 Comparison of predicted and experimental wall temperature for water, input heat flux of 556.97 W/m2, coolant temperature of 18.3 oC and air mass of 1.5 mg. 215
Chapter Five
Results and Discussion
3 Numerical Prediction
Rth (oC/W)
2.5
Experimental results
2 1.5 1 0.5 0 0
500
1000
1500
2000
2500
3000
Heat flux (W/m2)
Figure 5-154 Comparison of predicted and experimental thermal resistance for pure water for coolant temperature of 22 oC and air mass of 0.5mg.
3 Numerical Prediction
2.5
Experimental results
Rth (oC/W)
2 1.5 1 0.5 0 0
500
1000
1500
2000
2500
3000
Heat flux (W/m2)
Figure 5-155 Comparison of predicted and experimental thermal resistance for 5Vol. % of Al2O3 – water based nanofluid for coolant temperature of 22 oC and air mass of 0.5mg. 216
Chapter Five
Results and Discussion 3 Numerical Prediction
2.5
Experimental results
Rth (oC/W)
2 1.5 1 0.5 0 0
500
1000
1500
2000
2500
3000
Heat flux (W/m2)
Figure 5-156 Comparison of predicted and experimental thermal resistance for 5Vol. % of CuO – water based nanofluid for coolant temperature of 22 oC and air mass of 0.5mg.
217
Chapter Six
Conclusions and Recommendations
Chapter Six Conclusions and Recommendations
6.1 Conclusions The numerical model for the two – dimensional steady –state conditions for constant conductance heat pipe (CCHP) and variable conductance heat pipe (VCHP) were studied theoretically and experimentally with using water, Al2O3water based nanofluid and CuO- water based nanofluid as working fluids. Thus, the results obtained in the present study can be summarized as follows; 6.1.1 Theoretical Results of CCHP and VCHP 1. Increasing the input heat flux, increases the operating temperature, liquid and vapour velocities, liquid pressure drop, axial heat flux, the maximum heat transfer limit and the condenser active length in VCHP but decrease the capillary pressure and the thermal resistance in VCHP. While, the thermal resistance was nearly remains constant in CCHP. 2. Increasing the coolant (sink) temperature decreases the vapour velocity, liquid pressure drop, axial heat flux, the capillary pressure and increases the liquid velocity (slightly), the maximum heat transfer limit, the operating temperature, and the thermal resistance and the condenser inactive length in VCHP. But it has small effect on the heat pipe thermal resistance in CCHP. Furthermore, in the presence of non-condensable gas, increasing the coolant temperature enhancing the heat pipe thermal performance. 3. Utilizing the nanofluid instead of pure water as working fluid, decreases the operating temperature, the liquid and vapour velocities, liquid pressure drop, axial heat flux, the thermal resistance and the condenser active length in 218
Chapter Six
Conclusions and Recommendations
VCHP and increases the maximum heat transfer limit, the capillary pressure and the axial heat flux in VCHP. Additionally, utilizing the nanofluid enhancing the heat pipe performance. 4. Increasing the nanoparticles concentration within the nanofluid reduce the operating temperature, the liquid and vapour velocities, liquid pressure drop, the thermal resistance, axial heat flux in CCHP and the condenser active length in VCHP and increases the maximum heat transfer limit, the capillary pressure and the axial heat flux in VCHP. 5. In VCHP, increasing the mass of non-condensable gas (air), increases the operating temperature, axial heat flux, the maximum heat transfer limit and the thermal resistance and decreases the liquid and vapour velocities, liquid pressure drop, the capillary pressure, the condenser active length and reduce the heat pipe thermal performance. 6. In CCHP, the thermal resistance improvement reaches 31.49% and 34.04% at (qin=2784.86 W/m2, Ts=26 oC and NPC=5 Vol.%) for Al2O3- water based nanofluid and CuO- water based nanofluid, respectively. 7. In VCHP, the thermal resistance improvement reaches 4.07% and 4.17% at (qin=2784.86 W/m2, Ts=26 oC and NPC=5 Vol.%) for Al2O3- water based nanofluid and CuO- water based nanofluid, respectively. 6.1.2 Experimental Results of CCHP and VCHP 1. The optimal amount of the liquid charge for the heat pipes with the wire screen mesh (wick) in this work is obtained about 240% that of the charge estimated theoretically. 2. Increasing the input heat flux increases the wall temperature and the condenser active length in VCHP and decreases the thermal resistance in VCHP, while slightly decreases the thermal resistance in CCHP. 219
Chapter Six
Conclusions and Recommendations
3. Increasing the coolant (sink) temperature increases the wall temperature and decreases the thermal resistance and the condenser active length in VCHP. 4. Increasing the nanoparticles concentration reduces the wall temperature, the condenser active length and the thermal resistance. 5. In VCHP, increasing the mass of non-condensable gas (air), decreases the condenser active length and increases the wall temperature and the thermal resistance. 6. In CCHP, the thermal resistance improvement reaches 44.4% and 48.6% at (qin=2784.86 W/m2, Ts=26 oC and NPC=5 Vol.%) for Al2O3- water based nanofluid and CuO- water based nanofluid, respectively. 7. In VCHP, the thermal resistance improvement reaches 9.88% and 10.48% at (qin=2784.86 W/m2, Ts=26 oC and NPC=5 Vol.%) for Al2O3- water based nanofluid and CuO- water based nanofluid, respectively. 6.2 Recommendations 1. Developing the numerical model to study the thermal behaviour of the heat pipe at transient state. 2. An investigation of a heat pipe thermal performance by using a two layers of different types of the wire screen mesh (wick). 3. Experimental study to determine the optimum nanoparticles concentration within the working fluid. 4. Studying the thermal performance of a heat pipe with a wire screen wick by using hybrid nano-working fluid. 5. Comparing the thermal performance of a cylindrical heat pipe with another heat pipes have different cross section.
