Experimental and numerical study on heat transfer

Powder Technology 322 (2017) 340–352

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Experimental and numerical study on heat transfer performance of three-dimensional natural convection in an enclosure filled with DWCNTs-water nanofluid Alireza Rahimi a, Abbas Kasaeipoor b, Emad Hasani Malekshah c,⁎, Lioua Kolsi d,e a

Faculty of Energy, University of Kashan, Kashan, lran Faculty of Engineering, Department of Mechanical Engineering, University of Isfahan, Hezar Jerib Avenue, Isfahan 81746-73441, Iran c Department of Mechanical Engineering, Imam Hossein University, Tehran, Iran d College of Engineering, Mechanical Engineering Department, Haïl University, Haïl City, Saudi Arabia e Unité de Recherche de Métrologie et des Systèmes Énergétiques, Ecole Nationale d'Ingénieurs, University of Monastir, 5000 Monastir, Tunisia b

a r t i c l e

i n f o

Article history: Received 24 April 2017 Received in revised form 31 August 2017 Accepted 6 September 2017 Available online 13 September 2017 Keywords: Experimental/numerical study Natural convection Thermal analysis DWCNTs-water nanofluid

a b s t r a c t Three-dimensional natural convection in a cuboid enclosure filled with DWCNTs-water nanofluid is studied. The heat transfer performance due to convective flow of nanofluid inside the enclosure at different temperature differences between side hot and cold walls (ΔT = 20 °C, 30 °C, 40 °C and 50 °C) is analyzed experimentally and numerically. A setup has been manufactured to test the natural convection phenomenon within the enclosure. Moreover, in this work, the utilized nanofluid is prepared, the thermo-physical properties, thermal conductivity and dynamic viscosity, of the nanofluid are measured experimentally by means of modern measuring devices. The DWCNTs-water nanofluid is obtained in different solid volume fraction of 0.01%, 0.02%, 0.05%, 0.1%, 0.2%, and 0.5%, and thermo-physical properties have been measured in all solid volume fraction and temperature range of 300 to 340. The 3D computational study utilizing finite volume approach is performed with similar boundary condition with experimental setup and experimental properties of nanofluid to validate the experimental data. Height, length and depth of the enclosure are equal to 100 mm. the left and right side walls have constant and uniform hot and cold temperature respectively, and the other walls are insulated. The constant temperature of side walls is obtained by water channel supplied by circulating water bathes. The temperature of side walls is measured by nine LM-35 temperature sensors, and the temperature of nanofluid is measured by means of PT100 thermocouples inserting from watertight circular slots from back of enclosure. The numerical and experimental results are compared and a good consistency is observed. The temperature distribution between side walls at the mid-height of the enclosure, average heat transfer coefficient and average Nusselt number are presented for different Rayleigh numbers and solid volume fractions. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Due to widespread application of natural convection phenomenon within the confined volumes such as cuboid, rectangular and trapezoidal enclosure, many researchers studied the natural convection heat transfer performance experimentally and numerically. Solar collectors, lead-Acid batteries, ventilation of buildings, passive cooling, electronic components cooling, nuclear reactors, food industries, MEMS devices, heat exchanger, crystal growth and so on [1–8]. The natural convection has inherently weak heat transfer performance. As such, some methods have been developed by the researchers to improve the heat transfer performance of the natural convection ⁎ Corresponding author. E-mail addresses: [email protected], [email protected] (E.H. Malekshah).

http://dx.doi.org/10.1016/j.powtec.2017.09.008 0032-5910/© 2017 Elsevier B.V. All rights reserved.

