laminar flow and heat transfer characteristics in a three dimensional .... winglet type vortex generators (DWs) on forced convection heat transfer and friction loss ...... and the balance length of 630 mm served as the entry length for flow ...
OPTIMAL THERMOHYDRAULIC PERFORMANCE IN THREE SIDES ARTIFICIALLY ROUGHENED SOLAR AIR HEATER
A THESIS Submitted in fulfillment of the requirements of the award of the degree of DOCTOR OF PHILOSPHY In MECHANICAL ENGINEERING By ASHWINI KUMAR (2013PGPHDME08)
Under the supervision of Prof. Bishwa Nath Prasad & Dr. Krishna Deo Prasad Singh Department of Mechanical Engineering National Institute of Technology, Jamshedpur Jamshedpur-831014 (India) January 2017
NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR CERTIFICATE I hereby certify that the work presented in the thesis entitled " Optimal Thermohydraulic Performance In Three Sides Artificially Roughened Solar Air Heater" in partial fulfillment of the requirements for the award of the degree of Doctor of Philosophy in Mechanical Engineering, submitted in the Department of Mechanical Engineering, National Institute of Technology, Jamshedpur is an authentic record of my own work carried out under the supervision of Prof. B.N. Prasad and Dr. K.D.P. Singh, Department of Mechanical Engineering, National Institute of Technology, Jamshedpur. The matter presented in the thesis has not been submitted by me for the award of any other degree of this or any other institute.
Date:
(Ashwini Kumar)
This is to certify that the above statement made by the candidate is correct to the best of our knowledge.
(Dr. B.N. Prasad)
(Dr. K.D.P. Singh)
Professor
Associate Professor
Department of Mechanical Engineering
Department of Mechanical Engineering
NIT, Jamshedpur, India 831014
NIT, Jamshedpur, India 831014
The Ph.D. thesis Viva-voce Examination of Mr. Ashwini Kumar, Research Scholar was held on ______________.
Signature of Internal Examiner
Signature of External Examiner i
ACKNOWLEDGEMENTS The author expresses his deep sense of gratitude and indebtedness to Dr.B.N.Prasad, Professor and Dr.K.D.P.Singh, Associate Professor both from Mechanical Engineering Department, NIT Jamshedpur, who provided their valuable guidance, unfailing inspiration, whole hearted cooperation and help in carrying out this work. Their encouragement at each step of the work and painstaking efforts in providing in final shape to the text are gratefully acknowledged. The author gratefully acknowledges the facility provide by the institute and the department. Thanks are due to staff of Mechanical Engineering Department for their co-operation at the every step of the work. Last but not the least, the moral support and patience of my family members especially my parents Mr.Yogendra Roy & Mrs. Kiran Yadav, my brother Amit Kumar, my wife Mrs. Bandana Singh and motivation given by my fellow friends especially Ravi Kumar, Abhishek Priyam and Aruna Kumar Behura is highly acknowledged.
ASHWINI KUMAR
ii
My Work Is Dedicated To
My Parents And My Little Angel
Kashvi Kavya iii
ABSTRACT Solar air heaters are one of the simplest and cost effective solar energy utilization systems for various drying applications. The thermal efficiency of solar air heaters is found to be low due to low heat transfer coefficient on the air side. Attempts have been made to enhance the heat transfer rate from the absorber plate to air by using different roughness elements. Enhancement of heat transfer coefficient is achieved by providing artificial roughness, always goes with an increment of pressure drop and more pumping power is required. So, there is a need to optimize the system parameters to maximize heat transfer, while keeping the friction losses as low as possible. The present work aimed at obtaining the optimal thermo hydraulic performance condition in three sides roughened and glass covered solar air heaters to get the maximum heat transfer for minimum pumping power. An extensive experimental investigation has been carried out with the objective of obtaining and validating the results on heat transfer, friction factor, and thermal performance of three sides roughened and glass covered solar air heaters along with those on smooth and three sides glass covered solar air heaters. Roughened absorber plates were prepared by soldering small diameter wires on them. The operating parameters covered the range of relative roughness height, e/D, 8.35 × 10-3 – 3.75 × 10-2, relative roughness pitch, p/e, 10 – 30, flow Reynolds number, Re, 4000 – 20000 and Prandtl number, Pr, 0.7 for air. Data were collected on a similar sized three sides glass covered smooth solar air heater simultaneously. Calibrated copper constantan thermocouples were soldered on the absorber plates to measure local plate temperature, whereas, the temperature of air was measured by digital thermometer inserted midway into the air duct. Air was sucked through the collectors using a blower with electric power input controlled by an auto-variac to obtain variable flow rates, the flow rate being measured by a U-tube manometer fitted in a calibrated flange-tap orifice-meter. The intensity of global radiations was measured by digital pyranometer. The reduced data were further utilized to obtain the thermo hydraulic results. The results have been found to compare well with the available ones. Correlations have been developed for heat transfer and friction coefficient in three sides roughened and glass covered as well as three sides glass covered smooth solar air heaters, written under as:-
iv
𝑁𝑢3𝑟 = 0.1415 𝑝/𝑒
−0.0713
𝑒/𝐷
0.0871
𝑅𝑒
0.746
for 𝑒 + ≤ 23
𝑁𝑢3𝑟 = 0.0422 𝑝/𝑒
−0.0461
𝑒/𝐷
0.0375
𝑅𝑒
1.208
for 𝑒 + > 23
𝑓3𝑟 = 0.372 𝑝/𝑒
−0.319
𝑁𝑢3𝑔𝑠 = 0.0782 𝑃𝑟
0.5
𝑒/𝐷
0.354
0.7
𝑓𝑆
𝑅𝑒
𝑅𝑒
−1.76
0.932
A good agreement has been found between predicted and experimental values with a deviation of ±12% and±11% respectively, for Nusselt number and friction factor. The effects of roughness and flow parameters (p/e, e/D, Re) on heat transfer, friction factor and thermo hydraulic performance have been determined. Results show that the values of Stanton number are higher in three sides roughened and glass covered solar air heater and they are in the range of 36% to 65% more as compared to three sides glass covered smooth ones and the values of friction factor in three sides roughened and glass covered collector have been found to increase in the range of 28% to 38%, as compared to three sides glass covered smooth ones. The value of heat transfer enhancement factor of such solar air heaters have been found to lie in the range of0.378 to 0.487,resulting in an enhancement of about 50 to 59% in thermal performance over those of three sides glass covered smooth solar air heaters, in the range of the parameters investigated. The values of performance parameters, FR and F’ have been found to be more than those of three sides glass covered smooth solar air heaters by an amount of 51-60% and 41-49% respectively. Thermal performance equations in terms of the performance parameters have been derived. The roughness Reynolds numbers, 𝑒 + = 𝑒/𝐷
𝑓3𝑟 2
𝑅𝑒, have
been considered for optimizing the thermo hydraulic performance of three sides roughened and glass covered solar air heaters. The optimal thermo hydraulic performance of such solar + air heaters has been achieved at an optimal value of the optimization parameter, 𝑒𝑜𝑝𝑡 = 23.
The experimental results have been utilized to develop the correlations for thermo hydraulic efficiency written under as:Ƞ𝑡𝑒𝑟𝑚𝑜 = 0.102 𝑒 +
0.658
for 𝑒 + ≤ 23
Ƞ𝑡𝑒𝑟𝑚𝑜 = 11.91 𝑒 +
−0.913
for 𝑒 + > 23
The deviation between the predicted and the experimental values of thermo hydraulic efficiency was found to be ±7.23%. v
An uncertainty of +1.89% to +7.06% in the values of thermo hydraulic performance has + been found. The value of optimal thermo hydraulic performance corresponding to 𝑒𝑜𝑝𝑡 = 23
have been found to be 78.8% within the range of the parameters investigated. It can therefore be concluded that a solar air heater with three sides artificially roughened absorber plates and glass covers perform considerably better with respect to energy collection as compared to three sides glass covered smooth solar air heaters and the optimal thermohydraulic performance of three sides roughened and glass covered solar air heaters is + obtained when 𝑒𝑜𝑝𝑡 = 23.
Keywords: Relative roughness pitch, (p/e); Relative roughness height, (e/D); Flow Reynolds number, (Re); Stanton number, (St); Collector roughness and flow parameters; Collector performance parameters; Thermal performance; Roughness Reynolds number; and Thermo hydraulic performance.
vi
CONTENTS CERTIFICATE
i
ACKNOWLEDGEMENT
ii
ABSTRACT
iii
CONTENTS
vi
LIST OF FIGURES
ix
LIST OF TABLES
xii
NOMENCLATURE
xiii
Chapter No. 1
Title INTRODUCTION AND LITERATURE SURVEY
1-22
1.1 Solar thermal collectors
1
1.2 Solar air heaters
1
1.3 Solar air heater performance
2
1.4 Effect of roughness and flow parameters in solar air heaters
7
1.4.1
20
Optimization of the system parameters
1.5 Objectives of the present work
2
Page No.
OPTIMAL
THERMOHYDRAULIC
22
PERFORMANCE 23-40
ANALYSIS 2.1
Introduction
23
2.2
Optimization methodology
23
2.3
Effect of efficiency parameters
26
2.4
Thermohydraulic performance
36
vii
3
4
SYSTEM DEVELOPMENT AND INVESTIGATIONS
41-59
3.1
Introduction
41
3.2
Solar air heater ducts models
41
3.3
Experimental Set-up
42
3.3.1 Absorber plates and glass covers
43
3.3.2 Test section and entry section of the duct
43
3.4
48
Instrumentation
3.4.1 Blower and electric motor
48
3.4.2 Flow control arrangement
48
3.4.3 Air flow measurement
48
3.4.4 Temperature and Pressure drop measurement
51
3.4.5 Solar radiation intensity measurement
54
3.5
54
Experimental procedure
RESULTS AND DISCUSSIONS
60-110
4.1
Introduction
60
4.2
Data presentation, reduction and validation
60
Sample calculation
61
4.3
Variation of intensity and ambient temperature
62
4.4
Validation of the experimental data
66
4.5
Development of correlations for Nusselt number and 71
4.2.1
friction factor 4.5.1 Correlation for Nusselt number of three sides glass covered 78 smooth solar air heater 4.5.2 Correlation for friction factor of three sides roughened and 82 glass covered solar air heater 4.6 Effect of roughness and flow parameters on heat transfer and 91 friction factor 4.7 Heat transfer enhancement factor and friction loss factor
96
4.8 Thermal performance of solar air heater
96
viii
5
4.9 Collector heat removal factor and collector efficiency factor
101
4.10 Thermal performance curves
104
4.11 Optimal thermo hydraulic performance
106
CONCLUSIONS AND FUTURE SCOPE
111-112
5.1 Conclusions
111
5.2 Future scope of the work
112
REFERENCES
113-121
UNCERTAINTY ANALYSIS
122-124
LIST OF PUBLICATIONS FROM THIS WORK
125
ix
LIST OF FIGURES Figure No.
Title of Figures
Page No.
2.1(a)
Three sides roughened solar air heater duct
24
2.1(b)
Absorber plate with artificial roughness
24
2.2
Effect of e+ on B-1 for varying p/e
27
2.3
Effect of e+ on C-1 for varying p/e
29
+
-1
2.4
Effect of e on L for varying p/e
30
2.5
The efficiency parameter L-1 as a function of p/e and e+
31
2.6.(1-3)
Optimal thermo hydraulic performance curve for three sides 33-35 artificially roughened solar air heater
2.7
Optimum thermo hydraulic performance curves
37
2.8
Optimal range of e/D
39
3.1 (a,b)
Solar air heater duct models
42
3.2(a)
Schematic diagram of experimental set-up
44
3.2 (b)
Top view of the experimental set-up
45
3.3
Photograph of experimental set-up with two ducts
45
3.4
Photograph of experimental set-up with measuring instruments
46
3.5
Photograph of three sides roughened absorber plate
46
3.6
Typical three sides artificially roughened absorber plate
47
3.7
Typical three side smooth absorber plate
47
3.8
Photograph of digital pyranometer system
48
3.9
Orifice plate location and specification
49
3.10
Details of flange-taps orifice meter construction
50
3.11
Orifice meter calibration
52
3.12
Thermocouple arrangement on top and side of the absorber plates
53
3.13
Arrangement of air temperature and pressure taps along the duct 53 length
4.1
Typical variation of solar radiation and ambient temperature on a 64 day
4.2
Typical air and plate temperature in solar air heaters
65
4.3
Comparison of heat transfer data in smooth solar air heater
67
x
4.4
Comparison of friction factor data in smooth solar air heater
68
4.5
Comparison of heat transfer data in three sides roughened solar air 69 heater
4.6
Comparison of friction factor data in three sides roughened solar air 70 heater
4.7
Variation of Nusselt number with Reynolds number (𝑒 + ≤ 23)
4.8
3𝑟 Plot of (𝑅𝑒)0.746 versus p/e
𝑁𝑢
72 73
𝑁𝑢 3𝑟 (𝑅𝑒)0.746
4.9
Plot of
4.10
Variation of Nusselt number with Reynolds number (𝑒 + > 23)
4.11
3𝑟 Plot of (𝑅𝑒)1.208 versus p/e
(𝑝/𝑒)−0.0713 versus e /D
𝑁𝑢
74
75 76
𝑁𝑢 3𝑟 (𝑅𝑒)1.208
4.12
Plot of
4.13
Nusselt number versus flow Reynolds number for smooth solar air 79
(𝑝/𝑒)−0.0461 versus e/D
77
heater 4.14
𝑁𝑢 3𝑔𝑠
80
Plot of (𝑅𝑒)0.932 versus Pr 𝑁𝑢 3𝑔𝑠 0.932
4.15
Plot of (𝑅𝑒)
(𝑃𝑟 )0.5 versus fs
81
4.16
Variation of friction factor with Reynolds number
83
4.17
Plot of
𝑓3𝑟 (𝑅𝑒)−1.76
versus p/e
84
(𝑝/𝑒)−0.319 versus e/D
85
𝑓3𝑟 (𝑅𝑒)−1.76
4.18
Plot of
4.19
Comparison of experimental Nusselt number values to the predicted 86 ones
4.20
Comparison of experimental Nusselt number values to the predicted 87 ones
4.21
Predicted and experimental heat transfer data in solar air heater xi
89
4.22
Predicted and experimental values of friction factor data in solar air 90 heater
4.23
Effect of p/e on Stanton number in three sides artificially roughened 92 solar air heater
4.24
Effect of e/D on Stanton number in three sides artificially 93 roughened solar air heater
4.25
Effect of p/e on friction factor in three sides artificially roughened 94 solar air heater
4.26
Effect of e/D on friction factor in three sides artificially roughened 95 solar air heater
4.27
Heat transfer enhancement factor and friction loss factor versus 97 Reynolds number
4.28
Effect of roughened sides and glass covers on Stanton number in 99 solar air heaters
4.29
Thermal performance characteristics of solar air heaters
100
4.30
Collector heat removal factor in solar air heaters
102
4.31
Collector efficiency factor in solar air heaters
103
4.32
Thermal performance curves for solar air heaters
105
4.33
Effect of p/e and e+ on thermo hydraulic performance
107
+
4.34
Effect of e/D and e on thermo hydraulic performance
108
4.35
Thermohydraulic efficiency versus roughness Reynolds number
110
xii
LIST OF TABLES Table No.
Title of Tables
Page No.