220
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228
Appendix-A
Heat Pipe Working Fluid Properties
Appendix-A Heat Pipe Working Fluid Properties
A.1 Conventional Working Fluid (Water and Steam) Properties: The physical properties of water and steam at saturation state can be obtained from Ref. [59], and listed in following table: Liquid Vapour Liquid Liquid Vapour Liquid Vapour Thermal Thermal Surface Specific Specific Viscosity Viscosity Conductivity Conductivity Tension Heat Heat [Pa.s] [Pa.s] o o [W/m. C] [W/m. C] [N/m] [oC] [bar] [kJ/kg] [kg/m3] [kg/m3] [kJ/kg.oC] [kJ/kg.oC] x106 x106 x103 x103 x103 10 0.012282 2477.21 999.6501 0.009407 4.1958 1.8957 581.9 17.21 1306 9.238 74.221
Temp. Vapour Pressure
Latent Heat
Liquid Density
Vapour Density
20
0.023392 2453.55 998.1634 0.017313
4.1851
1.9057
599.5
17.95
1001.6
9.544
72.736
30
0.042467 2429.84 995.6094 0.030412
4.1803
1.918
615
18.71
797.2
9.86
71.194
40
0.073844
4.1788
1.9322
628.6
19.48
652.7
10.18
69.596
50
0.123513 2381.97 988.0056
0.08314
4.1798
1.9482
640.5
20.28
546.5
10.52
67.944
60
0.199458 2357.69 983.1778 0.130418
4.1829
1.9664
650.8
21.1
466
10.85
66.238
70
0.312006 2333.08 977.7465 0.198423
4.1882
1.9873
659.6
21.96
403.5
11.19
64.481
80
0.474147 2308.07 971.7795 0.293662
4.1956
2.0119
667
22.86
354
11.54
62.673
90
0.701824 2282.56 965.3069 0.423881
4.2051
2.0415
673
23.8
314.2
11.89
60.816
100
1.01418
2256.47 958.3501 0.598136
4.2166
2.0775
677.8
24.79
281.6
12.23
58.912
110
1.43376
2229.7
0.826863
4.2304
2.1212
681.3
25.85
254.6
12.58
56.962
120
1.98665
2202.15 943.1026 1.121952
4.2464
2.174
683.6
26.96
232
12.93
54.968
130
2.7026
2173.7
934.8328 1.496818
4.2648
2.237
684.8
28.15
212.9
13.27
52.932
140
3.61501
2144.24 926.1317 1.966495
4.286
2.3109
684.9
29.42
196.6
13.62
50.856
150
4.76101
2113.67 917.0105 2.547758
4.3103
2.3959
683.9
30.77
182.6
13.96
48.741
160
6.18139
2081.86 907.4493 3.259261
4.3379
2.4918
681.8
32.22
170.4
14.3
46.591
170
7.92053
2048.69 897.4566
4.12174
4.3695
2.5985
678.7
33.77
159.8
14.64
44.406
180
10.0263
2014.03 887.0045 5.158308
4.4056
2.7164
674.6
35.42
150.4
14.99
42.19
190
12.5502
1977.74 876.0863 6.394802
4.4468
2.8464
669.5
37.19
142
15.33
39.945
200
15.5467
1939.67 864.6704 7.860276
4.494
2.99
663.4
39.1
134.6
15.67
37.675
2406
992.1816 0.051237
950.95
A1
Appendix-A
Heat Pipe Working Fluid Properties
A.1.1 Thermodynamic Relations The thermodynamic relations of the working fluid (water and steam) physical properties are correlated from the information in the above table and presented in the following form: Pv= 9E-12 T5 + 1E-08 T4 - 7E-07 T3 + 7E-05 T2 - 0.001 T + 0.016
(A-1)
hfg = 2E-11 T5 - 3E-08 T4 - 6E-06 T3 + 0.0001 T2 - 2.3639 T + 2500.8 (A-2) ρl = 1E-10 T5 - 1E-07 T4 + 3E-05 T3 - 0.0065 T2 + 0.0206 T + 1000.1 (A-3) ρv = 9E-12 T5 + 2E-09 T4 + 2E-07 T3 + 3E-06 T2 + 0.0006 T + 0.0029 (A-4) Cpl = -5E-13 T5 + 6E-10 T4 - 2E-07 T3 + 3E-05 T2 - 0.0017 T + 4.2093
(A-5)
Cpv = -4E-12 T5 + 2E-09 T4 - 1E-07 T3 + 1E-05 T2 + 0.0009 T + 1.8852
(A-6)