phenomenon. One of the efficient approaches to reach this goal is using the fluids with high heat transfer performance. In this context, the metallic and non-metallic nanoparticles such as Cu [9,10], CuO [11], Al2O3 [12,13], ZnO [14], TiO2 [15], Ag [16], Fe3O4 [17], Mg(OH)2 [18], SiO2 [19], CNTs [20], MWCNTs [21,22] are added to the base fluids such as water, oil and ethylene glycol. In an experimental work, Heyhat et al. [23] investigated the turbulent convection heat transfer using Al2O3-water nanofluid. They concluded that the heat transfer coefficient will be increased up to 23% by increasing 2% of solid volume fraction. In another experimental study, the laminar forced convection using nanofluids types Al2O3-water (d = 20 nm) and CuO-water (d = 50–60 nm) was analyzed by Zeinali-Heris et al. [24]. The results showed that the heat transfer performance has direct relationship with the concentration of nanoparticles. Hwang et al. [25] studied the convective heat transfer characteristics of Al2O3-water nanofluid in fully developed laminar flow regime. They

A. Rahimi et al. / Powder Technology 322 (2017) 340–352

reported that the convective heat transfer coefficient of Al2O3-water nanofluid augments up to 8% at φ = 0.3 vol% with respect to pure water. Moreover, they claimed that this enhancement may not be predicted by Shah Equation. Salari et al. [21] carried out a threedimensional simulation of natural convection and entropy generation within the enclosure filled with stratified fluids of MWCNTs-water nanofluid and air. They showed that the Nusselt number enhances as solid volume fraction of considered nanofluid increases. Milani Shirvan et al. [26] studied the influences of wavy surface characteristics on the natural convection heat transfer performance within a cosine corrugated cavity which is filled with Cu-water nanofluid. They considered different solid volume fractions of nanofluid and concluded that the mean Nusselt number augments with escalation of solid volume fraction. Garoosi and Hoseininejad [27] studied the natural and mixed convection heat transfer between partially heated cylinders within a nanofluid filled adiabatic enclosure. They used three different types of nanoparticles namely Cu, Al2O3 and TiO2. They found that the rotation direction of hot and cold cylinders has pronounced influence on the heat transfer rate. Many researchers analyzed that natural convection phenomenon within the enclosures with different geometries, boundary conditions, operating fluids, numerical methods and so on. They studied the effects of different governing parameters on the convective flow and heat transfer. In this context, Darwish [28] carried out a numerical investigation on the natural convection within the trapezoidal cavity which was partially divided. They considered two kinds of thermal boundary conditions. For the first case, the right wall was kept in cold temperature and the left one was maintained at hot temperature and for the second case, they change this thermal boundary condition to opposite mode. They studied the influences of different parameters such as Prandtl number of 0.7, 10 and 130, Rayleigh number in range of 103 to 106, baffle height and baffle locations on the heat transfer function. Natural convection in a rectangular cavity with one partially hot wall and one partially cool wall was studied by Yücel [29]. Alam et al. [30] performed a numerical analysis on the natural convection by using finite element method in a rectangular cavity. The results showed that the local heat transfer enhances with increasing of aspect ratio, and maximum heat transfer occurs at square cavity. The entropy generation due to natural convection in a trapezoidal cavity with different Rayleigh number in

341

range of (103 b Ra b 106), Prandtl number (0.015 b Pr b 1000) and inclination angles (45 b θ b 90) studied by Basak et al. [31]. They considered two cases of thermal boundary conditions: 1) isothermal heating for bottom wall 2) non-isothermal heating for bottom wall. Also, many experimental investigations have been conducted to study the natural convection phenomenon. Malekshah and Salari [32] conducted an experimental work to analyze the natural convection heat transfer in an enclosure filled with a stratified system containing two fluids of water and air. They concluded that the height of liquid and Rayleigh number have significant effects on the temperature distribution. Some other works and related results are listed in Table 1. Some comprehensive investigations have been performed to measure the thermal conductivity and dynamic viscosity of nanofluids, experimentally. Amrollahi et al. [33] studied the characteristics of thermal conductivity of CNTs-EG nanofluid in a series of experiments. They reported that the thermal conductivity has strong relationship with the concentration of nanotubes and temperature of nanofluid. Duangthongsuk and Wongwises [34] measured the temperaturedependent viscosity of TiO2-water nanofluid. The results show that the viscosity enhances and decreases with increasing of concentration of solid particles and temperature of nanofluid, respectively. Also, to solve the fluid flow and heat transfer due to natural convection phenomenon in enclosures filled with nanofluid, two different approaches of single-phase and two-phase may be utilized in the numerical investigation. The single-phase method assumes that the nanofluid media is a continuous phase which is in thermal equilibrium. Many investigations have been performed in both natural convection and mixed convection phenomena [5,35,36]. Garoosi et al. [37] used two-phase model to simulate the natural convection and mixed convection in a square cavity filled with nanofluid. They found that thermophoretic effects of nanoparticles are negligible at high thermal conductivity. As such, as the thermal conductivity of nanoparticles is high, the single-phase can be used in all Rayleigh and Richardson numbers. Moreover, in another work, Garoosi et al. [38] used two-phase approach in simulating the mixed convection within a square cavity filled with nanofluid and included by internal and external heaters. The results indicated that the distribution of nanoparticles with dp ≥ 145 at low Richardson numbers is almost uniform which allows that the simulation may be performed with single-phase approach.