2.1
Range of efficiency parameter, L-1, as a function of e+ and p/e
2.2
+ Values of 𝑒𝑜𝑝𝑡 , for different roughness geometries for fully 36
32
developed turbulent flow 2.3
Values of Re, at varying value of e/D and p/e=10, for the optimal 40 condition
3.1
Test data collected during a typical run (Run no. 56)
55
3.2
Range of parameters investigated
56
4.1
Values of I, Ta, h, St and Nu as a function of time during the day 63 (Run no. 56)
4.2
Values of slope, intercept, collector heat removal factor and collector 104 efficiency factor
xiii
NOMENCLATURE
𝑨𝒄
Collector area, m2
𝑨𝟐
Throat area of orifice meter, m2
𝑨𝒇
Friction similarity function, m2
𝑩
Solar air heater duct height, m
𝑩−𝟏
Stanton number roughness parameter
𝑪𝑭
Dimensionless friction factor coefficient
𝑪𝑯
Dimensionless heat transfer coefficient
𝑪−𝟏
Efficiency roughness parameter
Cp
Specific heat at constant pressure of air, kJ/kg.K
𝑪𝒅
Discharge coefficient
𝑫, 𝑫𝒉
Hydraulic diameter of solar air heater duct, m
d1
Flow pipe diameter, m
d2
Throat diameter of orifice meter, m
d/W
Relative gap position
d/D
Relative print diameter
Dj/Dh Ratio of jet diameter to hydraulic diameter e 𝒆+ 𝒆+ 𝒆+ 𝒐𝒑𝒕
Artificial roughness height, m Roughness Reynolds number = 𝑒/𝐷 Roughness Reynolds number = 𝑒/𝐷
𝑓3𝑟 2 𝑓 2
𝑅𝑒 (Present case) 𝑅𝑒 (Prasad and Saini, 1991)
Optimal roughness Reynolds number 𝒆/𝑫 𝒆/𝑫𝒐𝒑𝒕
Relative roughness height Optimal relative roughness height
𝒇𝒔
Friction factor in four sided smooth duct
𝒇𝒓
Average friction factor in three sides roughened duct (Prasad et al., 2014)
𝒇𝟑𝒓
Friction factor for in three sides roughened duct (Present case)
𝒇
Average friction factor=(𝑓𝑠 + 𝑓𝑟 )/2, (Prasad and Saini, 1991)
𝒇
Friction factor
𝑭′
Collector efficiency factor xiv
𝑭"
Collector flow factor
𝑭𝑹
Collector heat removal factor
𝑭𝟎
Collector heat removal factor based on outlet temperature, 𝑡0
𝑭𝟎 𝑼 𝑳 𝑭𝟎 (𝝉𝜶)
Slope of the thermal performance curve Intercept of the thermal performance curve
𝑭𝒂𝒗
Average collector efficiency factor
𝒇𝑭
Friction loss factor
𝒇
Moderate pressure drop increase 𝒇𝟎 𝑮
Mass flow rate per unit collector area, kg/s.m2
g
Acceleration due to gravity, m/s2
g’
Heat transfer function
g/e
Relative gap width
g/p
Groove position to pitch ratio
GH
Heat transfer roughness function
𝒉
Convective heat transfer coefficient, W/m2.K
𝑰
Intensity of solar radiation, W/m2
k
Thermal conductivity of collector material, W/m.K
𝑲′
Geometric coefficient of collector, 𝐾 ′ = 𝐿/ 𝐵𝐷
L
Collector length, m
L-1
Efficiency parameter, L-1 = C-1 - B-1
L/e
Relative long way length
l/s
Relative length of metal grid
𝒎
Mass flow rate of air, kg/s
0.25
𝑵𝒖𝒓 , 𝑵𝒖 Nusselt number for top side roughened duct 𝑵𝒖𝒓
Average Nusselt number for three sided roughened duct (Prasad et al., 2014)
𝑵𝒖𝟑𝒓
Nusselt number for three sides roughened duct (Present case)
𝑵𝒖𝟑𝒈𝒔
Nusselt number for three sides glass covered smooth duct (Present case)
𝑵𝒖
Nusselt number
xv
𝑵𝒖𝑭
Heat transfer enhancement factor
𝑵𝒖𝟎
Nusselt number for fully developed flow smooth channel
𝑵𝒖 𝑵𝒖𝟎
Heat transfer augmentation
𝒑
Roughness pitch, m
P
Motor power
P1, P2 Pressure in two limbs of the manometer, N-m2 p/e
Relative roughness pitch
𝑷𝒓
Prandtl number
𝑷𝒓𝒕
Turbulent Prandtl number
QU
Useful heat gain, W
𝑹
Roughness function
𝑹𝒆
Reynolds number
𝑹𝒅
Throat Reynolds number
𝑺𝒕𝟑𝒓
Average Stanton number for three sides roughened duct (Present case)
𝑺𝒕 , 𝑺𝒕
Stanton number for top side roughened duct
𝑺𝒕𝒓 𝑺𝒕𝑺 𝑺𝒕𝟑𝒈𝒔
Average Stanton number for three sides roughened duct (Prasad et al., 2014) Stanton number for smooth solar air heaters Stanton number for three sides glass covered smooth solar air heaters
SWG Standard Wire Gauge 𝑻𝒂
Ambient air temperature, K
𝑻𝒊
Inlet temperature of air, K
𝑻𝟎
Outlet temperature of air
𝑻𝒇
Fluid temperature at different location of the collector
𝑻𝒑
Plate temperature at different location of the absorber plate
𝐓𝐟
Average temperature of fluid
𝑻𝒑
Average temperature of plate
𝜶
Rib angle of attack
𝝉𝜶
Transmittance-absorptance product
ƞ𝒕𝒉
Collector thermal efficiency
xvi
Ƞ
Optimization parameter
ƞ𝒕𝒉𝒆𝒓𝒎𝒐
Thermo hydraulic efficiency
𝑼𝑳
Overall heat transfer coefficient, W/m2.K
V2
Fluid velocity in the throat, m-s-1
Va
Volume flow rate of air, m3/s
𝑾
Solar air heater duct width
w
Width of rib, m
W/w Relative roughness width W/H Duct aspect ratio X
Distance in x-direction, m
Y
Distance in y-direction, m
X/Dh Ratio of streamwise pitch to hydraulic diameter Y/Dh Ratio of spanwise pitch to hydraulic diameter 𝝆
Air density, kg/m3
∆𝐩 Pressure drop, N/m2 ∆𝐓 Temperature rise 𝝑 kinematic viscosity 𝜷𝟏
Diameter ratio, 𝛽1 =
𝑑2 𝑑1
1r,1G One side roughened collector with only top side glass cover 3r,3G Three sides roughened collector with three sides glass covers (top and sides) S,1G Smooth collector with only top side glass cover S, 3G Smooth collector with three sides glass covers (top and sides)
xvii
CHAPTER- 1 INTRODUCTION AND LITERATURE SURVEY
Since the beginning of time, people have been fascinated by the power of sun. Ancient civilizations personified the sun, worshipping as a God. Throughout history, farming and agriculture efforts have relied upon the sun’s rays to grow crops and sustain population. However, we have developed the ability to harness the sun’s awesome power. The resulting technologies have promising implications for the future of renewable energy and sustainability. 1.1 SOLAR THERMAL COLLECTORS A solar thermal collector collects heat by absorbing sunlight. A collector is a device for capturing solar radiation. Solar radiation is energy in the form of electromagnetic radiation from the infrared (long) to the ultraviolet (short) wavelengths. The quantity of solar energy striking the earth's surface (solar constant) averages about 1000 watts per square meter under clear skies, depending upon weather conditions, location and orientation. The term ‘solar collector’ commonly refers to solar hot water panels, but may refer to installations such as solar parabolic troughs and solar or basic installations such as solar air heaters. Concentrated solar power plants usually use the more complex collectors to generate electricity by heating a fluid to drive a turbine connected to an electrical generator. Simple collectors are typically used in residential and commercial buildings for space heating. Solar collectors are either non-concentrating or concentrating. In the nonconcentrating type, the collector area (i.e., the area that intercepts the solar radiation) is the same as the absorber area (i.e., the area absorbing the radiation). In these types the whole solar panel absorbs light. Concentrating collectors have a bigger interceptor than absorber. 1.2 SOLAR AIR HEATERS Solar air heating is a solar thermal technology in which the energy from the sun is captured by an absorber and used to heat air flowing over it. Solar air heating is a renewable
1|Page
energy heating technology used to heat or condition air for buildings or process heat applications. It is typically the most cost-effective out of all the solar technologies. Solar air heaters are a system that collect solar energy and transfers the heat to passing air, which is either stored or used for space heating. The collectors are often black to absorb more of the sun's energy and a conductive material, often metal, acts as a heat exchanger. Solar air heaters can compliment traditional indoor heating systems by providing a free and clean source of heat. 1.3 SOLAR AIR HEATER PERFORMANCE The useful thermal energy for quasi-steady state condition, delivered by a solar collector is obtained from the energy balance between the energy absorption rate of the absorber & thermal energy losses directly and indirectly to the surroundings. It can be written as: Qu Ac
= I τα − UL (Tp − Ta )
(1.1)
The difficulty is to utilize the above equation, which lies in the calculation of mean absorber plate temperature, Tp , which is a function of the collector configuration, the incident solar radiation and entering fluid condition. Therefore, Eq. (1.1) is usually represented in a more practical form as: Qu Ac
= FR [I τα − UL Ti − Ta ]
(1.2)
where, the heat removal factor FR is defined as the ratio of rate of actual useful energy collected to the rate if the entire collector surface were at fluid inlet temperature and can be written as: FR = A
m C P (T o −T i ) c [I
(1.3)
τα −U L T i −T a ]
A very widely used basic equation (1.2), known as (Hottel-Whillier-Bliss equation) can be modified to include thermal efficiency as: Ƞth = FR
τα − UL
T i −T a I
(1.4)
2|Page
This equation expresses the thermal efficiency of the collector in terms of two major operating parameters, incidence solar radiation normal to the collector plate and temperature difference Ti − Ta . Eqs. (1.2) and (1.4) have been in wide use to compare the performance characteristics of different types of collectors and to investigate the effect of various design parameters. Heat removal factor FR is a function of plate efficiency factor F ′ defined by Bliss (1959), written under as: h
F ′ = h+U
(1.5)
L
The value of F ′ is a strong function of configuration parameters given by (Duffie et al. 1980). A third factor known as collector flow factor F ′′ has been included (Duffie et al. 1980) to present equations given below: m CP
FR = A F ′′ =
c UL
FR F′
=
1 − exp − m CP A c U L F′
A c U L F′
(1.6)
m CP
1 − exp −
A c U L F′
(1.7)
m CP
The collector flow factor F ′′ is a function of dimensionless collector capacitance rate,
m CP A c UL F′
.
The collector thermal efficiency, Ƞth , given by Eq. (1.4) can be written as: Ƞth = FR τα − FR UL
(T i −T a ) I
(1.8)
This can be seen to have the form of the equation of straight line, (y = mx + c), as the term FR and UL are usually nearly constant over the operating range of the collector. Thus, FR τα , is the intercept and −FR UL is the slope of the straight line drawn on a graph with abscissa units of
(T i −T a ) I
and ordinate of Ƞth .
The terms FR τα and FR UL are used as thermal performance parameters of the flat plate solar collectors. A solar air heater working on an open cycle which is drawing ambient air outside, the inlet temperature always coincides with the ambient temperature i.e. Ti = Ta. Under such operating conditions, the conventional equation (1.4) will not be meaningful as this reduces 3|Page
toȠth = FR τα . Therefore, for a solar air heater, it was considered useful to utilize the following equation given by (Duffie and Beckman, 1980; Reddy and Gupta, 1980; Biondi et al., 1988): Ƞth = F0
(T 0 −T a )
τα − UL
(1.9)
I
where,F0 is the heat removal factor referred to the outlet temperature, also expressed by Biondi et al (1988) as: F0 = GCP
e
U L F ′ /GC P
−1
(1.10)
UL
Further performance can also be expressed as: Ƞth = GCP
(T 0 −T i )
(1.11)
I
For Ti = Ta, the variable reduced temperatures if Eqns. (1.9) and (1.11) coincide. Therefore, Eqns. (1.9) and (1.11) could be represented on a single diagram having the same quantity in the abscissa (Reddy and Gupta, 1980; Biondi et al, 1988). This was considered the most suitable way to describe the characteristic behaviors of solar air collectors (Reddy and Gupta, 1908; Biondi et al, 1988; Khalid et al, 1987). According to Duffie and Beckman (1980), an approximate analytical correction can be made to FR τα and FR UL for flow rates for which actual test results are not available. It was proposed that the data be plotted as Ƞth versus Tav =
T i +T 0 2
T av −T a I
instead of usual
(T 0 −T i ) I
taking
. Then the performance equation could be in the form of:
Ƞth = Fav τα − Fav UL
T av −T a I
(1.12)
where, Fav approximated to F ′ and corrections for FR τα and FR UL could be obtained from the equations (Duffie and Beckman, 1980) given below: m CP
FR τα = Fav τα
m CP
AC F av U L 2 AC +
(1.13)
m CP
FR UL = Fav UL
m CP
AC F av U L 2 AC +
(1.14) 4|Page
However, if Ƞth is plotted against
(T 0 −T a ) I
, as is often done for air heater test data (Reddy
and Gupta, 1980; Biondi et al, 1988), the equation for Ƞth could be written as: Ƞth = F0 τα − F0 UL
(T 0 −T a ) I
(1.15)
and then the correction for FR τα and FR UL would be written as: m CP
FR τα = F0 τα
m CP m CP
F R UL = F 0 UL
m CP
AC
A C +F 0 U L
AC
A C +F 0 U L
(1.16)
(1.17)
(Gillet et al. 1983; Bernier and Plett, 1988) declared that the thermal performance representation, testing procedures and mathematical models associated with the solar air collectors had not been developed to the same extent as for liquid collector. The two basic differences between air and liquid collectors are (i) relatively poor thermal conductivity of the air resulting in lower absorber plate to air heat transfer coefficient as compared to that for liquid collectors, which implies that the former have a strong dependence on flow rate, (ii) most air collectors leak since it is not economical to build a perfectly sealed solar air collector. An important aspect of the analytical methods of performance prediction of solar air heaters is the heat transfer coefficient in between the absorber plate and air, and the pressure drop in the collector. A number of empirical relations have been predicted for different configurations and working conditions of the collectors. The correlation given by Kays (1966) for heat transfer for flow between parallel plates, with the upper being heated and lower plate insulated has been utilized by Duffie and Beckman (1980) and Khalid et al (1987) for fully developed turbulent flow as: NuS = 0.0158 Re0.8
(1.18)
For solar air heaters operating in the range of 2000 < Re < 10000, Jansen (1985) utilized the relation recommended by Shewen and Hollands (1980 &1978) based on the data of Kays and London (1964) as: NuS = 0.00269 Re
(1.19) 5|Page
The corresponding friction factor was given by Shewen and Hollands (1978) as: fS = 0.1335 Re−0.317
(1.20)
The equation suggested by Altemani and Sparrow (1980) for flow in a triangular duct with heated inclined surfaces and an insulated third surface utilized by Khalid et al (1987) for the mass flow rate between 0.01 – 0.05 kg/s.m2 was given as: NuS = 0.019 Re0.781
(1.21)
Biondi et al (1988) expressed Kays’ Eq. (1.18) by introducing into it, the geometric coefficient of collector given by: L
K ′ = BD 0.25
(1.22)
NuS = 0.0158
GK ′
0.8
D
μ
(1.23)
For fully developed turbulent flow inside tubes, the correlation for heat transfer and friction factor as recommended by Duffie and Beckman (1980) are: fs
Nus = 1.07+12.7√f8
Re P r s √8(p r
2/3 −1)
fS = 0.79 ln Re − 1.64
−2
(1.24)
(1.25)
Prasad and Mullick (1983) recommended for bare cover solar air heater duct in Reynolds number range of 5000 – 25000: Nus = 0.014 pr 0.5 fs 0.5 Re
(1.26)
Equation of Malik and Buelow (1975) which agreed within ±10 % for Reynolds number ranging from 10000 – 20000 in solar air heater could be written as: 0.01344 Re 0.75
Nus = 1−1.586 Re −0.125
(1.27)
The well known equation of Blasius utilized for the calculation of pressure drop for smooth surfaces in solar air heaters (Sukhatme and Nayak, 2008) for 5000 < Re < 30000 is written as:
6|Page
fs = 0.079Re−0.25
(1.28)
Another equation in this range (Kays, 1966) is given by: 1 √4f s
= −0.8 + 0.87 ln Re√4fs
(1.29)
and in the range of 30000 < Re < 100000 Eq. (1.29) closely can be approximated as: fs = 0.046 Re−0.2
(1.30)
Moody chart could also be utilized for friction data in fully developed flow in smooth ducts. However, a number of researchers have focused their study towards the enhancement of thermal performance of conventional solar air heaters, but are limited to only one side glass cover. As the glass covers provided in solar air heaters affect the thermal performance, the increment in the number of glass covers would be the reason behind the better thermal performance. As such, smooth solar air heaters if provided with glass covers on three absorber plate sides might result in better performance. 1.4 EFFECT OF ROUGHNESS AND FLOW PARAMETERS IN SOLAR AIR HEATERS Use of artificial roughness of different configurations has been used in plenty to enhance the heat transfer rate in solar air heaters during the last decades. Varying magnitudes of roughness result in varying values of heat transfer and friction factor enhancement. The wide range of relative roughness height covered was 0.001-0.0333. The data was correlated according to the law of wall similarity, by the friction similarity function (Webb et.al., 1971, a, b). + u+ = e e
2
2e D + 3.75 f + 2.5 ln
(1.31)
Dipprey and Sabersky, (1963) developed a heat momentum transfer analogy relation for flow in sand-grain roughened tubes. Three rough tubes were tested, having effective roughness ratios equal to 0.0488, 0.0138 and 0.0024 in the Reynolds number range of 60000 to 500000 in while the Prandtl number ranged from 1.2 to 5.95. The correlation developed was:-
7|Page
CF
2C H −1 CF
+ Af = g e+, Pr
(1.32)
2
Based on the approach considered by Han, (1984), analysis for the effect of artificial roughness was made by Prasad and Saini, (1988), for heat transfer and friction factor in a solar air heater using small diameter wire artificial roughness on the absorber surface, having relative roughness pitch of 10, 15, 20 and relative roughness height of 0.020, 0.027 and 0.033 to predict for a correlation for the average Nusselt number written under as: f/2
Nu = 1+
Re Pr
p e
(1.33)
f/2 4.5(e + )0.28 Pr 0.57 −0.95( )0.53
(Han et al., 1991) studied the effect of parallel and V-shaped staggered discrete ribs and found out that 600 staggered discrete V-shaped ribs provide higher heat transfer than that for the parallel discrete ribs. Experiments were conducted by (Lau et al., 1991 a, b, c) to study the effect of discrete V-shaped ribs on turbulent heat transfer and friction for fully developed flow of air in a square channel. They found that the average Stanton number for the inclined 450 and 600 ribs was 20-35% higher than in the 900 full rib cases. (Gupta et al, 1993) used transverse wire roughness on the top surface in a solar air heater to investigate for the effect of solar air heater duct aspect ratio and relative roughness height for a relative roughness pitch of 10 and flow Reynolds number of 3000-18000 to arrive at the following correlations: e
W
for e+ < 35, Nur = 0.000824(D )−0.178 ( H )0.288 (Re)1.62 e
W
for e+ ≥ 35, Nur = 0.00307(D )0.469 ( H )0.245 (Re)0.812
(1.34) (1.35)
Studies conducted by Saini and Saini, (1997) deals with the effect of expanded wire mesh geometry parameter of relative long way length of mesh, relative short way length of mesh and relative roughness height of mesh on heat transfer. Comparison of thermal performance of roughened absorber plate fixed with staggered discrete V-apex (up and down) was done by (Muluwork et al., 1998, 2000). The increase of relative roughness length ratio in the range of 3-7, increases Stanton number. Boosting in Stanton number ratio was found to be of order of 1.32-2.47. (Karwa et. al., 1999) developed heat transfer coefficient and friction factor correlations in rib-roughened solar air heater duct for transitional flow. 8|Page
Verma and Prasad, (2000) developed the correlation for heat transfer in a top side artificially roughened solar air heater for fully developed turbulent flow as under: p
e
p
e
Nur = 0.08596(e )−0.054 (D )0.072 (Re)0.728 , for
e+ ≤ 24
(1.36)
Nur = 0.02954(e )−0.016 (D )0.021 (Re)0.802 , for e+ > 24
(1.37)