kl = 1E-10 T5 - 1E-07 T4 + 4E-05 T3 - 0.0121 T2 + 2.0927 T + 562.17 (A-7) kv = 7E-13 T5 + 6E-10 T4 + 8E-07 T3 + 1E-05 T2 + 0.0734 T + 16.473 (A-8) µl = – 3.007E-08 T5 + 1.942E-05 T4 – 0.004941 T3 + 0.6359 T2 – 44.6 T + 1686
(A-9)
µv = 4E-13 T5 + 6E-10 T4 - 4E-07 T3 + 8E-05 T2 + 0.0284 T + 8.9477
(A-10)
σl = 8E-13 T5 - 2E-11 T4 + 2E-07 T3 - 0.0003 T2 - 0.1397 T + 75.647 (A-11) A.2 Nano-Working Fluid (Nanofluid) Properties: The effective thermal conductivity, heat capacity and viscosity for a mixture (nanofluid) with spherical particles is given by [60, 61]:
(
[
(
) ]
[
(
) ]
(
) (
)(
)
(
(A-12) )
(A-13) (A-14)
)
A2
Appendix-A
Heat Pipe Working Fluid Properties
The latent heat of vaporization and surface tension of Al2O3-water based nanofluid with 1, 3, and 5% concentration and 20±5 nm spherical particles is measured experimentally (see Appendix – G) and represented by the following equations: ( (
) )
(A-15) (A-16)
While, the latent heat of vaporization and surface tension of CuOwater based nanofluid with 1, 3, and 5% concentration and 25 nm spherical particles, also measured experimentally (see Appendix – G) and represented by the following equations: ( (
) )
(A-17) (A-18)
Where, the subscript nf, bf and φ refers to the nanofluid, base fluid (water) and the volume fraction of the nanoluid respectively.
A3
Appendix-B
Governing Equations Discretization
Appendix – B Governing Equations Discretization Using the Upwind Differencing Scheme
Upwind schemes represent a class of numerical discretization methods, in computational physics, for solving hyperbolic partial differential equations. Upwind schemes use an adaptive or solution-sensitive finite difference stencil to numerically simulate the direction of propagation of information in a flow field. The upwind schemes attempt to discretize hyperbolic partial differential equations by using differencing biased in the direction determined by the sign of the characteristic speeds. Historically, the origin of upwind methods can be traced back to the work of Courant, Isaacson, and Rees who proposed the CIR method [62]. B.1-First-Order Upwind Scheme B.1.1-Vapour Region By applying the finite difference method on Equation 3-31 the following form is obtained: (
( (
) (
(
) )
)
(
)
(
(
(
)
)
) (
) )
(
(
)
(
( )
(
) (
)
(
)
)
) (
)
(B-1)
The first-order upwind scheme method applied on Equation 3-32 to obtain the following form :
B1
Appendix-B
Governing Equations Discretization
*
+
*
+
(B-2)
Where: (B-3) (
)
(
)
(B-4)
(
)
(
)
(B-5)
The first-order upwind scheme represent the simplest upwind scheme. And, the conditions applying on Equations B-4 and B-5 is given by, [61]: (
)
(
(
)
(
*( (
(
)
(
Case (1)
)
(
)
(B-6)
)
(B-7) )
(
(B-8)
)
(B-9)
For ) (
)
(
)
)
[
(
(
)
(
) ( (
)
) )
(
) (
)+
]
(B-10) Case (2) *( (
)
For ) (
)
(
) [
(
(
)
(
) ( (
)
) )
(
) (
)+
]
(B-11)
B2
Appendix-B
Case (3) *( (
Governing Equations Discretization
For ) (
)
(
)
)
[
(
)
(
(
) ( (
)
)
)
(
) (
)+
]
(B-12) Case (4)
For
*( (
) (
)
(
)
)
[
(
)
(
(
) ( (
)
)
)
(
) (
)+
]
(B-13) Also, the first-order upwind scheme method applied on Equation 3-33 to obtain the following form : *