Table 1 A summary of some studies on experimental natural convection. Author

Year of Fluid publication

Type of study Rayleigh number Range

Popa et al. [41]

2012

Water

Wright et al. [42] Bairi et al. [43]

2006 2007

Air Air

Karatas and Derbentli [44] Bairi et al. [45]

2017

Water

Experimental and Numerical Experimental Experimental and Numerical Experimental

2010

Air

García de María et al. 2010 [46]

Air

Experimental and Numerical Experimental and Numerical Numerical

Ra=4×106 ,2×106 and 4×105

The presence of recirculation zone at channel outlet near unheated wall is approved

4850 b Ra b 54800 10 b Ra b 108

The central region has uniform temperature distribution with no stratification New correlations for Nusselt number in terms of Rayleigh number are proposed

2.16 × 105 b Ra b 5.06 × 107

Heat transfer correlations are obtained in terms of Rayleigh number

5

10 b Ra b 10

9

The investigations are done for high Rayleigh number represented the engineering applications

5 × 103 b Ra b 3 × 109

The Nusselt number in terms of Rayleigh number and inclination angle approve the existence of convective diode effect

103 b Ra b 106

The local Nusselt variation, heat transfer irreversibility and fluid friction irreversibility are depicted graphically.

Rahimi et al. [47,48] and Kasaeipoor et al. [49] Salari et al. [50]

2017

Hybrid nanofluid

2017

Khalili et al. [51]

2017

103 b Ra b 106 Al2O3-water Numerical nanofluid Al2O3-water Experimental 0.0992 × 107-0.51 × 108-1.53 × 108 nanofluid

Naghib et al. [52]

2017

Water

Result

Experimental 3.74 × 107 b Ra b 9.03 × 108

The fluid flow and heat transfer performance in a stratified system is analyzed. The average nanoparticle volume fraction difference between hot and cold wall is stronger for low Rayleigh number and weak for High Rayleigh number. The fluid flow is visualized by concurrent shadow graph and PIV image

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The main objective of present experimental and numerical investigation is to analyze the natural convection heat transfer within an enclosure filled with nanofluid. The thermal conductivity and dynamic viscosity of obtained DWCNTs-water nanofluid are measured experimentally. Afterwards, the obtained nanofluid is used to study the temperature distribution, average heat transfer coefficient and average Nusselt number using a setup. Furthermore, the measured thermophysical properties are utilized in numerical analysis which has been used to verify the experimental results.

Table 2 Properties of COOH-functionalized DWCNT. Properties of COOH-functionalized DWCNT Outer Inner diameter Length SSA True density Color Manufacturing method

2–4 mm 1–3 mm 50 μm N350 m2/g 2.1 g/cm3 Black CVD

2. Material and methods sedimentation. The stability of nanofluid is observed for at least one week with any sedimentation.