(Bhagoria et al., 2002) used wedge shaped transverse repeated rib roughness on one broad heated wall of solar air heater duct and generated data pertinent to friction and heat transfer. They analyzed that the presence of wedge shape ribs yield maximum enhancement in Nusselt number, about 2.4 times as compared to smooth duct. Nusselt number increases and attains maximum value at a wedge angle of about 100 and then sharply decreases with increasing wedge angle beyond 100. The correlations developed were:−4
e
1.21
Nu = 1.89 × 10 Re exp
−1.5 ln
φ
0.426
D
p
2.94
e
× exp
−0.71 ln
p
2
e
φ
−0.018
10
×
2
10
f = 12.44 e D
(1.38) 0.99
φ
0.49
10
Re−0.18
p
−0.52
(1.39)
e
(Momin et al., 2002) experimented on flow through duct roughened with V-shape ribs attached to the underside of one broad wall of the duct, to collect data on heat transfer and fluid flow characteristics. They observed that the Nusselt number increases with an increase of Reynolds number. It was found that for relative roughness height of 0.034 and for angle of attack of 600, the V-shaped ribs enhance the values of Nusselt number by 1.14 and 2.3 times respectively over inclined ribs and smooth plate case at Reynolds number of 17034 and arrived the correlations as:Nu = 0.067Re0.888 e D f = 6.266 e D
0.565
α
0.424
α
−0.093
60
−0.077
60
× exp
2 −0.782 ln α 60
2 Re−0.425 exp[−0.719ln α 60 ]
(1.40) (1.41)
Karwa, (2003) had conducted experimental study on heat transfer and friction characteristics in a high aspect ratio duct with transverse, inclined, V-up continuous and V-down 9|Page
continuous, V-up discrete ribs and V-down discrete ribs. He investigated that enhancement in Stanton number over smooth duct was found to be 65-90%, 87-112%, 102-137%, 110147%, 93-134% and 102-142% respectively. The friction factor ratio for V-up continuous and V-down continuous, V-up discrete ribs and V-down discrete ribs was found to be 3.92, 3.65, 2.47 and 2.58 respectively and the correlations arrived are: G = 32.26e−0.006 W/H
0.5
p/e
2.56
−0.4
p/e
exp 0.7343 ln p/e
2
e+
−0.08
(1.42)
for 7 ≤ e+ ≤ 20 R = 1.66 e+
−0.0078
W/H
2.695
exp −0.762 ln p/e
2
e+
−0.075
(1.43)
for 20 ≤ e+ ≤ 60 R = 1.325 e+
−0.0078
W/H
−0.4
p/e
2.695
exp −0.762 ln p/e
2
(1.44)
(Cho et al., 2003) experimentally investigated the effect of gap in the inclined ribs on heat transfer in square duct with rib to pitch height ratio of 8 and angle of attack of 600.Experiments were carried out by maintaining the gap width same as the rib width and by varying the gap position over the duct width for parallel and cross rib arrangement on two opposite walls, they investigated that, the inclined rib with a downstream gap shows significant enhancement in heat transfer as compared to that of continuous inclined rib arrangement. Sahu and Bhagoria, (2005) investigated effect of 900 broken transverse ribs on heat and fluid flow characteristics using roughness height of 1.5 mm, duct aspect ratio value of 8, pitch in the range of 10-30 mm and Reynolds number in the range of 3000-12000. Heat transfer enhancement was reported to be 1.25-1.4 times over smooth duct. From the experiment maximum thermal efficiency was found in the order of 83.5%. The effect of relative roughness pitch, relative roughness height and relative groove position on the heat transfer coefficient and friction factor has been studied experimentally by (Jaurkur et al., 2006) using rib-grooved roughness and the correlations arrived are:
10 | P a g e
Nu = 0.00206Re0.936 e/D p
2
0.349
2
3.318
exp −0.868 ln p/e
2
g/p
1.108
exp 2.486 ln g/
3
+ 1.405 ln g/p
(1.45)
f = 0.0012Re−0.199 e/D p
p/e
0.585
p/e
7.19
exp −1.854 ln p/e
3
+ 0.8662 ln g/p
2
g/p
0.645
exp 1.513 ln g/ (1.46)
CFD investigation using ten different ribs namely rectangular, square, chamfered, triangular etc. is done by (Chaube et al., 2006). FLUENT CFD code is used for analysis using the SST k-ἐ turbulence model. The heat flux of 1100 W/m2 is provided on the absorber plate only and rib surface is kept adiabatic. Their study reported that highest heat transfer is achieved with chamfered ribs and the best performance index is found with rectangular ribs of size 3×5. (Karmare et al., 2007) experimentally study the effect of heat transfer performance of a rectangular duct with metal grit ribs as roughness element, employed on one broad wall, transferring heat to the air flowing through it. The effect of relative length, height and pitch of the metal grid ribs on the heat transfer and friction factor has been studied for the flow range of Reynolds numbers 4000-17000. It has been found that maximum heat transfer rate was reported for the set of parameters and maximum friction factor was observed for the set of parameters. Correlations for Nusselt number and friction factor were developed based on the experimental results and were given by: Nu = 2.4Re1/3 e/D
0.42
f = 15.55Re−0.26 e/D
l/s
0.94
−0.146
l/s
p/e
−0.27
−0.27
p/e
−0.51
(1.47) (1.48)
(Varun et al., 2008) experimentally used a combination of transverse and inclined ribs as roughness geometry and examined the thermal performance for the range of Reynolds number (Re), 2000-14000, pitch of ribs (p), 5-13mm, roughness height (e), 1.6mm and aspect ratio (W/H), of 10. Results show that the collector roughened with this type of roughness provides best performance at relative roughness pitch (p/e) of 8 and the correlations developed were:-
11 | P a g e
p f = 1.0858(Re)−0.3685 ( e)0.0114
(1.49)
p Nu = 0.0006(Re)1.213 ( e)0.0104
(1.50)
(Ahrwal et al., 2008) studied the effect of width and position of gap in inclined split-ribs having square cross section on heat transfer and friction characteristics of a rectangular air heater duct. The increase in Nusselt number and friction factor was in the range of 1.48-2.59 times and 2.26-2.9 times of the smooth duct respectively for the range of Reynolds numbers from 3000-18000 and the correlations arrived are: Nu = 0.0102Re1.148 e/D f = 0.5Re−0.0836 e/D
0.51
1 − 0.25 − d/w 2 0.01 1 − g/e
2
0.72
(1.51) (1.52)
Experimental study was performed by (Huang et al., 2008) for a measurement of heat transfer coefficients in a square channel with a perforation baffle on Nusselt numbers. Local heat transfer enhancement at the downstream of step baffle was found to be more significant when Reynolds number was large and when baffle height was higher. Heat transfer coefficient off centre was found to be better because of secondary flows that appeared off centre after the air flow passes through the baffle. The heat transfer enhancement in case of a baffle with holes was reported greater than that without holes. Karwa and Maheshwari, (2009) made an experimental study of heat transfer and friction in a rectangular section duct with fully perforated baffles or half perforated baffles at relative roughness pitch of 7.2-28.8 affixed to one of the broader walls. They investigated that there was enhancement of 79-169% in Nusselt number over the smooth duct for the fully perforated baffles and 133-274% for the half perforated baffles while the friction factor for fully perforated baffles was found to be 2.98-8.02 times of that for the smooth duct and 4.42-17.5 times for the half perforated baffles. The correlations arrived are: Nu = 0.0893 Re0.7608
(1.53)
f = 0.1673 Re−0.0213
(1.54)
12 | P a g e
An experimental investigation had been carried out by Bopche and Tandale, (2009) to study the heat transfer coefficient and friction factor by using artificially roughness in the form of inverted U-shaped turbulators, on the absorber surface of an air heater duct. As compared to smooth one, the enhancement in heat transfer and friction factor was reported of the order of 2.82 and 3.72 times, respectively and the correlations developed are: Nu = 0.5429Re0.7054 e/D f = 1.2134Re−0.2076 e/D
0.3619
0.3285
p/e p/e
−0.1592
−0.4259
(1.55) (1.56)
A 3D solar air heater duct provided with artificial roughness in the form of thin circular wire in arc shaped has been analyzed by (Kumar et al., 2009), using CFD. Renormalization k-ἐ turbulence model is used for analysis in FLUENT CFD code. Their study reveals the maximum value of overall enhancement ratio as 1.7 for the range of parameters investigated. A parametric study of artificial roughness geometry of expanded metal mesh type in the absorber plate of solar air heater duct has been carried out by (Gupta et al. 2009). The performance evaluation in terms of energy augmentation ratio (EAR), effective energy augmentation ratio (EEAR) and exergy augmentation ratio (EXAR) has been carried out for various values of Reynolds number and roughness parameters of expanded metal mesh roughness geometry in the absorber plate of solar air heater duct. It was investigated that the augmentation ratios decrease at faster rate with Reynolds number in order of EAR, EEAR and EXAR. It was also studied that augmentation ratios increase with increase in duct depth and intensity of solar radiation. Thermal performance of wire-screen metal mesh was experimentally studied by (Paswan et al., 2009) as artificial roughness geometry on the underside of absorber plate. The thermal performance enhancement of a solar air heater was depended strongly upon the diameter of the wire and pitch, mass flow rate, insulation and inlet temperature. It was investigated that decreasing wire pitch, thermal performance of a solar air heater increases. Sriromrein and Promvong, (2010) studied that heat transfer and friction characteristic of a rectangular duct roughened artificially with Z-shaped ribs. The enhancement in heat transfer rate and best thermal performance was reported for Z-rib inclined at 45º. (Hans et al., 2010) developed multiple V-rib roughness and performed extensive experimentation to collect data 13 | P a g e
on heat transfer and fluid flow characteristics of a roughened duct. Maximum enhancement in Nusselt number and friction factor due to presence of multi v-rib roughness has been found to be 6 and 5 times, respectively, in comparison to the smooth duct. The maximum enhancement in heat transfer has been achieved corresponding to relative roughness width (W/w) of 6. It has been observed that Nusselt number attain maximum value at 600angle of attack. The correlations proposed were:Nu = 3.35 × 10−5 Re0.92 e D exp
2 −0.61 ln α 90
p
8.54
e
0.77
× exp
W
0.43
w
−2.0407 ln
α p
−0.49
90
× exp −0.1177
2 ln W w
×
2
e
(1.57)
f= 4.47 × 10−4 Re−0.3188 e D exp −0.52 ln
α 90
2
p
0.73 8.9
e
W
0.22
w
α
−0.39
90
exp −2.133 ln
p
× 2
e
(1.58)
(Champookham et al., 2010) carried out an experimental investigation to study the effect of combined wedge ribs and winglet type vortex generators on heat transfer and friction loss behaviors for turbulent air flow through a constant heat flux channel. Experimental investigations of heat transfer, flow friction and thermal performance factor characteristics in a tube fitted with delta winglet twisted tape, using water as working fluid was done by Eiamsa-ard et al., (2010). In the study, they described the influences of the oblique deltawinglet twisted tape and straight delta-winglet twisted tape arrangements and found that the oblique delta-winglet twisted tape is more effective turbulators giving higher heat transfer coefficient than the straight delta-winglet twisted tape. A numerical investigation had been carried out by Kwankaomeng et al., (2010) to study laminar flow and heat transfer characteristics in a 3D isothermal wall square-channel with 300 staggered angled-baffles. The studied the effect of different baffle heights at a single pitch ratio of 3 on heat transfer and pressure loss in the channel. The vortex flow was created by using the 300 angled baffle cavities leading to drastic increase in heat transfer in the channel. The order of enhancement is about 100-650% for using the angled baffles with blockage ratio of 0.1-0.3. The heat transfer augmentation was associated with enlarged pressure loss ranging from 1 to 17 times above the smooth channel. A thermal enhancement factor for the inclined baffles at 14 | P a g e
blockage ratio of 0.15 was found to be highest about 2.9. (Karmare et al., 2010) had carried out analysis using CFD on solar air heater with a absorber plate roughened with metal ribs of circular, square and triangular cross-section having 540, 560, 580,600 and 620 inclinations to the air flow. The system and operating parameters studied were: e/D = 0.044, p/e = 17.5 and l/ s = 1.72. Range of Reynolds number was 3600-17000. Their study reported that maximum heat transfer is obtained with the square cross-section ribs 580 angle of attack and there is 30% enhancement in the heat transfer for square plate over smooth surface. A numerical investigation had been carried out by Promvong et al., (2010) to examine the laminar flow and heat transfer characteristics in a three dimensional isothermal wall square channel with 450 angled baffles. In order to generate a pair of mainstream wise vortex flows through the tested section, baffles with an attack angle of 450 were mounted in tandem and in-line arrangement on the lower and upper walls of the channel. Effects of different baffle heights on heat transfer and pressure loss in the channel were studied and results of the 45 0 in-line baffle were also compared with those of the 900 transverse baffle and the 450 staggered baffle. The effect of wedge-shaped transverse ribs roughness on flow through a rectangular duct of a solar air heater is studied using CFD by Gandhi et al., (2010). A 2D CFD simulation is carried out using FLUENT on a duct having relative roughness pitch of 4.5, relative roughness height of 0.022 and rib wedge angle of 150. The results of numerical analysis are in good agreement with the experimental results in terms of velocity profile and turbulence intensity. To study the effect on the thermal performance of the ribbed channel, the parallel ribs have been installed either onto one wall of the channel or, in-line, onto two opposite walls with a rib pitch-to-height ratio ranging from 6.66-20.0. (Kumar et al., 2011) have investigated for the enhancement of heat transfer coefficient of a solar air heater having roughened air duct with a provision of artificial roughness in the form of 600 inclined discrete ribs. For the relative roughness pitch of 12, relative gap position of 0.35 and relative roughness height of 0.0498, the maximum heat transfer enhancement takes place. Statistical correlations for friction factor and Nusselt number have been derived as a function of gap position, rib depth, pitch and Reynolds number. The correlations have been established to predict the values of friction factor and Nusselt number with an average absolute standard deviation of 3.4% and 3.8% respectively and have been given by:15 | P a g e
Nu = 3 × 10−5 Re0.947 e D f = 0.0014Re−0.23 e D
p
0.29
0.804
p
5.885
e 4.516
e
d
d
0.115
W 0.097
W
× exp −1.237 ln
× exp −0.944 ln
p
p
2
(1.59)
e 2
(1.60)
e
An experimental investigation for heat transfer and friction factor was carried out by (Lanjewar et al., 2011), having the characteristics of a rectangular duct roughened W-shaped ribs, that is arranged at an inclination with respect to the flow direction. The duct used, had a width to height ratio of 8, relative roughness pitch of 10, relative roughness height of 0.03375 and angle of attack of flow of 300-750 and the correlations proposed were:R=
2
2e D + 3.75 f + 2.5ln
(1.61)
e+ = √ f 2 Re e D g′ =
f
(1.62) 2
2St − 1
f +R
(1.63)
An experimental investigation was conducted by (Bhushan et al., 2011) for a range of system and operating parameters in order to analyze the effect of artificial roughness on heat transfer and friction in solar air heater duct having protrusions as roughness geometry. Maximum enhancement of Nusselt number and friction factor has been found 3.8 and 2.2 times respectively in comparison to smooth duct for the investigated range of parameters. Maximum enhancement in heat transfer coefficient has been found to occur for relative short way length (S/e) of 31.25, relative long way length (L/e) of 31.25 and relative print diameter (d/D) of 0.294. The correlations developed are: Nu = 2.1 × 10−88 Re1.452 S/e D
−3.9
12.94
L/e
99.2
d/
exp −10.4{log S/e }2 exp −77.2{log
f = 2.32Re−0.201 S/e
−0.383
L/e
−0.484
d/D
L e
}2 exp −7.83{ln
0.133
d D
}2
(1.64) (1.65)
16 | P a g e
(Pomovonge et al., 2011) experimentally studied the effects of combined ribs and deltawinglet type vortex generators (DWs) on forced convection heat transfer and friction loss behaviors for turbulent air flow through a solar air heater channel. Rectangular channel with aspect ratio of 10, height of 30 mm with Reynolds number in the range of 5000-20000 was used. They reported that combined rib and the DW provides considerable heat transfer 𝑁𝑢
augmentations, 𝑁𝑢 = 2.3 − 2.6 and also causes a moderate pressure drop increase, 𝑓/𝑓0 = 0
4.7 − 10.1, depending on the attack angle and Re values. An experimental study has been carried out by (Yadav et al., 2012) to study the effect of heat transfer and friction characteristics of turbulent flow of air passing through rectangular duct which is roughened by circular protrusions arranged in angular arc fashion. The investigation reported the maximum enhancement in heat transfer and friction factor as 2.89 and 2.93 times as compared to smooth duct. The correlations arrived are: Nu = 0.154Re1.017 p/e f = 7.207Re−0.56 p/e
−0.38
−0.18
e/D
e/D
0.521
0.176
α/60
α/60
−0.213
0.038
exp −2.023 ln α/60
exp 1.412 ln α/60
2
2
(1.66) (1.67)
CFD analysis on solar air heater is done by (Sharma et al., 2012) using V-shaped ribs roughness on the underside of the absorber plate. Finite volume method with semi-implicit method for pressure linked equation algorithm is used for computations. Reynolds number range was from 5000-15000. The results obtained show that the combined effect of swirling motion, detachment and reattachment of the fluid were responsible for the increase of heat transfer rate during CFD analysis. Nusselt number increases and friction factor decreases with increase in Reynolds number for all combination of relative roughness height (e/D) and relative roughness pitch (p/e). An average percentage deviation predicted between CFD and exact solution was found less than ±3% V-shaped rib roughness found to give high rate of heat transfer. A numerical investigation on laminar flow and heat transfer characteristics in a 3D isothermal wall square-channel fitted with in-line 450 V-shaped baffles on two opposite wall was done by (Promvong et al., 2012). The in-line V-baffles with its V-tip pointing downstream and the angle of attack of 450 relative to the flow direction were mounted repeatedly on the lower and upper walls. The V-baffled channel flow was found to be fully developed periodic flow and heat transfer profiles at about x/D=8 downstream of the tested 17 | P a g e
channel inlet. It was reported that the P-vortex flow caused by the V-baffle induced impingement flows on the channel walls leading to drastic increase in the heat transfer rate. The heat transfer in the V-baffled channel was found to be about 1-21 times higher than the smooth channel with no baffle. Experimental investigation has been carried out by (Chauhan et al., 2013) to study heat transfer and friction factor characteristics using impinging jets in solar air heaters duct. The study shows that there is considerable enhancement in heat transfer and friction factor by 2.67 and 3.5 times respectively and the correlations arrived were: Nu = 1.658 × 10−3 Re0.8512 X/Dh
0.1761
Y/Dh
0.141