+
*
+
(B-14)
Where: (B-15) (
)
(
)
(
)
(
)
(B-16) (B-17)
For the first-order upwind scheme, the conditions applying on Equations B16 and B-17 is given by, [62]: (
)
(
(
(
(
)
)
)
(
(
)
(B-18)
)
(B-19)
)
(
(B-20)
)
(B-21)
B3
Appendix-B
Case (1)
Governing Equations Discretization
For
*( (
) (
)
(
) (
)
)
[
(
(
) ( (
)
)
(
) (
)+
)
]
(B-22) Case (2)
For
*( (
) (
)
(
)
) (
)
(
) (
(
[
(
)
)
(
) (
)+
)
]
(B-23) Case (3)
For
*( (
) (
)
(
) (
)
)
[
(
(
) ( (
)
)
(
) (
)+
)
]
(B-24) Case (4)
For
*( (
) (
)
)
(
) (
)
[
(
(
) ( (
)
)
(
) (
)+
)
]
(B-25) B.1.2-Wick Structure The same above procedure can be applied on Equation 3-58 to obtain the following form : *
+
*
(
*
+
)+ (B-26)
Where: (
) (
(B-27) )
(B-28) B4
Appendix-B
Governing Equations Discretization
(B-29)
⁄
B1 and B2 are the same in Equations B-4 and B-5. While, the conditions which applied are the same in Equations B-6 to B-9. Thus:
Case (1)
For
*( (
) (
(
)
(
(
)
(
)
)
(
) [
(
) ( (
)
(
)
) (
)+
]
)
(
(
) )
[
)
(
)
) (
[
(
)
]
(
(
)
(
)
(
)
(
)
(
)
)
(
)
(
)
]
(B-30) Case (2)
For
*( (
) (
[ (
[ (
(
)
)
(
)
)
(
(
)
(
)
) [
(
(
(
)
(
) ( (
)
)
(
)
) (
)+
]
)
(
)
)
(
]
) )
(
) (
(
)
(
)
)
(
)
(
)
]
(B-31)
B5
Appendix-B
Case (3)
Governing Equations Discretization
For
*( (
) (
(
)
(
(
)
)
(
(
)
(
)
) [
)
(
) ( (
)
)
)
(
) (
)+
]
)
(
)
(
( [
( [
)
)
]
(
(
(
)
)
(
)
(
)
(
)
)
(
)
(
)
]
(B-32) Case (4)
For
*( (
) (
(
(
(
)
)
(
(
)
(
)
) [
)
(
) ( (
)
)
)
(
) (
)+
]
)
(
)
(
) [
( [
(
)
)
]
(
(
)
(
)
(
(
)
)
(
)
)
(
)
(
)
]
(B-33) Also, the first-order upwind scheme method applied on Equation 3-59 to obtain the following form : *
+
*
+
(B-34)
Where: *(
) (
)(
)+
*(
) (
)(
)+
(
) (
)
(
(
(
)
(B-35)
) )
E1 and E2 are the same in Equations B-16 and B-17. While, the conditions which applied are the same in Equations B-18 to B-21. Thus: B6
Appendix-B
Case (1) *( (
Governing Equations Discretization
For ) (
(
)
) (
)
)
[
(
(
) ( (
)
(
)
) (
)+
)
]
(B-36) Case (2)
For
*( (
) (
)
(
) (
)
)
(
) (
(
[
(
)
(
)
) (
)+
)
]
(B-37) Case (3) *( (
For ) (
(
)
) (
)
)
[
(
(
) ( (
)
)
(
) (
)+
)
]
(B-38) Case (4)
For
*( (
) (
)
(
) (
)
)
[
(
(
) ( (
)
)
(
) (
)+
)
]
(B-39) B.1.3-Wall Region As in vapour region and wick structure the same above procedure can be applied on Equation 3-71 to obtain the following form : [( (
)
) (
)
(
) (
)
(
) (
[ (
)]
)
(
) (
)]
(B-40)
B.2-Second-Order Upwind Scheme The spatial accuracy of the first-order upwind scheme can be improved by including three data points instead of just two, which offers a more accurate finite difference stencil for the approximation of spatial derivative. For the second-order
B7
Appendix-B
Governing Equations Discretization
upwind scheme that be used in the boundary conditions as defined in the following equations, [62] : i- Forward difference upwind (
)
(
)
(
)
(
)
(
)
(
)
(B-41) (B-42)
ii- backward difference upwind (
)
(
)
(
)
(
)
(
)
(
)
(B-43) (B-44)
This scheme is less diffusive compared to the first-order accurate scheme and is called linear upwind differencing (LUD) scheme.