2.1. Nanofluid preparation Many investigations have been performed to analyze the thermophysical properties of different nanofluid such as Al2O3-water, CuOwater, Cu-water and TiO2-water. But, in this study one novel nanofluid is selected for analyzing its thermo-physical properties and using in the experimental setup to study the natural convection heat transfer. The COOH-functionalized double-walled carbon nanotubes with high purity of 60%, obtained from US research nanomaterials, Inc., are dispersed in the base fluid. The base fluid is considered pure water. Different solid volume fractions are considered in this study such as 0.01%, 0.02%, 0.05%, 0.1%, 0.2%, and 0.5%. It is worth to mention that the existence of COOH helps the better dispersion of nanotubes in the pure water. As such, adding surfactant in order to make the nanofluid stable is not necessary. In this context, the negative influences of functionalizing material on the thermos-physical properties of nanofluid are omitted by this way. In order to show the shape and approximate size of nanofluid, a TEM image of COOH-functionalized DWCNTs is presented in Fig. 1 (left side). Also, the picture of the obtained nanofluid at different solid volume fraction is depicted in Fig. 1 (right side). Furthermore, the properties of supplied nanotubes have been presented in Table 2. Moreover, the thermo-physical properties of both base fluid and nanoparticles are presented in Table 3. 2.2. Stability analysis For all solid volume fractions for this nanofluid, the appropriate amounts of COOH-functionalized DWCNTs are added to the base fluid which is the distilled water. Afterwards, the particles and water are mixed with a magnetic stirrer for 2.5 h. After mixing of the nanotubes and base fluid, the suspension is inserted to an ultrasonic processor (Hielscher Company, Germany) with the power of 400 W and frequency of 24 kHz for 5 h. this process prevents the agglomeration between the nanotubes and

2.3. Thermo-physical properties The two main properties of nanofluid namely thermal conductivity and dynamic viscosity are measured experimentally. Other thermophysical properties such as density, specific heat at constant pressure and thermal expansion coefficient can be calculated by following equations due to the low solid volume fraction: ρnf ¼ φρp þ ð1−φÞρbf

ð1Þ

βnf ¼ φβp þ ð1−φÞβbf

ð2Þ

Cp nf ¼ φCp p þ ð1−φÞCp bf

ð3Þ

2.4. Thermal conductivity measuring In order to measure the thermal conductivity of nanofluid, the reliable and fast method of transient hot-wire (THW) technique is utilized. In this context, a KD2 pre thermal properties analyzer (Decagon devices, Inc., USA), shown if Fig. 2, is utilized. The thermal conductivity analyzer device is calibrated with distilled water before starting the measurements, and the maximum error is measured equal to ± 5%. It should be noted that the each measurement is repeated three times to verify the obtained results. 2.5. Dynamic viscosity measuring The Brookfield viscometer of Brookfield engineering laboratories of USA, shown in Fig. 3, is utilized which has high accuracy of ± 5%. The viscometer is calibrated by using distilled water before starting the measuring process. All of the measurements are performed at room

Fig. 1. TEM image of the COOH-functionalized DWCNTs.


343

Table 3 Thermo-physical properties of water and nanoparticles at T = 310 K.

Water DWCNTs

ρ (kg/m3)

K (W/m·K)

CP (J/kg·K)

β × 105 (1/K)

μ × 106 (kg/m·s)