Dj /Dh
−1.9854
exp−0.3498{lnDj /
Dh }2
f=
(1.68)
0.3475Re−0.5244
X
0.4169
Dh
Y
D j −1.4848
0.5321
Dh
Dh
exp −0.22210{ln Dj /Dh }
(1.69)
2
Prasad, (2013) represented the experimental results on heat transfer and thereby thermal performance of artificially roughened solar air heaters for fully developed turbulent flow. Such solar air heaters have been found to give considerably high value of collector heat removal factor (FR ), collector efficiency factor (F ′ ) and thermal efficiency (ƞth ) as compared to the corresponding values of those of smooth collectors. In the range of the operating parameters investigated, the ratio of the respective values of the parametersFR , F ′ and ƞth for the roughened collectors to the smooth collectors have been found to be 1.786, 1.806 and 1.842 respectively and the correlations arrived were:-
Nu = f 2 RePr/ 1 +
f
2
2
f= [0.95
p
0.53
e
+2.5 ln D 2e −3.75]2
4.5 e+
0.28
Pr 0.57 − 0.95
p
0.53
e
(1.70)
(1.71)
A CFD based investigation of turbulent flow through a solar air heater is carried out by Yadav and Bhagoria, (2013, a) with square sectioned transverse rib roughness. The 2D 18 | P a g e
analysis of rectangular duct is performed using ANSYS FLUENT 12.1 software and using (RNG k-ἐ) turbulence model. Analysis using four different configurations of rib roughness keeping relative roughness pitch constant at p/e = 14.29 and six different values of Reynolds number, ranging from 3800-18000, revels that the relative roughness height is a vital factor and mainly affects the rate of heat transfer rate and the increase in flow friction. An investigation has been conducted by Yadav and Bhagoria, (2013, b) by using FLUENT 12.1 and (RNG k-ἐ) turbulence model on solar air heater, using square sectioned transverse rib roughness, with different values of relative roughness pitch (7.14 ≤ p/e ≤ 17.86). 2D CFD analysis to predict the effect of small diameter of transverse wire rib roughness on heat transfer enhancement in solar air heater is done by Yadav and Bhagoria, (2013, c). In this analysis also FLUENT 12.1 software is used with (RNG k-ἐ) turbulence model. (Prasad et al., 2014) have analyzed with respect to fluid flow and heat transfer in a novel solar air heater having artificial roughness on three sides (the two side walls and the top side) of the rectangular solar air heater duct, with three sides glass covers. Equations for friction factor and heat transfer parameter have been developed. The analytical values of friction factor and heat transfer parameter have been found to be 2 to 40% more and 20 to 75% more than those of the respective values of (Prasad and Saini, 1988) for the same range of the values of operating parameters p/e, e/D and Re and fixed values of W and B. The correlations developed are:f r /2
Nur = 1+
p f r /2 4.5(e + )0.28 Pr 0.57 −0.95( e )0.53
2
W +2B 0.95
fr =
p
0.53 e
2 +2.5 ln D 2e −3.75
2 W +B
Re Pr
(1.72)
+W f s
(1.73)
Behura et al., (2016), investigated experimentally the heat transfer, friction factor and thermal performance of a novel type of three sides artificially roughened and three sides glass covered solar air heaters under fully developed turbulent flow conditions and compare well with analytical values of Prasad et al., (2014). Theoretical investigations on thermal and thermohydraulic performance of wavy finned absorber plate solar air heaters have been 19 | P a g e
reported recently by Priyam and Chand (2016).Chouksey and Sharma, (2016), investigated for the thermal performance characteristics of solar air heater having its duct with blackened wire screen matrices. However, in all the above cases, provision of artificial roughness and glass cover has remained limited to only one side (top side) of the solar air heater duct except those of the recent ones (Prasad et al., 2014 and Behura et al., 2016), wherein it has been concluded that three sides roughened and glass covered solar air heaters perform even better than those of one side roughened and glass covered solar air heaters, but friction factor also increases. 1.4.1
Optimization of the System Parameters As the enhancement of heat transfer coefficient is attempted by providing artificially roughness, it always goes with an increment of pressure drop and the requirement of pumping power is increased. So, there is a need to optimize the system parameters to maximize heat transfer while keeping friction losses as low as possible. Despite plenty of works dealing with the effect of artificial roughness on heat transfer and friction factor in solar air heaters, very few dealt with the thermo hydraulic performance in 𝑒
them. The thermo hydraulic optimization parameter, 𝑒 + = 𝐷
𝑓 2
𝑅𝑒, known as roughness
Reynolds number, has been considered to arrive at the optimal thermo hydraulic performance condition. Covering a wide range of the values of heat transfer surface area, overall heat conductance and flow friction power, (Webb and Eckert, 1971), arrived at the conclusion that the value of the parameter, 𝑒 + = 20, gives the optimal thermo hydraulic performance. For optimal thermo hydraulic performance of circular tube roughened with ribs, Lewis, (1975), introduced new efficiency parameters (𝐿−1 , 𝐵 −1 , 𝐶 −1 , 𝐺𝐻 𝑎𝑛𝑑 𝑅𝑀 ) and arrived at the conclusion that the value of the roughness Reynolds number, + = 𝑒 + = 20, corresponds to the optimal thermo hydraulic condition. Sheriff and Gumbley, (1966), has studied for annulus with wire type roughness and found the value of roughness Reynolds number, 𝑒 + = 35, for the optimal thermo hydraulic condition. Optimal thermo hydraulic performance analysis in one side artificially roughened solar air heater of (Prasad and Saini, 1991), has obtained a particular set of values of roughness and flow parameters to give the value of roughness Reynolds number, 𝑒 + = 24, for optimal thermo hydraulic condition. 20 | P a g e
Verma et al., (1991) have given a technical note on ‘optimization of solar air heaters of different designs’, to obtain the optimum flow channel depth and mass flow rate in 10 different designs of solar air heaters and have found that a single glazing solar air heater operating under double flow configuration gives the best performance. Hegazy, (1995) has developed an analytical criterion to determine the optimal flow channel depth of conventional flat plate solar air heaters. Gupta et al., (1997) have shown the effect of roughness parameters on the thermal as well as the thermo hydraulic performance of roughened solar air heaters to design the optimal operating conditions. A technical note on ‘optimal thermo hydraulic performance of flat plate solar air heaters, operating with fixed or variable pumping power’, has been given by Hegazy, (1999). Optimal thermo hydraulic performance of solar air heaters has been investigated (Verma and Prasad, 2000), for the maximum heat transfer and minimum pressure drop to arrive at the conclusion that the value of 𝑒 + = 24,corresponds to the optimal thermo hydraulic performance. Saha and Mahanta, (2001) have investigated for the performance of second-law modeling of flat plate collectors with the objective of describing collector performance when entropy generation is minimum. Karwa et al., (2001) have investigated for thermo hydraulic performance of solar air heaters with chamfered repeated rib-roughness on the air flow side of the absorber plates for the range of flow Reynolds number, 3750-16350. Mittal and Varshney, (2005), has worked on optimal thermo hydraulic performance of wire mesh packed solar heater. Second law optimization of solar air heater having chamfered rib groove as a roughness element has been analyzed by Layek, et al., (2007). Karmare and Tikekar, (2008), have optimized the thermo hydraulic performance of solar air heater integrated with metal rib as roughness element. Karmare and Tikekar, (2009) have investigated for the effect of metal rib grifts on absorber plate at 600 of angle of attack to the flow direction of air on the thermo hydraulic performance of solar air heater. Siddhartha et al., (2012) have undertaken the work with an objective to develop and implement a trained particle swarm optimization algorithm for prediction of an optimized set of design and operating parameters for a smooth flat plate solar air heater. Yadav and Bhagoria, (2014), investigated numerically a CFD based thermo hydraulic performance analysis of an artificially roughened solar air heater having equilateral triangular sectioned rib roughness on the absorber plate. A numerical investigation is conducted (Yadav and Bhagoria, 2014) to analyze the two-dimensional 21 | P a g e
incompressible Navier–Stokes flows through the artificially roughened solar air heater for relevant Reynolds number range of 3800 to 18,000and twelve different configurations of equilateral
triangular
sectioned
rib
roughness (𝑝/𝑒 = 7.14– 35.71 and 𝑒/𝐷 =
0.021– 0.042). Sharma and Kalamkar, (2015), reviewed the thermo hydraulic performance of solar air heater having artificial roughness elements and reported the various artificial roughness geometries used by investigators to enhance the heat transfer, which is attained by increasing the pressure drop across the surfaces of the absorber plate of the solar air heater and its effect on heat transfer and friction factor through experiments.
1.5 OBJECTIVES OF THE PRESENT WORK All the above mentioned works on thermo hydraulic and optimal thermo hydraulic performance deal with one side roughened solar air heaters. Three sides roughened solar air heater of Prasad et al, (2014) and Behura et al, (2016), have been reported to be even more efficient than those of one side roughened solar air heater. Therefore, optimal thermohydraulic performance analysis and investigation of three sides roughened solar air heaters is required and the present work has been taken up with the following objectives: 1) To analyze for the optimal thermo hydraulic performance of the three sides artificially roughened solar air heater for maximizing heat transfer while keeping friction loss minimum. 2) To develop the experimental set-up to perform experiments under actual outdoor conditions for data collection with a view towards validation of the optimal thermo hydraulic performance analysis for such solar air heater. 3) To obtain the results with respect to Nusselt number, Stanton number and friction factor from the data collected in such solar air heater. 4) To derive the correlations for heat transfer and friction factor in such solar air heaters. 5) To represent and discuss the effect of roughness and flow parameters on heat transfer, friction factor, collector performance parameters and thermo hydraulic performance in such solar air heater. 6) To obtain and represent the thermal efficiency curves for such solar air heaters. 7) To obtain the optimal thermo hydraulic performance results and represent the optimal thermo hydraulic performance curves for such solar air heater. 22 | P a g e
CHAPTER - 2 OPTIMAL THERMOHYDRAULIC PERFORMANCE ANALYSIS
2.1 INTRODUCTION It has already been pointed out in the previous chapter that the provision of artificial roughness on the underside of the absorber plate of solar air heaters leads to the enhancement of heat transfer coefficient and friction losses. In view of this, there is a need to critically examine the quantitative influence of the roughness and flow parameters to attain the optimal thermo hydraulic performance condition, while keeping the pumping power as low as possible. The fundamental parameters which control the momentum and heat transfer for a roughened surface are momentum transfer function (RM) and heat transfer roughness function (GH). The present chapter has been devoted to the analysis of optimization aspects of three sides roughened and glass covered duct system that would possibly lead to the quantitative evaluation of various physical and flow parameters which would help in designing such solar air heaters. The effect of various efficiency parameters have been compared to those of the referred ones. 2.2 OPTIMIZATION METHODOLGY The solar air heater duct model of width, W, height, B and length, L, as shown in Fig 2.1a with provision of roughness elements at pitch, p of height, e on the absorber plates has been considered for analysis. The methodology of optimization adopted is similar to those of (Lewis, 1975 a, b; Prasad and Saini, 1991), that a dimensionless parameter, e+ (roughness Reynolds number), could plausibly form the basis to analyze the optimal thermo hydraulic performance of three sides artificially roughened solar air heaters. The correlations developed (Prasad et al., 2014), for friction factor and heat transfer written here under as Eqs. (2.1) and (2.2) respectively has been utilized. Fig. 2.1(b) shows typically the pitch and height of the roughened elements.
23 | P a g e
f3r = St 3r =
W +2B f r +W f s 2(W +B)
(2.1) f 3r /2
f 1+√( 3r )[4.5 2
p 0.53 e + 0.28 Pr 0.57 −0.95 ]
(2.2)
e
24 | P a g e
where, W/B>>1, and fr is as that of (Webb et al., 1971), considered by (Prasad and Saini, 1991), written under as Eq. (2.3) 2
fr = 0.95
p 0.53 D +2.5 ln e 2e
(2.3)
2
−3.75
Consequently, substituting forfr , Eq. (2.1) could be written to be Eq. (2.4) as under: 2 2 p 0.53 D 0.95 +2.5 ln −3.75 e 2e
W +2B
f3r =
+W f s
(2.4)
2 W +B
Now,
substituting
for
the
parameters,
heat
transfer
roughness
function, GH = 4.5(e+)0.28 pr0.57 and momentum transfer roughness function, R M = 0.95 P e St 3r =
0.53
, Eq. (2.2) could be written as Eq. (2.5) under:
f 3r /2
1
f 1+√( 3r ) 2
G H −R M
where, e+ = e D
f 3r 2
(2.5)
Re
(2.6)
The optimization parameter, Ƞ,for the present case of three sides roughened solar air heater is defined as (Lewis, 1975; Prasad and Saini, 1991) S t 3r
Ƞ=
3
S t 3gS f 3r
= f 3r , GH , R M
(2.7)
fs
which can further be written as: Ƞ = Ƞ f 3r , B−1 , C −1
(2.8)
and could further also be represented as: Ƞ = Ƞ f 3r , L−1
(2.9)
25 | P a g e
where, B−1 = GH − Pr t R M = 4.5(e+)0.28 Pr 0.57 − Pr t × 0.95(p/e)0.53 C−1 = 2.5ln (e+) + 5.5 − R M = 2.5ln (e+)5.5 − 0.95
p
(2.10)
0.53
(2.11)
e
L−1 = C−1 − B−1 = 2.5ln (e+) + 5.5 − GH − R M 1 − Pr t
(2.12)
Also, that, the following equations for smooth solar air heater are used in Eq. (2.7) fS = 0.079Re−0.25
(2.13)
St s = 0.023Re0.2 pr −2/3
(2.14)
The values of fr , fs and St s have been worked out by substituting the values of geometrical and operating parameters W, B, p/e, e/D and Re in Eqs. (2.3), (2.13) and (2.14) respectively, which have further been utilized to work out for the values of f 3r , St r and Ƞ, by the respective equations. 2.3 EFFECT OF EFFICIENCY PARAMETERS The values of the parameters, e+, B-1, C-1, and L-1 have also been worked out by the respective equations, taking the value of the turbulent Prandtl number, Pr t , equal to 0.90. The values of the parameters as above have been worked out, assuming that W/B >>1, p/e ≥ 10 and e/D, so selected that the roughness height is of the order of or slightly greater than the viscous sub-layer thickness of the hydrodynamic boundary layer over a flat plate. The values of flow Reynolds number vary from 4000 to 20,000. Since, the parameter, e+, has remained the optimization parameter in literature, Figs. 2.2, 2.3 & 2.4 have been drawn to see the effect of e+ on the parameters C-1, B-1, and L-1, for the present analysis and that of (Prasad and Saini, 1991). It could be seen from Figs. 2.2 & 2.3 that the values of the parameters B-1 and C-1 increase with increasing values of e+.
. 26 | P a g e
(1) p/e=10(Preasent case) (2) p/e=10(Prasad and Saini,1991) (3) p/e=20(Present case) (4) p/e=20(Prasad and Saini,1991) (5) p/e=30(Present case) (6) p/e=30(Prasad and Saini,1991)
Re 4000 20000 e/D=0.0225 (Preseant Case) e/D=0.0205 (Prasad and Saini,1991)
(1)
10 (3)
8
(2)
(5)
(4)
6
-1
B 4
(6)
2
0 5
10 15 20 25 30 35 40 45 50 55 60 65 70
e e / D f 3r / 2 Re +
-1
Fig. 2.2. Effect of e on B for varying p/e
27 | P a g e
Figs. 2.2 & 2.3 also show the curves for one side artificially roughened solar air heater, based on the heat transfer as friction factor correlations developed (Prasad and Saini, 1988), and written under as Eqs. (2.15) and (2.16): f=
St =
W +2B f S +W f r
(2.15)
2(W +B) f/2
(2.16)
p 0.53 1+ f 2[4.5 e + 0.28 Pr 0.57 −0.95 ] e
It is clear from Figs. 2.2 & 2.3 that values of both the parameters, B-1 and C-1 are higher in the case of three sides artificially roughened solar air heater than those of only one side artificially roughened solar air heater (Prasad and Saini, 1988). Fig. 2.4 shows that the value of the efficiency parameter L-1,increases with the increasing value of e+, up to certain maximum value when after its value decreases with increasing value of e +, for every curve drawn for varying values of the relative roughness pitch, p/e, equal to 10, 20 and 30. It appears that the maximum values of the parameter, L-1, could be expected between 20-30. To ascertain the particular value of e+, Table-2.1 and Fig. 2.5 have been prepared, which show that e+ = 23 gives the maximum value of the efficiency parameter, L-1, for all values of p/e. Therefore, the optimal thermo hydraulic performance equation for three sides artificially roughened solar air heater could be written as: e e+ opt = D
f 3r 2
Re = 23
Hence, the roughness Reynolds number, e+ = e D
(2.17) f 3r 2
Re constituting a specific set of
values of roughness and flow parameters, p/e, e/D and Re to obtaine+ opt = 23, could result in the maximum heat transfer for minimum pressure drop. The set of values of p/e, e/D and Re, vary with variance in either of the values of p/e, e/D and Re, individually or combined, which may form the basis for preparing design curves to give the optimal thermo hydraulic performance of three sided artificially roughened solar air heaters in a similar way as those of (Prasad and Saini, 1991).
28 | P a g e
Re 4000 20000
(1) p/e=10(Present Case) (2) p/e=10(Prasad and Saini,1991) (3) p/e=20(Present Case) (4) p/e=20(Prasad and Saini,1991) (5) p/e=30(Present Case) (6) p/e=30(Prasad and Saini,1991)
e/D=0.0225 (Present Case) e/D=0.0205 (Prasad and Saini,1991)
14
(1)
12
(3)
(2)
10
(4)
(5)
8 C
(6)
-1
6
4
2 5 10 15 20 25 30 35 40 45 50 55 60 65 70
e e / D f 3r / 2 Re +
-1
Fig. 2.3. Effect of e on C for varying p/e 29 | P a g e
e/D = 0.0225 (constant for p/e= 10,20 &30) (1) p/e=10 Re 4000 20000 (2) p/e=20 4.8 (3) p/e=30
4.6 4.4 4.2 4.0 3.8 3.6 -1
L
(1)
(2)
(3)
3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 5
10
15
20
25
30
35
40
45
50
55
60
65
e e / D f 3r / 2 Re +
-1
Fig.2.4. Effect of e on L for varying p/e
30 | P a g e
4.2
eopt 23
e
+
23 25 22 26 24 28 30 17 34
4.1
4.0 -1
L
3.9
3.8
10
15
20
25
30
35
40
p/e -1
+
Fig.2.5. The efficiency parameter L as a function of p/e & e
31 | P a g e
Table-2.1 Range of efficiency parameter L-1 as a function of e+ and p/e p/e = 10 e+
p/e =20 L-1
e+
p/e =30 L-1
e+
L-1
17
4.143224
17
4.000322
17
3.793982
22
4.180075
22
4.037173
22
3.830833
23
4.181923
23
4.039021
23
3.832681
24
4.177088
24
4.034186
24
3.827846
25
4.181683
25
4.038781
25
3.832441
26
4.179871
26
4.036969
26
3.830629
28
4.17343
28
4.030528
28
3.824188
30
4.163822
30
4.02092
30
3.81458
34
4.137277
34
3.994375
34
3.788035
Therefore, the optimal thermo hydraulic performance equation given under as, e+ opt = e
D
f 3r 2
Re = 23, has formed the basis for preparing optimal performance curves for three
sides artificially roughened solar air heater as shown in Figs. 2.6.1, 2.6.2 and 2.6.3.