B8
Appendix-C
Nanofluid Preparation
Appendix – C Nanofluid Preparation
One of the important heat transfer limitations is the thermal conductivity of conventional fluids which always have low value compared with the solids. Therefore, a numerous attempts have been made by scientists and engineers, for over a century since Maxwell (1873), to overcome the fundamental limits and enhance the liquids thermal conductivities by dispersing millimeter or micrometer sized particles in them. However, these attempts were disappointed due to the rapid settling of such large particles. This problem was continued until emergence the concept of nanofluids after the nanotechnology appearance. Therefore, a new kind of engineered heat transfer fluids are obtained, at Argonne National Laboratory by Choi in 1995. Nanofluids are solid-liquid mixtures consisting of solid nanoparticles with average particle size in the range of 1-100 nm, suspended in a base fluid. Thus, due to the high thermal conductivities which exhibited by nanofluids compared to the conventional fluids, the enhancement of heat transfer is attained.
C-1. Nanoparticles Specifications Two types of nanoparticles, Al2O3 (alumina) and CuO (copper oxide), are used in this study. The specifications of these particles are listed in the following table;
C1
Appendix-C
Nanofluid Preparation
Table C-1 Specification of the nanoparticles. Al2O3 Name
Type Purity % Average Particle Size True Density SSA Thermal Conductivity Heat Capacity Color Particle Morphology Source
The
CuO
Aluminum Oxide (alumina) nanoparticles gamma 99.97 20 nm 3890 kg/m3 138 m2/g 36 880 White nearly spherical US Research Nanomaterials, Inc. USA
transmission
electron
Name
Copper Oxide nanoparticles
Type Purity % Average Particle Size True Density SSA Thermal Conductivity Heat Capacity Color Particle Morphology Source
micrograph
(TEM),
-------------99.5 25 nm 6400 kg/m3 13.98 m2/g 42 550 Black nearly spherical US Research Nanomaterials, Inc. USA presented
by
the
manufacturer, of alumina and copper oxide powders are shown in figures C-1 and C-2. Particle size is relatively consistent with a uni-modal distribution and an average diameter of 20 ±5 nm for alumina and 25 ±5 nm for copper oxide. The particles are basically spherical or near spherical.
C2
Appendix-C
Nanofluid Preparation
Figure C-1 TEM micrograph of nano-alumina.
Figure C-2 TEM micrograph of nano-Copper oxide.
C-2. Preparation of nanofluids A two steps method is used to prepare water-based Al2O3 and CuO as nanofluids. The nanofluid was prepared by directly dispersing Al2O3 or CuO C3
Appendix-C
Nanofluid Preparation
nanoparticles into the distilled water in a 100 ml Pyrex flask which can be sealed by a PVC cap. The flask fixed to the stainless steel basket inside the ultrasonic water bath (type Elmasonic P180H and supply by Elma, Germany, see figure C-3), while the basin of the ultrasonic device filled with distilled water over the mixture level in the flask by 3 cm. Then, the degas mode is switched on to remove air from the mixture. After this, the flask sealed by the cap and oscillated continuously from 10 h for Al2O3 and 15 h for CuO in the ultrasonic water bath with a working frequency of 37 kHz and power efficiency of 100% at 60–70 °C so that the nanoparticles can be uniformly dispersed, as shown in figures C-4 and C-5. No surfactants were added into the nanofluid because they have considerable effects on the thermophysical properties of nanofluid. The evaporation of the distilled water in the ultrasonic bath is avoided by sealing the container with cap during sonication. The volume fraction, which was the ratio of the volume of nanoparticles to that of the base fluid, was used to describe the nanoparticle concentration. In the experiments, the volume fractions of the nanofluids are 1, 3 and 5 Vol.%. Some researches considered the mass concentration (w) for the nanofluid. Whereas, the volume fraction of the nanofluid when the mass concentration is known can be estimated by the following correlation [50]: (C-1) Where: w : The nanofluids mass concentration. : The nanoparticles density. : The base fluid density. : The nanofluids volume fractions.
C4
Appendix-C
Nanofluid Preparation
Figure C-3 Elma ultrasonic water bath.
(a) after 1 minute
(b) after 200 minute
Figure C-4 Pictorial view of 5 Vol.% Al2O3 nanoparticles dispersed in DI water. C5
Appendix-C
Nanofluid Preparation
(a) after 1 minute
(b) after 120 minute
Figure C-5 Pictorial view of 5 Vol.% CuO nanoparticles dispersed in DI water.