993 2100

0.628 –

4178 710

36.2 6.00E−06

695 –

temperature and repeated three times to be ensured that the results are reliable. 3. Experimental study The experiments were done in the cuboid enclosure filled with Al2O3 nanofluid. The experiments were done for different temperature differences (ΔT = 20 °C, 30 °C, 40 °C, and 50 °C) at constant form of geometry and operating fluid. Fig. 4 shows the experimental setup to test the natural convection heat transfer in the cuboid enclosure. Also, the schematic of the water channels at the sides of the enclosure to create the constant hot and cold temperature is presented in Fig. 5. Furthermore, the schematic of above-view of the enclosure is presented in Fig. 6 to show the details of the components at the back of the setup such as watertight circular slots and PT-100 thermocouples. It can be observed the details of used component at the inside of the water channels such as honeycombs, copper plate and LM-35 temperature sensors. To create a comprehensive view on the experimental setup, five main parts of setup are as follows: 1) Heating and cooling systems (water channels, circulating water baths and power supplier) 2) test section (cuboid enclosure with side copper walls and other sides are made by White Polyvinyl Chloride sheets) 3) measurement tools (PT-100 thermocouple, LM-35 temperature sensors, computer, date logger) 4) insulating components (insulating materials). The length, height and depth of the enclosure are denoted with L = 100 mm, H = 100 mm and D = 100 mm, respectively. As it is shown in Fig. 4, the left and right walls are included with water channel with constant hot and cold temperature respectively, obtained by circulating water bathes. It should be noted that the inner side of the water channels are made by the copper plates to conduct the temperature uniformly and smoothly, and the other side walls are made from White Polyvinyl Chloride sheets which are thermal insulator as well. Moreover, the other side walls of the enclosure are made by the

Fig. 2. KD2 pre thermal properties analyzer (Decagon devices, Inc., USA).

Fig. 3. Brookfield viscometer of Brookfield engineering laboratories of USA.

White Polyvinyl Chloride sheets as well. It is worth to mention that the test section and water channels, after conjoining different components, are covered with several layers of White Polyvinyl Chloride sheets to prevent heat losing from system. Circulating water through the channels lets the side walls to obtain the constant temperature. In this context, two circulating water bathes PR20R-30 Polyscience with temperature range between −30 °C and 200 °C with high accuracy of 0.005 °C are utilized. Moreover, the constant thermal circulated water is maintained at the appropriate volume flow rate and constant desired temperature for the level of experiments. The volume flow rate is measured by two ultrasound flow meters named Burkert type 8081 with a range of flow between 0.0666 and 0.3333 L/s with a high accuracy of ±0.01% full scale +2% of measured value. To distribute the water entered to water channel from four used inlets, the two honeycombs are applied at the adjacent of inlet and outlet. Nine LM-35 temperature sensors are applied at the surface of the copper plate inside the water channels. The temperature of the side hot and cold walls are calculated by making average value from the obtained temperature from these temperature sensors. All of the obtained temperature values from these sensors have very close value to each other which shows that the temperature of the side walls is uniform. To screen the temperature of the operating nanofluid at the inside of the enclosure two main components are used as PT-100 thermocouple and watertight circular slots. Nine different watertight circular slots are mounted at the back and mid-height of the enclosure. The PT-100 thermocouple is allowed to penetrate to the inside of the enclosure by means of these watertight slots without any nanofluid leakage to the outside of the enclosure. The PT100 sensor was calibrated in range of 15–80 °C by steps of 5 °C. Finally, all data are recorded by means of National Instrument (NI) data logger named SCXI-1303 which has 32 channel input, and send the data to computer system.

344


Fig. 4. Schematic of experimental natural convection tester setup.

Each experiment took place at room temperature of 20 °C. The temperature measuring were begun at least after 1 h after starting the setup to ensure that the thermal steady-state condition for side walls and operating nanofluid is obtained. The measurements were repeated at least three times for each case to ensure the repeatability. The dimensionless cavity dimensions (X , Y , Z) are defined by ratio of distances on x , y , z axes to their corresponding cavity dimensions respectively The measurements are done for four different Rayleigh numbers and six solid volume fractions. The temperatures value of the side hot and cold walls are an average of nine obtained temperature from LM-35 sensor at the surface of copper plates: The temperature of hot wall is given as follow:

Th ¼

T1h þ T2h þ T3h þ T4h þ T5h þ T6h þ T7h þ T8h þ T9h 9

ð4Þ

The temperature difference of two side walls is given as follows: ΔTEn ¼ Th −Tc

ð6Þ

To evaluate the heat generation rate in the water channels, the following equation is given: _ p ΔTEx _ p ðTinlet −Toutlet Þ ¼ mc q_ ¼ mc