32 | P a g e
0.09
0.08
0.07
0.06
e/D
4000
0.05
5000 6000
0.04
7000 8000
0.03
0.02 10
15
20
25
30
35
40
p/e Fig.2.6.1 Optimal thermohydraulic performance curves for three sides artificially roughened solar air heater
33 | P a g e
0.030 0.028 Re=9000
0.026
10000 0.024
11000 0.022
12000 13000
0.020
e/D
14000
0.018 0.016 0.014 0.012 10
15
20
25
30
35
40
p/e Fig.2.6.2 Optimum thermohydraulic performance curves for three sides artificially roughened solar air heater
34 | P a g e
0.018
Re=15000
0.016
16000 17000 e/D
0.014
18000 19000 20000
0.012
0.010
10
15
20
25
30
35
40
p/e Fig.2.6.3 Optimum thermohydraulic performance curves for three sides artificially roughened solar air heater
35 | P a g e
Table – 2.2 shows the optimum values of roughness Reynolds number e+ opt found in literature for different roughness geometry with range of values of roughness and flow parameters for fully developed turbulent flow, with the present value of e+ opt = 23. Table-2.2 Values of 𝒆+ 𝒐𝒑𝒕 for different roughness geometries for fully developed turbulent flow Sl.No
References
Roughness and flow p/e
e/D
Re
0.018-
1×104–
0.035
2×103
0.01-
6×103–
0.04
10×103
0.02-
1×104–
0.10
1×107
Prasad and Saini, Rectangular with top 10-40
0.020-
3×103–
(1991)
0.033
20×103
0.010-
5×103– 20×103
. 1.
duct geometry Sheriff
and Annulus with wires
10
Gumley, (1966) 2.
Webb and Eckert, Rectangular with ribs
10-40
(1971) 3.
Lewis, (1975 b)
Circular
tubes
with 2-60
ribs 4.
5.
7.
+ 𝑒𝑜𝑝𝑡
side wires
Verma
and Rectangular with top 10-40
Prasad, (2000)
side wires
0.030
Present case
Rectangular with three 10-30
0.013 – 4×103–
sides wires
0.025
35
20
20
24
24
23
20×103
2.4 THERMO HYDRAULIC PERFORMANCE Fig. 2.7 compares the optimal thermo hydraulic performance curves, corresponding to the e equation e+ opt = D
f 3r 2
Re = 23 for the present solar air heater and those of (Prasad and
e Saini, 1991), corresponding to the equation, e+ opt = D
f 2
Re = 24 for given values of
Reynolds number. This figure shows that for the same value of flow Reynolds number and relative roughness pitch, p/e, values of relative roughness height,(e/D) is low for the present solar air heater.
36 | P a g e
(1) Re=4000
0.10 0.09
(2) Re=4000
0.08 0.07 +
0.06
e =24 (Prasad and Saini,1991)- 1,3,5 +
e =23 (Present case)- 2,4,6
e/D 0.05 0.04 (3) Re=10000 (4) Re=10000
0.03 0.02
(5) Re=20000 (6) Re=20000
0.01 10
15
20
25
30
35
40
p/e Fig. 2.7 optimal thermohydraulic performance curves
37 | P a g e
Fig. 2.8 shows the optimal range of relative roughness height, (e/D), for 10 ≤ p/e ≤ 30, at varying values of flow Reynolds number from 4000-20000, for the present case and that of (Prasad and Saini, 1991), which shows that the range of optimal values of (e/D),for the present case is lower than that of (Prasad and Saini, 1991), and that too decreases with increasing values of flow Reynolds number. It could also be seen that the range of the value of (e/D) , goes on decreasing for increasing values of flow Reynolds number. Table -2.3 shows the values of flow Reynolds number for varying values of e/D at given values of relative roughness pitch, p/e, equal to 10 for the present case of e+ opt = 23 and that of (Prasad and Saini, 1991), e+ opt = 24.It could be seen that for the same values of p/e and e/D, lower values of flow Reynolds number for the present case, correspond to the optimal thermo hydraulic performance. Lower value of flow Reynolds number yields in higher grade energy collection, since mass flow rate involved will be less. For three sides roughened solar air heater (Prasad et al., 2014) the value of the average friction factor, f3r will be more than that of the one side roughened solar air heater, f, of (Prasad and Saini, 1988) for comparison, the present optimal thermo hydraulic performance Eq. (2.18) is written under together with the optimal thermo hydraulic performance equation of (Prasad and Saini, 1991), as Eq. (2.19): e e+ opt = D e e+ opt = D
f 3r 2
f 2
Re = 23
Re = 24, (Prasad and Saini, 1991)
(2.18)
(2.19)
Now, it can be attributed that smaller value of e+ opt , for the present case, will lead to smaller value of flow Reynolds number to result in higher grade energy collection. Therefore, it could be concluded from the present analysis that three sides roughened solar air heaters are quantitatively even better than those of one side roughened solar air heaters of (Prasad and Saini, 1991), w.r.t. optimal thermo hydraulic performance conditions.
38 | P a g e
(e / D)opt for10 p / e 30
0.10
e/D
0.08
1
0.06
2 1
+
(e/D)optRange for e =24 (Prasad and Saini,1991) [1-1-1-1] +
(e/D)optRange for e =23 (Present case) [2-2-2-2]
2 0.04
0.02 1 2 1
2
0.00 0
Re2Re1
4000
8000
12000
16000
20000
Re Fig.2.8 .Optimal range of e/D
39 | P a g e
Table-2.3 Values of Re at varying value of e/D and p/e=10, for the optimal thermo hydraulic condition
e/D
Re1
(e+=24),
Prasad Re2 (e+=23), present case
&Saini,1991
0.01
24413.65
19901.10
0.02
12206.83
11450.553
0.03
8137.885
7300.369
0.04
6103.413
5725.277
0.05
4882.731
4780.221
0.06
4368.942
4074.184
0.07
4187.665
3904.158
0.08
3951.707
3862.638
From Fig. 2.8, it can be concluded that the range of the values of the parameter, (e/D) at lower values of flow Reynolds number is more than those at higher values of flow Reynolds number, providing more options for selecting the values of (e/D) . The optimal range of (e/D),(Prasad and Saini, 1991), represented above that of the present case, in this figure, would attribute that for the same range of the value of(e/D) , one side roughened and glass covered solar air heaters (Prasad and Saini, 1991), will have higher value of flow Reynolds number, resulting in lower grade of energy collection under optimal thermo hydraulic condition than that of three sides roughened and glass covered solar air heaters. For example, at a value of 𝑒/𝐷 = 0.06, the value of flow Reynolds number for the present case of Re2 lower than that of Re1 (Prasad and Saini, 1991). Therefore, for the similar operating condition three sides roughened and glass covered solar air heaters will perform thermo hydraulically better than those of one side roughened and glass covered solar air heaters.
40 | P a g e
CHAPTER – 3 SYSTEM DEVELOPMENT AND INVESTIGATIONS
3.1 INTRODUCTION To verify the expressions developed for heat transfer and friction factor parameters (Prasad et al, 2014) in three sides artificially roughened solar air heater, experimental results have been reported by the authors (Behura et al, 2016) with respect to the effect of roughness and flow parameters on heat transfer and friction factor. Similarly, an experimental set up has been developed to perform experiment and collect wide range of data, to validate the analyzed expressions developed for optimal thermo hydraulic performance of three sides roughened and glass covered solar air heater. Similar size of glass covered smooth solar air heater has been developed for experimentation. 3.2 SOLAR AIR HEATER DUCT MODELS Figs. 3.1 (a) and (b) show the two solar air heater duct models of similar size having high aspect ratio: (i) smooth with three sides glass covers and (ii) three sides roughened with three sides glass covers. Circular wire of different diameters has been provided on the absorber plate at varying pitches to serve as an artificial roughness element. The two ducts have been made similar in dimensions under similar conditions. Ambient air has been induced by two separate inlets but, exhausted by means of a single outlet. Wooden bottom sheet of 25 mm thickness has been used for back insulation in both solar air heater ducts and two sides insulation in smooth solar air heater duct. 4mm thick glass covers have been provided. An air gap of 25 mm has been provided for each duct resulting in a duct cross section of 200 mm × 25 mm each.
41 | P a g e
Figs. 3.1 (a) and (b) Solar air heater duct models
Out of the total duct length of 2130 mm, 1500 mm portion was utilized for instrumentation and the balance length of 630 mm served as the entry length for flow stabilization. In three sides roughened and glass covered solar air heater duct, the roughness elements of small diameter wires have been provided on the flow side of the absorber plate normal to the ambient air flow direction at varying pitch.
3.3 EXPERIMENTAL SET-UP Figs. 3.2 (a) and (b) show the schematic diagram and top view of experimental set-up respectively, combining the two solar air heater ducts (three sides roughened and smooth) with a single blower to run simultaneously. Directions denoted by arrows X and Y represent the ambient air flow in the roughened and smooth ducts respectively. Both the ducts are having three sides glass covers. Thermocouples were provided on the absorber plates to measure temperature, while digital thermometers were used to measure the air temperature in the air duct. The photographs of experimental set- up with instruments used have been shown in Figs. 3.3, while Fig 3.4 shows the experimental set up with instrumentation.
42 | P a g e
3.3.1
Absorber Plates and glass covers Black painted 22 SWG, G.I. sheets of 2000 mm length, 200 mm width and 25 mm height has been used as absorber plates in both the ducts. Fig.3.5 shows a typical artificially roughened absorber plate. Thin circular wires were soldered to the underside of the absorber plate to provide artificial roughness. Figs. 3.6 and 3.7 show the respective three sides roughened and smooth absorber plates.
3.3.2
Test Section and Entry Section of the Duct As mentioned in the previous section, an absorber plate length of 2000 mm has been instrumented to form test section, in which the entry length of 500 mm which also included about 100 mm long bell-mounted-converging section, that was 10 times the hydraulic diameter. Test sections and entry sections for both the roughened and smooth ducts were similar in dimensions. Entry and test length segments of both the ducts were provided with wooden covers and glass covers of 4 mm thickness. The entry section has the roughness geometry similar to the test section in the roughened duct.
43 | P a g e
All dimensions are in mm X-Three sides roughened and glass covered solar air heater duct inlet Y- Smooth and three sides glass covered solar air heater duct inlet P- Unheated wooden covered entry section Q- Glass covered test section R- Glass covers S- Flange tape orifice-meters
Fig. 3.2(a) Schematic diagram of the experimental set-up
44 | P a g e
Fig. 3.2 (b) Top view of the experimental set-up
Fig. 3.3 Photograph of experimental set-up with two ducts
45 | P a g e
Fig. 3.4 Photograph of experimental set-up with measuring instruments
Fig.3.5 Photograph of the roughness layout on top side of three sides roughened solar air heater
46 | P a g e
Fig. 3.6 Typical three sides artificially roughened absorber plates
Fig. 3.7 Typical three sides smooth absorber plates
47 | P a g e
Fig. 3.8 Photograph of digital pyranometer system 3.4
INSTRUMENTATION
3.4.1
Blower and Electric Motor The ambient air was sucked through the solar air heater duct system by means of a blower powered by a 3-phase, 5 H.P. motor. The power of the motor has to be such that it is capable of sucking air simultaneously through both the duct systems at desired mass flow rates to provide the maximum Reynolds number of 20000.
3.4.2
Flow Control Arrangement Air flow rate through the smooth and three sides roughened duct system was controlled by means of 3- phase auto-variac connected in series with the blower motor. Voltage regulation of the variac provided controlled supply of power to motor resulting in desired blower speeds.
3.4.3
Air Flow Measurements Air flow measurement was accomplished by a calibrated flange-taps type orifice-meter which was designed, fabricated and finally fitted in the 76.2 mm diameter pipe that carried the air flow from the duct system. Figs.3.9 and 3.10 show the details, specification and location of orifice-meter. The mass flow rate through the orifice-meter is expressed in the
48 | P a g e
terms of physical parameters of the orifice-meter and the pressure difference across it, by Eq. (3.1) written under: m = Cd A2
2ρ P 1 −P 2 1/2 1−β 41
(3.1)
where, Cd is the coefficient of discharge.
Fig. 3.9 Orifice plate location and specification 49 | P a g e
Fig. 3.10 Details of the flange-taps orifice meter construction 50 | P a g e
Coefficient of discharge of the orifice-meter has been determined by the observation of flow rate values through a pitot-tube. The flow rate has been determined by measuring average flow velocity using a pitot-tube, using the relationship: V = √2∆P/ρ
(3.2)
where, ∆P is pressure difference by pitot-tube. The mass flow rate has been determined by using the relationship: m = ρAC V
(3.3)
where, AC is the cross-sectional area of the pipe. The experimental values of Cd in Eqn. (3.1) have been plotted as a function of throat Reynolds number in Fig. 3.11, by using Murdock equation (Ozisik, 1985) for an orificemeter with flange-taps and are given by: Cd = C0 + C
10 4
a
Rd
(3.4)
where, the values of C0 and C for 76.2 mm diameter pipe, can be seen from Table no. 21.5 of the reference (Ozisik, 1985) as, C0 = 0.60394, C = 0.03270 and the exponent a=1, for flange-taps. Mass flow rate in the orifice-meter pipe bas been determined from Eq. (3.1) using experimental values of pressure p1 and p2. 3.4.4
Temperature and Pressure Drop Measurement Calibrated copper-constantan thermocouples of 28 SWG have been used to measure the plate temperature and the air temperature was measured by a digital thermometer. Thermocouples were soldered on the absorber plates at six sections. The thermocouple wires passing through connectors were connected to selector switch through copper connecting wires of 28 SWG. Plate and air temperature readings were noted from the digital display. Thermocouple arrangement for the plate temperature measurement has been shown in Fig. 3.12.The duct pressure drop was measured by means of a multi-tube manometer. The pressure signals were fed to the manometer through PVC piping attached to pressure taps of 6 mm diameter PU-hose connector inserted along the centre line of the bottom wall of the 51 | P a g e
duct. Pressure taps arrangement for pressure drop measurement and digital thermometer for air temperature measurement has been shown in Fig. 3.13.
1.0
10 4 C d 0.60394 0.03270 Rd
a
Experimental values of C
d
0.8
0.6
Cd
0.4
0.2
0.0 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
(Throat Reynolds Number) Rd 103 Fig. 3.11 Orifice-meter Calibration
52 | P a g e
Dimensions are in mm Fig. 3.12 Thermocouple arrangement on top and side of the absorber plates
Fig. 3.13 Arrangement of air temperature sensors and pressure taps along the duct length 53 | P a g e
3.4.5
Solar Radiation Intensity Measurement Intensity of solar radiation was measured by means of a standard digital display pyranometer system in terms of W/m2.
3.5
EXPERIMENTAL PROCEDURE Test runs were conducted under controlled conditions of mass flow rate (i.e. flow Reynolds number, 𝑅𝑒) and the roughness parameters (𝑝/𝑒, 𝑒/𝐷), under actual outdoor conditions with varying values of intensity of solar radiation at quarter hourly intervals each day between 11 AM to 2 PM in the months of February to May 2015. Parameters measured were: 1) Pressure difference across orifice-meter 2) Pressure drop across inclined tube manometer 3) Temperature of the absorber plates 4) Temperature of air flowing in the duct 5) Ambient temperature 6) Intensity of solar radiation In 105 numbers of runs, 15 sets of three sides roughened absorber plate, along with the smooth absorber plate, each under 7 values of mass flow rate were tested. Typical test data collected during a test run are shown in Table 3.1 and range of parameter investigated is shown in table 3.2.
54 | P a g e
Table-3.1 Test Data Collected During a Typical Run (Run No. 56)
55 | P a g e
Table-3.2 Range of Parameters Investigated Set No.