C6
Appendix-D
Heat Pipe Losses Calculations
Appendix – D Calibration of NTC Sensor
The NTC10K and PTC sensors are widely used as sensing probe (input) with LTR-5 (Single output ON/OFF or PID thermostat or humidistat) device, see figures D-1 and D-2. The technical data of the LTR-5CSRE which used in this study is shown in table D-1. The calibration of NTC10K sensor consists of recording each of the measured temperature by the sensor and the indication of a standardized thermometer, the calibration process occurred in a constant bath temperature for each temperature recording. The result of the calibration is shown in figure D-3.
Table D-1 Specification of LTR-5CSRE. Power supply
LTR-5…E 230Vac ± 10%, 50/60Hz, 2W
Relay outputs (LTR-5..R..)
LTR-5.SR.. OUT1 16(4) A
Inputs
LTR-5C…: NTC 10KΩ at 25°C
Measuring Range
LTR-5C…: -40 to 125°C
Measuring accuracy Operating conditions
LTR-5C…: < ±0.3°C -40 to 100°C; ±1°C out of that range -10 to +50°C; 15 to 80% R.H.
D1
Appendix-D
Heat Pipe Losses Calculations
Figure D-1 Pictorial view of LTR-5CSRE.
Figure D-2 schematic diagram of NTC10K – LTR-5CSRE connection.
D2
Appendix-D
Heat Pipe Losses Calculations
100
Reading of NTC sensor (oC)
90 80 70 60 50 40 30 20 10
0 0
20
40
60
80
Reading of mercury thermometer (oC)
Figure D-3 Calibration of the NTC10K sensor.
D3
100
Appendix-E
Heat Pipe Losses Calculations
Appendix – E Heat Pipe Losses Calculations
In this appendix, the heat losses from the heat pipe insulation to the surrounding are calculated by two methods as follows: Firstly, the net heat output from the condenser of the heat pipe was calculated as: (E-1) (E-2) E-1. First Method: In this method the heat losses from the outer surface of the insulation to the surrounding are calculated based on, [33]: i – The Radiation Equation: This loss is calculated after obtained the insulation surface temperature of the evaporator, adiabatic and condenser sections experimentally. (
)
(E-3)
Where: QR : heat losses by radiation (W). ε : emissivity of the insulation surface. D : outer diameter of insulation = 0.082 m. L
: evaporator, adiabatic or condenser length (m).
Ti : insulation surface temperature (K). Ta : ambient temperature (K). ii – Free Convection Correlations: (
)
(E-4) E1
Appendix-E
(
Heat Pipe Losses Calculations
)
(E-5) (E-6) (E-7)
(
)
(E-8)
Where: Qc : heat losses by convection (W). h : heat transfer coefficient (W/m2.C). Nu : average Nusselt number. k : thermal conductivity of air (W/m.C). Ra : Rayleigh number. n, c : constants, depends on the geometry and the (Ra) range. Gr : Grashof number. Pr : Prandtl number. g : acceleration due to gravity =9.81 (m/s2). β : volume coefficient of expansion =1/T (for ideal gas). υ : kinematic viscosity of air (m2/s). Ti , Ta : insulation surface and ambient temperatures (oC). E-2. Second Method: In this method the heat losses from the outer surface of the insulation to the surrounding are calculated based on the amount of heat gained by the condenser cooling water. ̇
(
)
(E-9)
Where: Qout : heat output by the cooling water (W). ̇ : cooling water mass flow rate (kg/s). Cpw : water specific heat =4.185*103 J/kg.K . E2
Appendix-E
Heat Pipe Losses Calculations
Tw.out : condenser section outlet water temperature (K). Tw.in : condenser section inlet water temperature (K). For example, based on the first method and from one test data which are given in the following table: 25.03
Qin (W) ̇
8.33*10-3
(kg/s)
Ta (oC)
19.5
Ti For evaporator (oC)
23.5
Ti For adiabatic (oC)
20.7
Ti For condenser (oC)
21.1 18
Tw.out (oC) Tw.in (oC) Evaporator (m)
18.62
Adiabatic (m)
0.308
condenser (m)
0.097
0.15
The heat losses by radiation from the insulation of evaporator, adiabatic and condenser sections are: Qr.e = 0.7694 W Qr.a = 0.4672 W Qr.c = 0.1966 W The total heat losses by radiation = 1.4332 W The heat losses by free convection from the insulation of evaporator, adiabatic and condenser sections are: Qc.e = 0.5971 W Qc.a = 0.2729 W Qc.c = 0.1231 W E3
Appendix-E
Heat Pipe Losses Calculations
The total heat losses by free convection = 0.9931 W Thus, the total heat losses from the heat pipe equal to 2.4263 W. Finally, the heat losses percentage ((Qloss/Qin)*100%) is equal to 9.7%. Also, using the second method the heat losses can be calculated as follows: (
)
Then, the heat losses percentage equal to 13.62%
E4
Appendix-F
Calibration of Rotameter
Appendix – F Calibration of Rotameter
The calibration process consists of recording the volume flow rate which measured by the standard method and the indication of Rotameter. Whereas, in the standard method a cylinder with known volume and timer (stop watch) to measure the time need to fill the cylinder are used, and then by dividing the volume of cylinder by the observation time obtain the volume flow rate, the
calibration
process occurred at constant ambient temperature and the calibration curve as in figure F-1.
Reading of Rotameter (L/min)
3 2.5 2 1.5 1 0.5 0 0
0.5
1 1.5 2 2.5 Standard volume flow rate reading (L/min)
Figure F-1 Calibration of Rotameter.
F1
3
Appendix-G
Specific Latent Heat of Vaporization and Surface Tension Measurements
Appendix – G Specific Latent Heat of Vaporization and Surface Tension Measurements
G.1 Specific Latent Heat of Vaporization Calculations The specific latent heat of vaporization of water and nanofluids can be determined by measuring the energy required to boil away a known mass of water or different concentration nanofluid. Figure G-1 shows the schematic of the experimental rig. While, the procedure of calculations can be described as follows: 1. Fill the S.Steel cup (800 ml volume) with about 300 ml of water or nanofluid (with 1, 3 or 5 Vol.% nanoparticles concentration) through the charging tube. 2. Switch on the heater and wait until the liquid reaches the boiling state. 3. At this point switch on the weight meter and record the following, after specified (observation) time. A-The cross weight of the S.Steel cup at the beginning and end of the observation time. B-The power consumed by the heater during this time. C-Value of this specified time. 4. After taking all information, switch off the heater and start the calculations, as follows: Subtract the weight of S.Steel cup from the cross weight to obtain the liquid net weight at the beginning and end of the observation time during the
G1
Appendix-G
Specific Latent Heat of Vaporization and Surface Tension Measurements
boiling state. Whereas, the mass of the liquid has been boiled away can be given by: (G-1) Where: : The liquid mass at the beginning of the observation time (kg). : The liquid mass at the end of the observation time (kg). The specific latent heat of vaporization (hfg) of water or nanofluid in (kJ/kg) is given by: (G-2) Where: P : The power that is consumed by the heater (J/s). t : Observation time (s). : Mass of liquid boiled away (kg). For example, the latent heat of vaporization of water calculated experimentally as follow: P = 1 kW t = 120 s = 0.05 kg kJ/kg The standard latent heat of vaporization of water at the atmospheric pressure equals to 2256.9 kJ/kg. Thus;
While, the latent heat of vaporization of water based-Al2O3 nanofluid with 1% concentration is increased by 14% and equals to (2400*1.14= 2736 kJ/kg).
G2
Appendix-G
Specific Latent Heat of Vaporization and Surface Tension Measurements
And, the latent heat of vaporization of water based-CuO nanofluid with 1% concentration is increased by 15.4% and equals to (2400*1.154= 2769.6 kJ/kg). In addition to the atmospheric pressure, the above procedure is carried out for 1, 3 and 5 Vol.% of water based-Al2O3 and CuO nanofluids at the operating pressure of 0.2, 0.5 and 0.7 bar, by evacuating the S.Steel cup. The experimental tests showed that, at the same NPC, there is small decrement in the increase of the latent heat of vaporization of the nanofluids with the increase of the operating pressure. Therefore, these results are considered to obtain the equations which used to calculate the latent heat of vaporization of the nanofluids in terms of nanoparticles concentration (φ), as seen in Appendix – A.
G.2 Surface Tension Calculations The surface tension of water and nanofluid with different concentration can be determined using the Drop Shape method. Figure G-2 shows the schematic of the rig that used for surface tension measurements. The principal assumptions in using the Drop Shape method are [63]: The drop is symmetric about a central vertical axis:
this means it is
irrelevant from which direction the drop is viewed. The drop is not in motion in the sense that viscosity or inertia are playing a role in determining its shape: this means that surface (or interfacial) tension and gravity are the only forces that shaping the drop. The procedure of calculations can be described as follows: 1. Fill the syringe with about 0.6 ml of the required liquid. 2. Fix the syringe in the rig and adjust the lower tip of the micrometer over the upper syringe surface as shown in figure G-2.