1
2
3
4
Run no. 1
Date
𝑚,(Kg/s)
𝑅𝑒
15.02.2015
0.0375
19498
2
16.02.2015
0.0282
13572
3
17.02.2015
0.0271
14127
4
18.02.2015
0.0187
9749
5
19.02.2015
0.0175
6894
6
20.02.2015
0.0118
6166
7
21.02.2015
0.0085
4356
8
22.02.2015
0.0354
18576
9
23.02.2015
0.0227
12575
10
24.02.2015
0.0251
13125
11
25.02.2015
0.0243
9347
12
26.02.2015
0.0169
6263
13
27.02.2015
0.0108
6145
14
28.02.2015
0.0076
4243
15
01.03.2015
0.0361
18778
16
02.03.2015
0.0262
13451
17
03.03.2015
0.0284
14124
18
04.03.2015
0.0194
9554
19
05.03.2015
0.0161
6374
20
06.03.2015
0.0112
6151
21
07.03.2015
0.0077
4254
22
08.03.2015
0.0345
18463
23
09.03.2015
0.0232
13472
24
10.03.2015
0.0231
14117
25
11.03.2015
0.0157
9249
26
12.03.2015
0.0155
6194
27
13.03.2015
0.0098
6106
28
14.03.2015
0.0069
4156
𝑝,(mm) 𝑒,(mm)
𝑝/𝑒
𝑒/𝐷
11.0
1.1
10
0.0250
16.5
1.1
15
0.0250
22.0
1.1
20
0.0250
27.5
1.1
25
0.0250
56 | P a g e
5
6
7
8
29
15.03.2015
0.0376
19698
30
16.03.2015
0.0296
13772
31
17.03.2015
0.0262
14227
32
18.03.2015
0.0191
9049
33
19.03.2015
0.0189
6994
34
20.03.2015
0.0121
6366
35
21.03.2015
0.0085
4368
36
22.03.2015
0.0344
19198
37
23.03.2015
0.0252
13272
38
24.03.2015
0.0241
13827
39
25.03.2015
0.0157
9449
40
26.03.2015
0.0135
7079
41
27.03.2015
0.0109
5966
42
28.03.2015
0.0063
4056
43
29.03.2015
0.0364
19398
44
30.03.2015
0.0272
13472
45
31.03.2015
0.0261
14027
46
01.04.2015
0.0177
9649
47
02.04.2015
0.0165
6794
48
03.04.2015
0.0108
6076
49
04.04.2015
0.0073
4256
50
05.04.2015
0.0304
18498
51
06.04.2015
0.0242
12572
52
07.04.2015
0.0231
13127
53
08.04.2015
0.0117
9649
54
09.04.2015
0.0135
6794
55
10.04.2015
0.0101
5865
56
11.04.2015
0.0094
4886
33.0
1.1
30
0.0250
10.0
1.0
10
0.0225
15.0
1.0
15
0.0225
20.0
1.0
20
0.0225
57 | P a g e
9
10
11
12
57
12.04.2015
0.0354
19476
58
13.04.2015
0.0262
13549
59
14.04.2015
0.0252
14105
60
15.04.2015
0.0167
9727
61
16.04.2015
0.0155
6872
62
17.04.2015
0.0102
6143
63
18.04.2015
0.0079
4334
64
19.04.2015
0.0363
19483
65
20.04.2015
0.0271
13557
66
21.04.2015
0.0259
14112
67
22.04.2015
0.0176
9734
68
23.04.2015
0.0164
6879
69
24.04.2015
0.0107
6151
70
25.04.2015
0.0072
4342
71
26.04.2015
0.0361
19208
72
27.04.2015
0.0269
13282
73
28.04.2015
0.0258
13837
74
29.04.2015
0.0174
9459
75
30.04.2015
0.0162
6604
76
01.05.2015
0.0052
5876
77
02.05.2015
0.0071
4066
78
03.05.2015
0.0375
19512
79
04.05.2015
0.0251
11450
80
05.05.2015
0.0268
14124
81
06.05.2015
0.0191
9781
82
07.05.2015
0.0181
7301
83
08.05.2015
0.0123
6503
84
09.05.2015
0.0079
4101
25.0
1.0
25
0.0225
30.0
1.0
30
0.0225
6.0
0.6
10
0.0130
9.0
0.6
15
0.0130
58 | P a g e
13
14
15
85
10.05.2015
0.0352
19228
86
11.05.2015
0.0259
13302
87
12.05.2015
0.0248
13857
88
13.05.2015
0.0164
9479
89
14.05.2015
0.0152
6624
90
15.05.2015
0.0095
5896
91
16.05.2015
0.0062
4086
92
17.05.2015
0.0377
19499
93
18.05.2015
0.0283
13573
94
19.05.2015
0.0272
14128
95
20.05.2015
0.0188
9750
96
21.05.2015
0.0176
6895
97
22.05.2015
0.0119
6167
98
23.05.2015
0.0086
4357
99
24.05.2015
0.0378
19504
100
25.05.2015
0.0284
13577
101
26.05.2015
0.0273
14132
102
27.05.2015
0.0189
9754
103
28.05.2015
0.0177
6899
104
29.05.2015
0.0121
6172
105
30.05.2015
0.0087
4361
12.0
0.6
20
0.0130
15.0
0.6
25
0.0130
18.0
0.6
30
0.0130
59 | P a g e
CHAPTER – 4 RESULTS AND DISCUSSIONS 4.1 INTRODUCTION The present chapter reports the data presentation, reduction and validation. Based on the experimental results, correlations of Nusselt number and friction factor have been developed as a function of flow and roughness parameters. The effect of roughness and flow parameters on heat transfer, friction factor, collector performance parameters and thermo hydraulic performance has been presented. Thermo hydraulic performance results have been obtained. Thermal and thermo hydraulic performance curves have been presented to design such solar air heaters
4.2 DATA PRESENTATION, REDUCTION AND VALIDATION The experimental data with respect to the relative roughness height, relative roughness pitch, flow Reynolds number, intensity of solar radiation, plate and air temperatures, pressure drops along the duct length and orifice-meters have been reduced to obtain the results, using the relevant expressions. The experimental values of heat transfer coefficient have been obtained using the following Eq. (4.1):
𝑚𝐶𝑃 𝑇0 − 𝑇𝑖 = 𝐴𝐶 𝑇𝑃 − 𝑇𝑓
(4.1)
where, the values of mass flow rate have been calculated by using Eq. (3.4). The values of heat transfer coefficient, h, have been further used to calculate the values of Nusselt number by the following Eq. (4.2):
𝑁𝑢 =
𝐷 𝐾
(4.2)
The values of Nusselt number have been further used to obtain the values of Stanton number by Eq. (4.3) written under: 𝑁𝑢
𝑆𝑡 = 𝑅𝑒 𝑃𝑟
(4.3) 60 | P a g e
The respective values of Stanton numbers 𝑆𝑡3𝑟 and 𝑆𝑡3𝑔𝑠 , for the respective solar air heaters have been worked out using Eq. (4.3). However, to obtain the analytical values of Stanton number, the following Eq. (4.4) of Prasad et al. (2014) has been utilized: 𝑁𝑢3𝑟 =
𝑓3𝑟 /2 𝑓 1+√( 3𝑟 )[4.5 2
𝑝 0.53 𝑒 + 0.28 𝑃𝑟 0.57 −0.95 ]
𝑅𝑒 𝑃𝑟
(4.4)
𝑒
where, 𝑓3𝑟 , has been taken from Eq.(2.4). For smooth solar air heater, Eq. (2.14) has been used to obtain the value of 𝑆𝑡3𝑔𝑠 . The experimental values of friction factor, 𝑓3𝑟 , have been worked out from Eq. (3.13) and the values of 𝑓𝑆 have been found out from Eq.(2.13). 4.2.1
Sample Calculation Experimental results have been presented in the form of Nusselt Reynolds number, friction factor, temperature rise of air, intensity of solar radiation and the roughness parameters (𝑝/𝑒 and 𝑒/𝐷). Sample calculations for Run no. 56 (Table 3.1 and 3.2) have been illustrated as under:
(a) Average Temperature Average fluid temperature and average plate temperature for three sides roughened and the smooth ones have been calculated by using the following Eqs. (4.5) and (4.6) to be 35.290C & 50.140C respectively for three sides roughened duct and 33.60C & 51.430C for the smooth ones. 𝑇𝑓 = 𝑇𝑃 =
𝑇𝑓1 +𝑇𝑓2 +𝑇𝑓3 +𝑇𝑓4 +𝑇𝑓5 +𝑇𝑓6 +𝑇𝑓7 7 𝑇𝑃 1 +𝑇𝑃 2 +𝑇𝑃 3 +𝑇𝑓𝑃 4 +𝑇𝑃 5 +𝑇𝑃 6 +𝑇𝑃 7 7
(4.5) (4.6)
(b) Reynolds Number For a pressure drop of 25 mm of water across orifice-meter, throat velocity of air (V2) can be calculated using Eq. (7) under: 𝑉2 =
1/2
2∆𝑝 𝜌 1−𝛽 1
4
(4.7)
which works out to be 22.95 m/s for, 𝛽1 = 0.5. And hence, throat Reynolds number (Rd) as calculated using Eq. (8) under: 61 | P a g e
𝑅𝑑 =
𝑉2 𝑑 2 𝜗
(4.8)
is 45105. Discharge coefficient from Eq. (3.4) using the value of throat Reynolds number is worked out to be 0.6112. Mass flow rate given by Eq. (3.1), works out to be 0.00941kg/s, which gives a value of air flow velocity of 1.47 m/s through each duct, corresponding to a Reynolds number values of 4886 in each of the duct (three sides roughened and smooth) which remains invariant during a day. (c) Heat Transfer Coefficient Values of heat transfer coefficient from Eq. (4.1) work out to be 47.73 W/m2.K and 27.94 W/m2.K for three sides roughened and smooth respectively, giving the value of respective Nusselt numbers equal to 78.27& 45.81which yield in the value of Stanton numbers equal to 0.0228 & 0.0134 for the respective cases. (d) Friction Factor Values of friction factor have been calculated using Eq. (4.9) under: 2∆𝑃𝐷
𝑓 = 4𝐿𝜌 𝑣 2
(4.9)
are worked out be 0.0353 and 0.0251 for three sides roughened and smooth one respectively. (e) Temperature Rise of Air The difference of outlet and inlet temperatures of air through Eq. (4.10) in three sides roughened and smooth solar air heaters. ∆𝑇 = 𝑇0 − 𝑇𝑖
(4.10)
Table 4.1 shows the values of different resulting parameters for test Run no. 56. 4.3 VARIATION OF INTENSITY AND AMBIENT TEMPERATURE Fig. 4.1 shows typically the variation of intensity of solar radiation and ambient temperature. Fig. 4.2 shows the instantaneous plate and fluid (air) temperature in three sides roughened and smooth solar air heaters, across the collector length. Fig. 4.2 shows that the plate temperature in smooth solar air heater is more than that in three sides roughened one, but air temperature in three sides roughened solar air heater is more than that in smooth one. Higher values of plate temperature and lower values of air temperature in three sides glass covered 62 | P a g e
smooth solar air heater than those in three sides roughened and glass covered solar air heater indicate higher rate of heat transfer in three sides roughened collector than that in smooth collector. Table- 4.1Values of I, Ta, h, St and Nu as a Function of Time During the Day (Run No. 56)
Time
𝐼
, 𝑇𝑎 , 0C
𝑆𝑡3𝑟
𝑆𝑡3𝑔𝑠
(hours) w/m2
3𝑟 ,
𝑁𝑢3𝑟
W/m2K
3𝑔𝑠
,
𝑁𝑢3𝑔𝑠
W/m2K
11.00
733
29.0
0.02286
0.01337
46.73
78.18
26.37
45.73
11.15
746
29.2
0.02287
0.01341
47.84
78.23
27.48
45.84
11.30
756
29.6
0.02257
0.01308
46.72
77.18
26.27
44.72
11.45
766
30.4
0.02288
0.01339
47.73
78.27
27.94
45.81
12.00
811
30.9
0.02259
0.01292
46.62
77.27
26.27
44.17
12.15
844
31.3
0.02253
0.01289
46.09
77.06
26.91
44.06
12.30
877
31.8
0.02283
0.01319
47.13
78.09
27.31
45.11
12.45
899
32.3
0.02284
0.01318
47.12
78.11
27.21
45.09
13.00
842
33.1
0.02289
0.01327
47.39
78.29
27.93
45.37
13.15
816
33.5
0.02262
0.01295
46.29
77.37
26.92
44.29
13.30
786
34.1
0.02299
0.01317
47.02
78.02
27.21
45.02
13.45
777
34.7
0.02274
0.01311
46.81
77.79
26.18
44.81
14.00
748
35.1
0.02304
0.01340
47.78
78.81
27.87
45.79
63 | P a g e
Fig. 4.1 Typical variation of solar radiation and ambient temperature on a day
64 | P a g e
.
m 0.00835 0.0375Kg / s
56 54
Legends TP Tf S, 3G 3r, 3G
52 50 48 46 44
36
0
Tf ( C)
40
TP ( C),
42
0
38
34 32 30 28 0
150 300 450 600 750 900 1050 1200 1350 1500
Collector length, L (mm) Fig. 4.2 Typical air and plate temperature in solar air heaters
65 | P a g e
4.4 VALIDATION OF THE EXPERIMENTAL DATA The experimental values of Nusselt number and friction factor obtained for smooth solar air heater have been compared with those calculated by using the relevant Eqs. (4.11) and (4.12) respectively and have been shown in Figs. 4.3 and 4.4. It could be seen that the experimental values of Nusselt number and friction factor compare well with a deviation of ±2.7% and ±2.5% respectively. 𝑁𝑢𝑆 = 0.023𝑅𝑒 0.8 𝑃𝑟 0.4 (Dittus-Boelter equation)
(4.11)
𝑓𝑆 = 0.085𝑅𝑒 −0.25 (Modified Blasius equation)
(4.12)
Similarly, the present experimental values of heat transfer and friction factor data in three sides roughened solar air heaters have been compared with those of the experimental values of Behura et al., (2016) and are shown in Figs. 4.5 and 4.6 respectively. It could be seen from Figs. 4.5 and 4.6 that the present values of heat transfer and friction factor data compare well with those of the experimental values of Behura et al., (2016), with a maximum variation of ±4.5% and ±4.1% respectively. Since, the present results on heat transfer and friction factor have been validated, correlations for heat transfer and friction factor have been developed utilizing the present data value results.
66 | P a g e
Present experimental values Dittus -Boelter Eq.(4.11)
70
60
50
40
Nu 30
20
10 3000
6000
9000
12000
15000
18000
21000
Re Fig.4.3 Comparison of heat transfer data in smooth solar air heaters
67 | P a g e
Present experimental values Modified Blasius Eq.(4.12) 0.036 0.032 0.028
f 0.024 0.020 0.016 3000
6000
9000
12000
15000
18000
21000
Re
Fig. 4.4 Comparison of friction factor data in smooth solar air heaters
68 | P a g e
Present experimental values Behura et al. (2016) 80 70
60 50
Nu3r , Nur
40 30
20 10 4000 6000 8000 10000 12000 14000 16000 18000 20000 Re Fig. 4.5 Comparison of heat transfer data in three sides roughened solar air heater
69 | P a g e
Behura et al. (2016) Present experimental values 0.052 0.048 0.044 0.040
f3r , fr 0.036 0.032 0.028 0.024 4000 6000 8000 10000 12000 14000 16000 18000 20000 Re
Fig. 4.6 Comparison of friction factor data in three sides roughened solar air heaters
70 | P a g e
4.5 DEVELOPMENT
OF
CORRELATIONS
FOR
NUSSELT
NUMBER
AND
FRICTION FACTOR On the basis of experimental data of heat transfer and friction factor, the correlations for three sides roughened and glass covered solar air heaters, have been developed by using the method of regression analysis, as a function of roughness and flow parameters. A correlation for heat transfer for three sides glass covered smooth solar air heater has also been developed. Since, Nusselt number and friction factor both are the strong function of roughness and flow parameters, the following functional relationship for 𝑁𝑢3𝑟 and 𝑓3𝑟 can be written for three sides roughened solar air heater as under: 𝑝 𝑒
𝑁𝑢3𝑟 = 𝑓1 (𝑅𝑒, 𝑒 , 𝐷 )
(4.13)
𝑝 𝑒
𝑓3𝑟 = 𝑓3 (𝑅𝑒, 𝑒 , 𝐷 )
(4.14)
In order to determine a functional relationship between Nu and Re, all the experimental values of Nusselt number, for 𝑒 + ≤ 23, were plotted against entire range of Reynolds number, as shown in Fig. 4.7. The well known regression analysis method (curve fitting method by using origin pro 9.0, 32 Bit) for forced convective heat transfer has been utilized to determine the functional equation, written under as: 𝑁𝑢3𝑟 = 𝐴0 𝑅𝑒
0.746
(4.15)
where, 𝐴0 is the function of relative roughness pitch (𝑝/𝑒). 𝐴0 =
𝑁𝑢 3𝑟 𝑅𝑒 0.746
, is plotted
against all the experimental values of 𝑝/𝑒, as shown in Fig. 4.8. The regression analysis to fit a straight line through these points has been given by: 𝑁𝑢 3𝑟 𝑅𝑒 0.746
= 𝐵0 (𝑝/𝑒)−0.0713
(4.16) 𝑁𝑢 3𝑟
where, 𝐵0 is the function of relative roughness height (𝑒/𝐷). 𝐵0 =
𝑅𝑒 0.746
(𝑝/𝑒)−0.0713 ,
is plotted against entire experimental values of e/D, as shown in Fig. 4.9. The regression
71 | P a g e
analysis to fit a straight line through these points, yield the following correlation for Nusselt number of three sides roughened and glass covered solar air heaters for 𝑒 + ≤ 23 : 𝑁𝑢3𝑟 = 0.1415 𝑝/𝑒
−0.0713
𝑒/𝐷
0.0871
𝑅𝑒
0.746
(4.17)
Similarly, the correlation for Nusselt number corresponding to (𝑒 + > 23), were developed by using the method, same as that of the above. Figs. (4.10-4.12), show the plots between the obtained results, whenafter, applying regression analysis method, the following correlation for Nusselt number for three sides roughened and glass covered solar air heaters corresponding to 𝑒 + > 23, were developed:
𝑁𝑢3𝑟 = 0.0422 𝑝/𝑒
−0.0461
𝑒/𝐷
0.0375
𝑅𝑒
1.208
Nu3r=A0(Re)
for
𝑒 + > 23
12000
16000
(4.18)
0.746
Nusselt number
90
60
30
0 0
4000
8000
20000
Reynolds number
Fig.4.7 Variation of Nusselt number with Reynolds number
72 | P a g e
0.00045 0.00040 0.746
0.00035
Nu3r=B0(Re) (p/e)
-0.0713
Nu3r/(Re)
0.746
0.00030 0.00025 0.00020 0.00015 0.00010 0.00005 8
12
16
20
24
28
32
p/e
Fig. 4.8 Plot of
𝑁𝑢 3𝑟 𝑅𝑒 0.746
versus p/e
73 | P a g e
0.0016
0.746
-0.0713
0.0871
0.030
0.035
Nu3r=C0(Re) (p/e)
0.0012
[{Nu3r/(Re)
0.746
}/(p/e)
-0.0713
]
0.0014
(e/D)
0.0010
0.0008
0.0006 0.015
0.020
0.025
0.040
e/D
Fig.4.9 Plot of
𝑁𝑢 3𝑟 𝑅𝑒 0.746
(𝑝/𝑒)−0.0713 versus e/D
74 | P a g e
100
Nu3r=A0(Re)
1.208
Nusselt number
80
60
40
20
0 0
4000
8000
12000
16000
20000
Reynolds number Fig.4.10 Variation of Nusselt number with Reynolds number
75 | P a g e
0.00045 0.00040 0.00035
1.208
Nu3r=B0(Re) (p/e)
-0.0461
Nu3r/(Re)
1.208
0.00030 0.00025 0.00020 0.00015 0.00010 0.00005 8
12
16
20
24
28
p/e Fig. 4.11 Plot of
𝑁𝑢 3𝑟 versus 𝑅𝑒 1.208
p/e
76 | P a g e
0.0018
0.0016 ] -0.0461
}/(p/e) 1.208
[{Nu3r/(Re)
1.208
-0.0461
0.030
0.035
Nu3r=C0(Re) (p/e) 0.0014
0.0012
0.0010
0.0008
0.0006 0.015
0.020
0.025
0.040
0.045
e/D
Fig.4.12 Plot of
𝑁𝑢 3𝑟 𝑅𝑒 1.208
(𝑝/𝑒)−0.0461 versus e/D
77 | P a g e
4.5.1
Correlation for Nusselt Number for Three Sides Glass Covered Smooth Solar Air Heater Nusselt number of smooth solar air heaters is the function of Prandtl number (Pr) friction factor (fS) and flow Reynolds number (Re), expressed as Eq. (4.19) under: 𝑁𝑢3𝑔𝑠 = 𝑓(𝑅𝑒, 𝑃𝑟, 𝑓𝑆 )
(4.19)
and hence, to determine the functional relationship between the flow Reynolds number and Nusselt number for three sides smooth solar air heater, all the experimental values of flow Reynolds number were plotted against all the experimental value of Nusselt number, as shown in Fig.4.13. The regression analysis method has been utilized to determine the functional equation, written by Eq. (4.20) under: 𝑁𝑢3𝑔𝑠 = 𝐴1 𝑅𝑒
0.932
(4.20)
where, 𝐴1 is the function of 𝑃𝑟. 𝐴1 =
𝑁𝑢 3𝑔𝑠 𝑅𝑒 0.932
, is plotted against all the experimental values
of 𝑃𝑟 , as shown in Fig. 4.14. The regression analysis to fit a straight line through these points has been given by: 𝑁𝑢 3𝑔𝑠 𝑅𝑒 0.932
= 𝐵1 (𝑃𝑟)0.5
(4.21) 𝑁𝑢 3𝑔𝑠
where, 𝐵1 is the function of 𝑓𝑆 . 𝐵1 =
𝑅𝑒 0.932
(𝑃𝑟)0.5 , is plotted against entire
experimental values of 𝑓𝑆 , as shown in Fig.4.15. The regression analysis to fit a straight line through these points, yields the following correlation for Nusselt number in three sides glass covered smooth solar air heaters:
𝑁𝑢3𝑔𝑠 = 0.0782 𝑃𝑟
0.5
𝑓𝑆
0.7
𝑅𝑒
0.932
(4.22)
78 | P a g e
70
60
0.932
Nu3gS=A1(Re)
50
40
Nu3sg 30
20
10 3000
6000
9000
12000
15000
18000
21000
Re Fig.4.13Nusselt number versus flow Reynolds number for smooth solar air heater
79 | P a g e
0.0018 0.0016 0.0014 0.932
Nu3gS=B1(Re) (Pr)
Nu3gS/(Re)
0.932
0.0012
0.5
0.0010 0.0008 0.0006 0.0004 0.0002 0.690
0.692
0.694
0.696
0.698
0.700
Pr Fig.4.14 Plot of
𝑁𝑢 3𝑔𝑠 𝑅𝑒 0.932
versus 𝑃𝑟
80 | P a g e
0.0037 0.0036
[{Nu3gS/(Re)
0.932
}/(Pr)
0.5
]
0.0035
0.932
0.5
Nu3gS=C1(Re) (Pr) (fS)
0.7
0.0034 0.0033 0.0032 0.0031 0.0030 0.025 0.026 0.027 0.028 0.029 0.030 0.031 0.032
fS 𝑁𝑢 3𝑔𝑠
Fig.4.15 Plot of
𝑅𝑒 0.932
(𝑃𝑟 )0.5 versus 𝑓𝑆
81 | P a g e
4.5.2
Correlation for Friction Factor of Three Sides Roughened and Glass Covered Solar Air Heater For the determination of functional relationship between the flow Reynolds number and friction factor, all the experimental values of flow Reynolds number were plotted against all the experimental value of friction factor, as shown in Fig. 4.16. The regression analysis method has been utilized to determine the functional equation, written under as: 𝑓3𝑟 = 𝐴2 𝑅𝑒
−1.76
(4.23)
Where, 𝐴2 is the function of /𝑒. 𝐴2 =
𝑓3𝑟 𝑅𝑒 −1.76
, is plotted against all the experimental
values of 𝑝/𝑒, as shown in Fig. 4.17. The regression analysis to fit a straight line through these points has been given by: 𝑓3𝑟 𝑅𝑒 −1.76
= 𝐵2 (𝑝/𝑒)−0.319
(4.24)
Where, 𝐵2 is the function of 𝑒/𝐷 . 𝐵2 =
𝑓3𝑟 𝑅𝑒 −1.76
(𝑝/𝑒)−0.319 , is plotted against entire
experimental values of 𝑒/𝐷, as shown in Fig. 4.16. The regression analysis to fit a straight line through these points, yield the following correlation for Nusselt number of three sides glass covered smooth solar air heaters : 𝑓3𝑟 = 0.372 𝑝/𝑒
−0.319
𝑒/𝐷
0.354
𝑅𝑒
−1.76
(4.25)
82 | P a g e
0.044 -1.76
f3r=A2(Re) 0.040
0.036
f 3r 0.032
0.028
0.024 4000 6000 8000 10000 12000 14000 16000 18000 20000
Re
Fig. 4.16 Variation of friction factor with Reynolds number
83 | P a g e
0.5
-1.76
f3r=B2(Re) (p/e)
-0.319
f3r/(Re)
-1.76
0.4
0.3
0.2
8
12
16
20
24
28
p/e Fig. 4.17 Plot of
𝑓3𝑟 𝑅𝑒 −1.76
versus 𝑝/𝑒
84 | P a g e
0.18 -1.76
-0.319
0.354
0.016
0.018
0.020
f3r=C2(Re) (p/e)
(e/D)
0.14
[{f3r/(Re)
-1.76
}/(p/e)
-0.319
]
0.16
0.12
0.10
0.012
0.014
0.022
0.024
0.026
e/D
Fig.4.18 Plot of
𝑓3𝑟 𝑅𝑒 −1.76
(𝑝/𝑒)−0.319 versus 𝑒/𝐷
85 | P a g e
100
Predicted Nusselt number
80
60
+12% 40
-12% 20
0 0
20
40
60
80
100
Experimental Nusselt number Fig.4.19 Comparison of experimental Nusselt number values to the Predicted ones
86 | P a g e
0.05
Predicted friction factor
0.04
0.03
+11% 0.02
-11%
0.01
0.00 0.00
0.01
0.02
0.03
0.04
0.05
Experimental friction factor Fig. 4.20 Comparison of experimental friction factor values to the Predicted ones
87 | P a g e
It can seen from the Figs. 4.19 and 4.20, that the experimental values of the Nusselt number and friction factor compare well with that of the predicted ones with the average deviations of ±12% and ±11%, respectively, which are within the acceptable limit. Hence, the correlations developed are reasonably satisfactory for the prediction of Nusselt number and friction factor in three sides artificially roughened and glass covered solar air heaters. Fig. 4.21 shows the comparison of heat transfer data for three sides roughened and glass covered solar air heater and three sides glass covered smooth one with those of predicted Eq. (4.17) and (4.22) respectively. The experimental values of Nusselt number for both three sides roughened and three sides glass covered smooth solar air heaters are seen to compare well with those of the predicted Eqs. (4.17) and (4.22) respectively. For the entire range of experimental values of heat transfer for three sides roughened and three sides glass covered smooth solar air heaters, the maximum deviation was found to be about ±12% and ±10%, respectively, which are reasonably satisfactory for the predicted correlations. Fig. 4.22 shows the comparison of friction factor values for three sides roughened and glass covered solar air heater with those of predicted Eq. (4.25).The experimental values of friction factor are seen to compare well with those of the predicted Eq. (4.25).The maximum deviation was found to be about ±11%.
88 | P a g e
(1)
Predicted Eq. (4.17) Present experimental (Nu3r)
(2)
Predicted Eq. (4.22) Present experimental (Nu3gs)
80
(1) 70
60
50
Nu3gs Nu3r
(2)
40
30
20
10 4000 6000 8000 10000 12000 14000 16000 18000 20000
Re Fig. 4.21Predicted and experimental heat transfer data in solar air heater
89 | P a g e
Predicted Eq. (25) Present experimental (f3r) 0.052 0.048 0.044 0.040
f 3r
0.036 0.032 0.028 0.024 4000 6000 8000 10000 12000 14000 16000 18000 20000 Re
Fig. 4.22 Predicted and experimental values of friction factor data in solar air heater
90 | P a g e
4.6 EFFECT OF ROUGHNESS AND FLOW PARAMETERS ON HEAT TRANSFER AND FRICTION FACTOR The experimental values of Nusselt number have been used to get the values of Stanton number by the following conventional Eq. (4.26), which have been further taken as the heat transfer data to see the effect of roughness and flow parameters on it. 𝑆𝑡 = 𝑁𝑢/ 𝑅𝑒 𝑃𝑟
(4.26)
Figs.4.23 and 4.24 show the effect of the roughness and flow parameters, 𝑝/𝑒, 𝑒/𝐷 and 𝑅𝑒 on Stanton number in three sides roughened solar air heater. It could be seen from these figures that the values of Stanton number in three sides roughened collector decrease with increasing values of relative roughness pitch, 𝑝/𝑒, for a given value of relative roughness height, 𝑒/𝐷 and decreasing values of relative roughness height, 𝑒/𝐷, for a given value of relative roughness pitch, 𝑝/𝑒. The values of Stanton number are found to decrease with increasing values of flow Reynolds number. Stanton number for three sides smooth solar air heater for varying values of Reynolds number is also shown in these Figs. 4.23 and 4.24. It could be worked out from Figs. 4.23 and 4.24 that the values of Stanton number are more in three sides roughened and glass covered collector in the range of 36% to 65%, as compared to the three sides glass covered smooth ones. Fig. 4.25 shows the effect of 𝑝/𝑒 on friction factor for a given value of 𝑒/𝐷, equal to 0.0225. It could be seen from the figure that the values of friction factor increase with decrease in the value of the relative roughness pitch, 𝑝/𝑒, and decrease with increasing values of the flow Reynolds number, 𝑅𝑒. Fig. 4.26 shows the effect of 𝑒/𝐷 on friction factor for a given value of 𝑝/𝑒, equal to 20. It is quite clear from the figure that the values of friction factor increase with the increase in the value of relative roughness height, 𝑒/𝐷 and decrease with increasing values of flow Reynolds number, 𝑅𝑒. The values of friction factor in three sides roughened and glass covered collector have been found to increase in the range of 28% to 38%, as compared to the three sides glass covered smooth ones.
91 | P a g e
p/e=10 p/e=20 p/e=30 smooth
e/D= 0.0225
0.008
0.007
0.006
St 3 r , St3 gs
0.005
0.004
0.003
0.002 4000
8000
12000
16000
20000
Re Fig. 4.23 Effect of p/e on Stanton number in three sides artificially roughened solar air heater
92 | P a g e
e/D=0.0250 e/D=0.0225 e/D=0.0130 smooth
p/e=20 0.008
0.007
0.006
St3r , St3gs
0.005
0.004
0.003
0.002 4000
8000
12000
16000
20000
Re Fig. 4.24 Effect of e/D on Stanton number in three sides artificially roughened solar air heater
93 | P a g e
p/e= 10 p/e= 20 p/e= 30 smooth
0.044
e/D=0.0225
0.040
0.036
f 3r , fS
0.032
0.028
0.024 4000
6000 8000 10000 12000 14000 16000 18000 20000
Re
Fig. 4.25 Effect of p/e on friction factor in three sides artificially roughened solar air heater
94 | P a g e
0.044
p/e=20
e/D= 0.0250 e/D= 0.0225 e/D= 0.0130 smooth
0.040
0.036
f 3r , fS
0.032
0.028
0.024
0.020 4000
6000
8000 10000 12000 14000 16000 18000 20000
Re
Fig. 4.26 Effect of e/D on friction factor in three sides artificially roughened solar air heater
95 | P a g e
4.7 HEAT TRANSFER ENHANCEMENT FACTOR AND FRICTION LOSS FACTOR Fig. 4.27 shows the results of heat transfer enhancement factor, 𝑁𝑢𝐹 and friction loss factor, 𝑓𝐹 with increasing values of Reynolds number for a given value of 𝑒/𝐷, equal to 0.0225 at varying values of 𝑝/𝑒. The values of 𝑁𝑢𝐹 and 𝑓𝐹 have been given by Eqs. (4.27) and (4.28) respectively:
𝑁𝑢𝐹 = 𝑓𝐹 =
𝑁𝑢 𝑟 −𝑁𝑢 𝑆 𝑁𝑢 𝑆
𝑓𝑟 −𝑓 𝑆 𝑓𝑆
(4.27) (4.28)
It could be seen from the figure that the values of both heat transfer enhancement factor and friction loss factor increase with the increasing values of Reynolds number. Fig. 4.27 also shows that for a given value of e/D the rate of increment of 𝑓𝐹 is slight higher than that in 𝑁𝑢𝐹 at varying values of p/e. Therefore, the three sides roughened solar air heaters have been found to perform better both quantitatively and qualitatively as compared to the smooth ones. 4.8 THERMAL PERFORMANCE OF SOLAR AIR HEATER Three sides artificially roughened and glass covered solar air heaters have been found more efficient than those of only top side roughened ones (Prasad et al., 2014; Behura et al., 2016). This is due to the fact that three sides roughened and glass covered solar air heaters have more absorber plate area and enhanced heat transfer coefficient than those of only one side roughened and glass covered solar air heaters. The absorber plate area of only top side glass covered roughened as well as smooth (Prasad, 2013) solar air heater is equal to: 𝐴𝐶 = 𝑊𝐿
(4.29)
whereas, the absorber plate area of three sides roughened and glass covered solar air heater and the three sides glass covered smooth one is equal to: 𝐴𝐶 = 𝑊𝐿 + 2(𝐵𝐿)
(4.30)
96 | P a g e
p/e=10(NuF)
0.50
p/e=10(fF) p/e=20(NuF)
e/D=0.0225
p/e=20(fF)
0.48
p/e=30(NuF) p/e=30(fF)
0.46
NuF fF
0.44
0.42
0.40
0.38 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Re Fig. 4.27 Heat transfer enhancement factor and friction loss factor versus Reynolds number
97 | P a g e
The absorber plate area for three sides roughened and glass covered solar air heater and three sides glass covered smooth solar air heater is more by a magnitude of, 2(𝐵𝐿), than those of one side glass covered roughened as well as smooth solar air heater, which results in more heat collection for the same value of mass flow rate. Fig. 4.28 shows the comparative values of Stanton number for the respective solar air heaters. It could be observed from this figure that the solar air heater having three roughened sides and glass covers has the higher value of Stanton number, followed by the solar air heaters: one roughened side and glass cover; smooth and three sides glass covers; smooth and one side glass cover respectively. Thermal performance for three sides roughened & glass covered and three sides glass covered smooth solar air heaters, operating without recycling of air, has been presented on the basis of outlet fluid temperature. Based on the conventional performance equation (1.8) of (Bliss, 1959), replaced by Eq. (1.9), for solar air heaters without air recycling, thermal performance has been presented in Fig. 4.29. This figure represents typically the performance characteristics of the roughened solar air heaters for p/e =10, e/D = 0.0247: (i) three sides roughened and glass covered, (ii) top side roughened and glass covered, as well as of the smooth solar air heater: (i) smooth and three sides glass covered and (ii) smooth and only top side glass cover, all at varying mass flow rates. The efficiency data values given by the following equation: ƞ𝑡 = 𝑚𝐶𝑝 (𝑇0 − 𝑇𝑖 )/𝐼𝐴𝐶
(4.31)
shown by the respective lines are represented for each mass flow rate from the origin, resulting in the respective lines for the respective mass flow rates. Utilizing the efficiency data values, the respective curves A−𝐵3𝑟,3𝐺 , 𝐶 − 𝐷1𝑟,1𝐺 , 𝐸 − 𝐹𝑆,3𝐺 and 𝐺 − 𝐻𝑆,1𝐺 , have been obtained by the least square fit method for three sides roughened and glass covered solar air heater (present case), one side roughened and glass covered solar air heater (Prasad, 2013), smooth and three sides glass covered solar air heater (present case) and smooth and only top side glass covered solar air heater (Prasad, 2013), respectively. As could be seen from this figure that three sides roughened and glass covered solar air heater has higher value of thermal efficiency than those of only one side roughened and glass covered solar air
98 | P a g e
heater, followed by smooth and three sides glass covered solar air heater having slightly more thermal efficiency than that of smooth and only top side glass covered solar air heater.
p/e=20 e/D=0.0225
0.008
.
m 0.00835 0.0375Kg / s
S, 3G Present case 1r, 1G Prasad (2013) S, 1G Prasad (2013) 3r, 3G Present case
0.007
0.006
S t3r , St3 gs
0.005
0.004
0.003
0.002 4000
8000
12000
16000
20000
Re Fig. 4.28 Effect of roughened sides and glass covers on Stanton number in solar air heaters
99 | P a g e
m
kg/s 3r,3G(Present case) 1r,1G(Prasad, 2013) S,3G(Present case) S,1G(Prasad, 2013)
m1 0.0085 p/e=10 e/D=0.0247
m2 0.0118 m3 0.0175 m4 0.0187 m5 0.0271 m6 0.0282 m7 0.0375
90
m7
80
m6
70
m5
A
m4
60
m3
th%
50
m2
C
40 30
m1
E B3r,3G D1r,1G(Prasad, 2013)
G
20
FS,3G HS,1G(Prasad, 2013)
10 0 0.000
0.004
0.008
0.012 0
0.016
0.020
2
(T0-Ti)/I, C-m /W Fig 4.29 Thermal performance characteristics of solar air heaters
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4.9 COLLECTOR HEAT REMOVAL FACTOR (𝐅𝐑 ) AND COLLECTOR EFFICIENCY FACTOR (𝐅 ′ ) Using the values of the slope,F0 UL and intercept, F0 τα ,of the respective performance characteristic curves, obtained from Fig. 4.29, values of the performance parameters FR UL and FR τα have been obtained using equations (1.10, 1.16 and 1.17) of Duffie and Beckman, (1980). In three sides roughened and glass covered solar air heater, for mass flow rate, 𝑚, equal to 0.0375 Kg/s and Cp equal to 1005 J/Kg K, the value of 𝐹𝑅 𝑈𝐿 and 𝐹𝑅 𝜏𝛼 , worked out from Eqs. (1.16) and (1.17) comes out equal to 8.881 W/m2K and 0.697 respectively. For 𝜏𝛼 , equal to 0.84, the value of 𝐹𝑅 coming to 0.823, gives the value of 𝑈𝐿 equal to 10.701 W/m2K and that of 𝐹 ′ equal to 0.891. Figs. 4.30 and 4.31 show the values of collector heat removal factor, (𝐹𝑅 ) and collector efficiency factor,(𝐹 ′ ), respectively for three sides roughened & glass covered and three sides glass covered smooth ones.It could be seen that the values of collector heat removal factor, 𝐹𝑅 , and collector efficiency factor, 𝐹 ′ , increases in three sides roughened and glass covered solar air heater as compared to smooth and three sides glass covered solar air heater. The values of the collector heat removal factor,𝐹𝑅 and plate efficiency factor, 𝐹 ′ , have been found to enhance in the range of 51 to 60% and 41 to 49% respectively, as compared to three sides glass covered smooth solar air heater, within the range of the parameters investigated.
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1.1
p/e= 20,e/D=0.0225
3r,3G S, 3G
.
1.0
m 0.00835 0.0375Kg / s
0.9 0.8 0.7
FR 0.6 0.5 0.4 0.3 0.2 0.1 4000 6000 8000 10000 12000 14000 16000 18000 20000
Re Fig. 4.30 Collector heat removal factor in solar air heaters
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e/D=0.0225 .