G3
Appendix-G
Specific Latent Heat of Vaporization and Surface Tension Measurements
3. Turn the micrometer tip to press on the syringe stem, in this case you will show a pendant drop from the needle tip which grows with the micrometer pressing. The pressing by the micrometer on the stem will be stopped immediately after separation of the pendant drop. 4. Repeat step 3 above, but stop the pressing immediately before the separation of the pendant drop from the needle tip, here record the displacement of the syringe stem (δ). The weight of a pendant drop that can be supported on a round tip is described by Tate’s Law [63]: (G-3) Where: W : Weight of drop (N). D : Diameter of wetted tip (m). : Surface tension (N/m2). Also, the weight of a pendant drop can be calculated from the following principle Law: (G-4) Where: d : Internal syringe diameter (m). : Micrometer or syringe stem displacement (m). : Acceleration of gravity (m/s2). Finally, by equating G-3 and G-4 the surface tension can be determined for different liquid temperatures. For example, the surface tension of water at 20 experimentally as follow: = 0.173 mm G4
o
C is calculated
Appendix-G
Specific Latent Heat of Vaporization and Surface Tension Measurements
d = 4.71 mm D = 0.125 mm (
)
= 0.0751 N/m The standard surface tension of water at 20 oC is equal to 0.072736 N/m. Thus;
While, the surface tension of water based-Al2O3 nanofluid with 1% cocentration at 20 oC increased by 2% and equal to (0.0751*1.02= 0.0766 N/m). And, the surface tension of water based-CuO nanofluid with 1% cocentration at 20 oC increased by 2.09% and equal to (0.0751*1.0209= 0.07667 N/m). The effect of temperature on the increase in the surface tension has approximately the same trend for all the nanofluid concentrations. Therefore, surface tension equations in terms of nanoparticles concentration (φ) which displayed in Appendix - A are considered.
G5
Appendix-G
Specific Latent Heat of Vaporization and Surface Tension Measurements
Pressure gage
Water Condensation Chamber Insulation
Stainless Steel Cup
Service Valve
Liquid Level
Heater AC-Multimeter
Variac
Weight meter
Figure G-1 Schematic diagram of experimental rig for latent heat of vaporization measurement.
Depth Micrometer
Syringe Stem
Syringe Needle Pendant Drop
Figure G-2 Schematic diagram of experimental rig for surface tension measurement. G6
Appendix-H
Publish Paper from Thesis
Appendix – H Publish Paper from Thesis
NUMERICAL INVESTIGATION OF THE EFFECT OF WIRE SCREEN MESH SPECIFICATION AND EVAPORATOR LENGTH ON THERMAL PERFORMANCE OF CYLINDRICAL HEAT PIPE
ABSTRACT A numerical model has been developed to determine the effect of the wire screen mesh (wick) type on the heat transfer performance of copper–water wicked heat pipe. This model represented as steady-state incompressible flow. The governing equations in cylindrical coordinates have been solved in vapor region, wick structure and wall region, using finite difference with forward-backward upwind scheme. The results show that increasing the mesh number led to decreasing the maximum heat transfer limit and increasing the capillary pressure. While, for the same heat input the operating temperature of the heat pipe increases when the mesh number increases. Also, it was found that increasing the evaporation length, with constant condensation length, decrease the operating temperature and increase the maximum heat transfer limit. For verification of the current model, the results of liquid pressure drop for a heat pipe have been compared with the previous study for the same problem and a good agreement has been achieved.
H1
Appendix-H
Publish Paper from Thesis
الخالصة: حى حطوٌش ًَورج ػذدي نحغاب حأثٍش َوع انفخٍم انشبكً ػهى اداء اَخقال انحشاسة ألَبوب حشاسي رو فخٍم شبكً يٍ انذاخم ويصُوع يٍ انُحاط وٌغخخذو انًاء كًائغ نهؼًم .هزا انًُورج يثم كدشٌاٌ ال اَضغاطً فً انحانت انًغخقشة .انًؼادالث انحاكًت بصٍغت االحذاثٍاث االعطواٍَت حهج فً يُاطق انبخاس, انفخٍم انشبكً وخذاس االَبوب ,باعخخذاو طشٌقت انفشوقاث انًحذدة يغ َظاو اياو-خهف يغ انشٌح .انُخائح بٍُج اٌ صٌادة سقى انشبكت ٌؤدي انى َقصاٌ حذ اَخقال انحشاسة االػظى وصٌادة انضغظ انشؼٍشي .بًٍُا ,نُفظ كًٍت انحشاسة انذاخهت فاٌ دسخت حشاسة انؼًم نألَبوب انحشاسي حضداد يغ صٌادة سقى انشبكت .اٌضا ,وخذ باٌ صٌادة طول انًبخش ,يغ بقاء طول انًكثف ثابجٌ ,قهم دسخت حشاسة انؼًم وٌضٌذ حذ اَخقال انحشاسة االػظى .يٍ اخم انخأكذ يٍ صحت انًُورج انحانً ,فاٌ َخائح هبوط ضغظ انًاء نألَبوب انحشاسي قوسَج يغ انذساعت انغابقت نُفظ انًغانت وكاٌ هُانك حوافق خٍذ.
H2
Appendix-H
Publish Paper from Thesis
H3
Appendix-H
Publish Paper from Thesis
H4