1.1
m 0.00835 0.0375Kg / s
p/e=20
3r,3G S, 3G
1.0
0.9
0.8
0.7
F' 0.6
0.5
0.4
4000
6000
8000 10000 12000 14000 16000 18000 20000
Re
Fig. 4.31 Collector efficiency factor in solar air heaters
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Table- 4.2 represents the comparative view of the values of the slope, intercept, collector heat removal factor and collector efficiency factor obtained presently and those of Prasad, (2013), respectively. Higher values of the parameters, 𝐹𝑅 and 𝐹 ′ , indicate higher value of thermal efficiency. Table- 4.2 Values of Slope, Intercept, Collector Heat Removal Factor and Collector Efficiency Factor Slope,
𝐹0 𝑈𝐿 Intercept,
2
𝐹0 𝜏𝛼
(w/m .K)
3𝑟, 3𝐺
Collector heat Collector removal
efficiency
factor, 𝐹𝑅
factor, 𝐹 ′
(Present 8.56
0.725
0.822
0.918
(Prasad, 6.50
0.536
0.545
0.591
(Present 3.94
0.321
0.410
0.504
(Prasad, 3.60
0.291
0.391
0.496
case) 1𝑟, 1𝐺 2013) 𝑆, 3𝐺 case) 𝑆, 1𝐺 2013)
4.10 THERMAL PERFORMANCE CURVES Thermal performance equations (4.32) and (4.33) have been derived based on the conventional Eq. (1.8) and presented by thermal performance curves respectively in Fig. 4.32. It has been found that three sides roughened & glass covered solar air heater is 50 to 59% more efficient than that of three sides glass covered smooth one. 𝑇𝑖 −𝑇𝑎
ƞ𝑡(3𝑟,3𝐺) = 0.822 𝜏𝛼 − 0.822𝑈𝐿
ƞ𝑡(𝑆,3𝐺) = 0.41 𝜏𝛼 − 0.41𝑈𝐿
𝐼
𝑇𝑖 −𝑇𝑎 𝐼
(4.32)
(4.33)
104 | P a g e
th
90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0
3r, 3G (Present work)
S, 3G (Present work)
0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0
2
(Ti-Ta)/I, C-m /w
Fig. 4.32 Thermal performance curves for solar air heaters
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4.11 OPTIMAL THERMOHYDRAULIC PERFORMANCE Thermo hydraulic performance of solar air heater is expressed by Eq. (4.34) written under as: 𝑆𝑡 3𝑟
Ƞ𝑡𝑒𝑟𝑚𝑜 =
𝑆𝑡 3𝑔𝑠
𝑓3𝑟
(4.34)
𝑓𝑆
The values of thermo hydraulic performance worked out by utilizing Eq.(4.34) have been represented in Fig. 4.33, as a function of the parameter, e+, given by Eq.(2.6) to see the effect of the parameter, e+, on thermo hydraulic performance for varying values of p/e and given value of e/D, equal to 0.0225. Similarly, Fig. 4.34 represents the data for varying values of e/d and given value of p/e, equal to 20. It could be seen from these figures that for every value of p/e and e/D, the value of thermo hydraulic performance increases with increasing values of e+, and attains the maximum value at 𝑒 + = 23, whenafter, its value decreases for increasing values of e+. Since, e+, has remained the optimization parameter to arrive at the optimal thermo hydraulic performance + condition in literature, the value of 𝑒𝑜𝑝𝑡 = 23 , has the optimal thermo hydraulic
performance in three sides roughened and glass covered solar air heaters which validates the thermo hydraulic optimization analysis presently.
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p/e=30 p/e=20 p/e=10
90 85
Re=4000-20000
e/D=0.0225
80 75
thermo %
70 65 60 55 50 45 40 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
e e / D f 3r / 2 Re
Fig. 4.33 Effect of p/e and e+ on thermohydraulic performance
107 | P a g e
e/D=0.0130 e/D=0.0225 e/D=0.0250
90 85
Re=4000-20000
p/e=20
80 75
thermo %
70 65 60 55 50 45 40 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
e e / D f 3r / 2 Re
Fig. 4.34 Effect of e/D and e+ on thermohydraulic performance
108 | P a g e
Covering the total range of experimental data, Fig. 4.35 has been drawn to see the effect of the optimization parameter, e+, on thermo hydraulic performance. It could be seen from this figure that the optimal value of thermo hydraulic performance is achieved at the value of + 𝑒𝑜𝑝𝑡 = 23 , which validates the present analysis. Based on the experimental results,
correlations for thermo hydraulic efficiency have been obtained by using regression analysis method. The correlations are given below as: Ƞ𝑡𝑒𝑟𝑚𝑜 = 0.102 𝑒 +
0.658
for
𝑒 + ≤ 23
(4.34)
Ƞ𝑡𝑒𝑟𝑚𝑜 = 11.91 𝑒 +
−0.913
for
𝑒 + > 23
(4.35)
The present optimal value of thermo hydraulic performance in such solar air heaters could + be read from the Fig.4.35 to be about 78.8% for optimal value of 𝑒𝑜𝑝𝑡 = 23.
The value of the optimization parameter, 𝑒 +, combines in itself the values of the roughness and flow parameters, under varying conditions of the roughness and flow parameters. As also, the effect of either of the parameters on it may affect the values of other parameters to result in the same value of it. An increase in the value of one parameter, might be compensated by an equivalent decrease in the values of other parameters, to result in the + similar value of 𝑒𝑜𝑝𝑡 . Since, performance of solar air heaters is very much mass flow rate
dependent, flow Reynolds number greatly affects the heat transfer coefficient as well as the friction factor. Results show that heat transfer coefficient increases with increasing values of flow Reynolds number but friction factor decreases with increasing values of it. The value of + 𝑒𝑜𝑝𝑡 = 24, for one side roughened solar air heater (Prasad and saini, 1991; Verma and + Prasad, 2000), and 𝑒𝑜𝑝𝑡 = 23, for three sides roughened solar air heaters, presently, differ
marginally, which might be due to the two additional roughened sides of the present solar air heater duct . Three sides roughened and glass covered solar air heater has been found to have more value of the heat transfer coefficient than that of one side glass covered + roughened solar air heater (Prasad et al., 2014; Behura et al., 2016). The value of 𝑒𝑜𝑝𝑡 , is
mainly affected by the values of p/e, e/D and Re. As the heat transfer and pressure drop results have been found to compare well within the parameters investigated with those of the available ones, it gives the authentication of the 109 | P a g e
+ present investigation and therefore, 𝑒𝑜𝑝𝑡 = 23, is the only condition established for three
sides roughened and glass covered solar air heaters. The correlations developed for heat transfer, friction factor and thermo hydraulic efficiency are also valid within the parameters investigated.
85
Re=4000-20000 p/e=10-30 e/D=0.0130-0.0250
80 75
thermo(%)
70 65 60 55 50 6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
e
+
Fig. 4.35 Thermohydraulic efficiency versus roughness Reynolds number
110 | P a g e
CHAPTER 5 CONCLUSIONS AND FUTURE SCOPE 5.1 CONCLUSIONS The following conclusions have been derived based on the present results:1. The optimal value of the optimization parameter, 𝑒 + , for optimal thermo hydraulic performance in three sides roughened and glass covered solar air heaters has been obtained + to be 𝑒𝑜𝑝𝑡 = 23 and validated.
2. The heat transfer and fluid flow characteristics of three sides artificially roughened and glass covered solar air heaters as also three sides glass covered smooth solar air heater have been investigated under actual outdoor conditions. 3. Experimental data on heat transfer and friction factor compare well those of the analytical data within the range of the parameters investigated. 4. Correlations for Nusselt number and friction factor have been developed in terms of roughness and flow parameters as under: 𝑁𝑢3𝑟 = 0.1415 𝑝/𝑒
−0.0713
𝑒/𝐷
0.0871
𝑅𝑒
0.746
for
𝑒 + ≤ 23
𝑁𝑢3𝑟 = 0.0422 𝑝/𝑒
−0.0461
𝑒/𝐷
0.0375
𝑅𝑒
1.208
for
𝑒 + > 23
𝑓3𝑟 = 0.372 𝑝/𝑒
−0.319
𝑁𝑢3𝑔𝑠 = 0.0782 𝑃𝑟
0.5
𝑒/𝐷 𝑓𝑆
0.7
0.354
𝑅𝑒
𝑅𝑒
0.932
−1.76
5. The values of Stanton number worked out using the experimental value of Nusselt number in three sides roughened and glass covered solar air heater have been utilized to see the effect of roughness and flow parameter on it and represent the thermo hydraulic performance results. 6. The values of Stanton number in three sides artificially roughened and glass covered solar air heaters enhance by 36% to 65% as compared to smooth and three sides glass covered solar air heaters for the same range of values of parameters investigated. 7. The value of heat transfer enhancement factor of three sides roughened and glass covered solar air heater have been found to be 0.378 to 0.487 times over and above the three sides glass covered smooth solar air heater in the range of parameters investigated. 111 | P a g e
8. Collector heat removal factor, 𝐹𝑅 , and collector efficiency factor, 𝐹 ′ , in three sides artificially roughened and glass covered solar air heaters have been found to enhance by about 51 to 60% and 41 to 49% respectively, over those of three sides glass covered smooth solar air heaters. 9. Three sides roughened and glass covered solar air heaters are thermally 53-57%, more efficient than those of three sides glass covered smooth solar air heaters. 10. Correlations for thermo hydraulic efficiency have been developed for three sides glass covered and roughened solar air heater as under: Ƞ𝑡𝑒𝑟𝑚𝑜 = 0.102 𝑒 +
0.658
for
𝑒 + ≤ 23
Ƞ𝑡𝑒𝑟𝑚𝑜 = 11.91 𝑒 +
−0.913
for 𝑒 + > 23
+ 11. The value of optimal thermo hydraulic performance corresponding to 𝑒𝑜𝑝𝑡 = 23, have been
found to be 78.8%, within the range of the parameters investigated. 12. Thermal performance equation have been derived for three sides roughened and smooth solar air heaters with three sides glass covers as under: 𝑇𝑖 −𝑇𝑎
ƞ𝑡(3𝑟,3𝐺) = 0.822 𝜏𝛼 − 0.822𝑈𝐿 ƞ𝑡(𝑆,3𝐺) = 0.41 𝜏𝛼 − 0.41𝑈𝐿
𝐼
𝑇𝑖 −𝑇𝑎 𝐼
Therefore, three sides glass covered and roughened solar air heaters are thermally more efficient than those of three sides glass covered smooth solar air heaters, and there exists an + optimal thermo hydraulic performance condition at 𝑒𝑜𝑝𝑡 = 23, in three sides roughened
solar air heaters results in the maximum heat transfer for minimum friction factor. 5.2 FUTURE SCOPE OF THE WORK The present work has been investigated for the optimal thermo hydraulic performance of three sides roughened and glass covered solar air heaters by providing transverse wire roughness. The work may be extended to: 1. Use of three sides inclined wire roughness in such solar air heaters may enhance the heat transfer rate and hence may give better thermal and thermo hydraulic performance. 2. Use of booster mirror in such solar air heaters may be the reason behind better performance. 112 | P a g e
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UNCERTAINTY ANALYSIS Uncertainty analysis has been done by using the method [J.P.Holman], given by the following form of equation: 𝑈𝑥 =
𝜕𝑥 𝜕𝑦 1
𝑈𝑦1
2
+
𝜕𝑥 𝜕𝑦 2
𝑈𝑦2
2
+ ……………+
𝜕𝑥 𝜕𝑦 𝑛
2
𝑈𝑦𝑛
(A-1)
where, 𝑦1 , 𝑦2 … . 𝑦𝑛 are the variables affecting the parameters X and U stands for the uncertainty. One of the most important parameter in this work is the thermal efficiency calculation, given by the following equation: ƞ𝑡 = 𝑚𝐶𝑝 (𝑇0 − 𝑇𝑖 )/𝐼𝐴𝐶
(A-2)
From Eqs. (A-1) and (A-2), the uncertainty in the thermal efficiency of solar air heaters, U is given by: 𝑈Ƞ = −
𝐶𝑝 𝑇0 −𝑇𝑖 𝐼𝐴𝐶
𝑚 𝐶𝑃 𝑇0 −𝑇𝑖 𝐴𝐶 𝐼 2
𝑈𝐼
2
𝑈𝑚
+
𝑚 𝑇0 −𝑇𝑖 𝐼𝐴𝐶
1 2
𝑈𝐶𝑝
2
+
𝑚 𝐼𝐴𝐶
𝑈 𝑇0 −𝑇𝑖
2
+ −
𝑚 𝐶𝑃 𝑇0 −𝑇𝑖 𝐼𝐴𝐶 2
𝑈𝐴𝐶 + (A-3)
Where, 𝑈𝑚 , 𝑈𝐶𝑝 , 𝑈(𝑇0 −𝑇𝑖 ) , 𝑈𝐴𝐶 and 𝑈𝐼 are the uncertainties in mass flow rate of air, specific heat of air, air temperature rise, area of collector and intensity of solar radiation respectively. A.1 EXPERIMENTAL DATA For a particular test run (Test Run no. 56) typical data have been used to illustrate and workout for uncertainties, which are length of test section of solar air heater, L = 1500mm, width of test length of solar air heater, W = 200mm, internal diameter of orifice pipe, d1 = 76mm, throat diameter of orifice plate, d2 = 38mm, pressure drop across orifice meter, ∆p = 22mm of water, air temperature rise, (T0 – Ti), intensity of solar radiation, I = 899 W/m2. Dimensions of orifice pipe and throat diameters are measured with the help of vernier caliper for which uncertainties are: 𝑈𝑑1 = 𝑈𝑑2 = 0.02 𝑚𝑚
(A-4) 122 | P a g e
Length and width of solar air heater duct are measured with standard steel scale for least count equal to 1mm for which uncertainties are: 𝑈𝐿 = 𝑈𝑤 = 1 𝑚𝑚
(A-5)
Uncertainties in pressure drop and temperature are: 𝑈∆𝑝 = 1𝑚𝑚
(A-6)
𝑈𝑇0 −𝑇𝑖 = 0.10 𝐶
(A-7)
The value of intensity of solar radiation has been taken from standard digital pyranometer and therefore, the uncertainty in intensity of solar radiation is: 𝑈𝐼 = 0
(A-8)
A.2 UNCERTAINTY IN MASS FLOW RATE MEASUREMENT Mass flow rate through the duct has been calculated by the Eq. (3.4) and rewritten as: m = Cd A2
2ρ P 1 −P 2 1/2
(A-9)
1−β 41
Where, ∆p is pressure drop orifice meter. An uncertainty in the mass flow rate is given by: 2
𝑈𝑚 =
Cd
Cd A2 2ρ
1 A 2 2∆p 2 1 1 ρ 2 1−β 41 2
1
U∆p
1
2 1−β 41 ∆p 2
+
1−β 41
1 2
2
UA 2
2
+ 2Cd A2 2ρ∆p
1 2
β 31
3
2 1−β 41 2
Uβ 1
+
1
2
Uρ
2ρ∆p
+
A 2 2ρ∆p 1
1−β 41 2
1 2
2 2
UC d
(A-10)
Where, U∆p , UA 2 , Uβ 1 , Uρ and UC d are uncertainties in pressure drop across orifice meter, area of throat, diameter ratio, density of air and coefficient of discharge of orifice meter respectively. The values of density of air and coefficient of discharge are taken from standard tables and therefore, the uncertainties are: Uρ = 0
(A-11)
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UC d = 0
(A-12)
Uncertainties in UA 2 and Uβ 1 have been worked out to be 0.0003×10-5 and 17.04×10-7 respectively. Therefore, uncertainties in the mass flow rate work out to be: 𝑈𝑚 = 2.02287 × 10−9
(A-13)
A.3 UNCERTAINTY IN COLLECTOR AREA 𝑈𝐴𝐶 =
𝐿𝑈𝑤
2
+ 𝑊𝑈𝐿
2 1/2
(A-14)
= [(1500×1)2 + (200×1)2]1/2 = 1.5133 × 10-3 A.4 UNCERTAINTY IN SPECIFIC HEAT The value of specific heat of air has been taken from standard table, therefore, the uncertainty in specific heat is: 𝑈𝐶𝑝 = 0
(A-15)
A.5 UNCERTAINTY INTHERMAL EFFICIENCY When substituted for the values of various quantities in Eq. (A-3), the maximum uncertainty in the value of thermal efficiency is worked out to be 1.76%.
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LIST OF PUBLICATIONS FROM THIS WORK 1. Prasad B.N., Kumar Ashwini and Singh K.D.P., 2015. Optimization Of Thermo Hydraulic Performance In Three Sides Artificially Roughened Solar Air Heaters, Sol. Energy, 111, 313-319. 2. Kumar Ashwini, Prasad B.N., and Singh K.D.P., 2016. Performance Characteristics Of Three Sides Glass Covered Smooth Solar Air Heater, Transylvanian Review, 24, (11), 32473256. 3. Kumar Ashwini, Prasad B.N. and Singh K.D.P., 2018. Development Of Correlations Of Heat Transfer And Fluid Flow Characteristics For Three Sides Artificially Roughened Solar Air Heaters, J P Journal of Heat and Mass Transfer, 15, (1), 93-123. 4. Kumar Ashwini, Prasad B.N., and Singh K.D.P., 2017. Thermal And Thermo Hydraulic Performance Of Three Sides Artificially Roughened Solar Air Heaters, Int. Res. J. of Advanced Engineering and Science, 02, (2), 215-231. 5. Kumar Ashwini, Prasad B.N., and Singh K.D.P., 2017. Analysis Of Collector Performance Parameters In Three Sides Artificially Roughened And Glass Covered Solar Air Heater, Int. Res. J. of Advanced Engineering and Science, 02, (3), 224-229. 6. Kumar Ashwini, Prasad B.N., and Singh K.D.P., 2017. Heat Transfer And Fluid Flow Characteristics Of Three Sides Artificially Roughened And Glass Covered Solar Air Heaters, Int. Res. J. of Advanced Engineering and Science, 02, (3), 230-244. 7. Kumar Ashwini, Prasad B.N and Singh K.D.P., 2016. Performance Characteristics Of Three Sides Artificially Roughened Solar Air Heaters, proceedings, Global Conference on Renewable Energy, National Institute of Technology, Patna, India, GCRE-2016, 14, 132137. 8. Kumar Ashwini, Singh K.D.P. and Prasad B.N., 2016. Enhancement Of Collector Performance Parameters In Three Sides Artificially Roughened Solar Air Heater, proceedings, International Conference on Advances in Steel, Power and Construction Technology, O P Jindal University, Raigarh, India. 9. Kumar Ashwini, Prasad B.N., and Singh K.D.P., 2017. Investigation For Optimal Thermo Hydraulic Performance Of Three Sides Roughened And Glass Covered Solar Air Heater, Int. J. of Green Energy, Taylor and Francis. (Under Review).
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10. Kumar Ashwini, Prasad B.N. and Singh, K.D.P., 2018. Optimal Thermo Hydraulic Performance Of Three Sides Roughened And Glass Covered Solar Air Heaters, Int. J. of Heat and Fluid Flow, Elsevier. (Under Review). 11. Kumar, Ashwini, Prasad, B.N., Singh, K.D.P., 2018. Thermo Hydraulic Performance Of Three Sides Roughened And Glass Covered Solar Air Heater, International Energy Journal, Thailand. (Under Review).
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