ð7Þ

The average heat transfer coefficient hnf for the natural convection of the nanofluids calculated, the following is given: hnf ¼

q_ q_ ¼ AðTh −Tc Þ AΔTEn

ð8Þ

The area of side hot and cold walls are calculated as follows: A¼LH

ð9Þ

The temperature of cold wall is given as follows: The Nusselt number is calculated as follows: Tc ¼

T1c þ T2c þ T3c þ T4c þ T5c þ T6c þ T7c þ T8c þ T9c 9

ð5Þ

Nu ¼

hnf H knf

ð10Þ

The Rayleigh number is calculated as follows: Ra ¼

3 gβnf H3 ΔTEn gβnf ρnfCp nf H ðTh −Tc Þ ¼ νnf αnf μ nf knf

ð11Þ

The dimensionless temperature is defined as follows: θ¼

T−Tc ; where ΔTRef ¼ 20 ° C ΔTRef

ð12Þ

3.1. Uncertainty analysis Uncertainty in the experimental results is determined by calculation of deviation of different parameters such as transferred heat energy, temperature, thermal conductivity and area of heater and cold walls. By taking logarithm from Eq. (7), we have: Fig. 5. Schematic of water channel.

_ þ Ln Cp þ LnΔT Ln q_ ¼ Ln m

ð13Þ


345

Fig. 6. View from above of the enclosure.

The error propagation of the temperature difference of two side walls is calculated as follows:

The error propagation of the transferred heat to enclosure is calculated as follows:

∂ΔTEn ΔTh þ ∂ΔTEn ΔTc ¼ ΔTh þ ΔTc ΔTEn ¼ ∂T ∂Th c

∂q_ ∂q_ Δq_ ∂q_ _ ¼ Δm þ Δcp þ ΔðΔTEx Þ _ ∂cp ∂ðΔTEx Þ ∂m q_ _ Δcp ΔðΔTEx Þ Δm þ þ ¼ _ m ΔTEx cp

The error propagation of the area of the side walls is calculated as follows:

ð14Þ

∂A ΔA ∂A ΔL ΔH ¼ ΔL þ ΔH ¼ þ A L H ∂L ∂H

By applying same procedure, the error propagation of the hot wall is calculated as follows: ∂T ∂T ∂T ∂T ΔTh ¼ h ΔT1h þ h ΔT2h þ h ΔT3h þ … þ h ΔT9h ∂T1h ∂T2h ∂T3h ∂T9h 1 ¼ ðΔT1h þ ΔT2h þ ΔT3h þ … þ ΔT9h Þ 9

ð18Þ

The error propagation of the average heat transfer coefficient hnf for the natural convection of the nanofluids is calculated as follows: Δhnf

ð15Þ

hnf

The error propagation of the cold wall is calculated as follows: ∂Tc ΔT1c þ ∂Tc ΔT2c þ ∂Tc ΔT3c þ … þ ∂Tc ΔT9c ΔTc ¼ ∂T ∂T ∂T ∂T1c 2c 3c 9c 1 ¼ ðΔT1c þ ΔT2c þ ΔT3c þ … þ ΔT9c Þ 9

ð17Þ

∂h ∂h ∂h nf ¼ nf Δq_ þ þ nf ΔA þ ΔðΔTEn Þ ∂ΔTEn ∂q_ ∂A Δq_ ΔA ΔðΔTEn Þ þ ¼ þ A ΔTEn q_

ð19Þ

The error propagation of the Nusselt number is calculated as follows: ∂Nu ∂Nu ΔNu ∂Nu Δhnf ΔH Δknf þ þ ¼ Δh þ Δk ¼ ΔH þ ∂hnf nf ∂H ∂knf nf H knf Nu hnf

ð16Þ

ð20Þ

Table 4 Uncertainty analysis of different parameters. Parameter

q_

Th Temperature of hot wall

Tc Temperature of cold wall

A Area of side walls

K Thermal conductivity

±0.32 °C

±0.32 °C

±1 m2

±2%

Heat transfer rate Error

±0.65 W

hnf

Nu

Heat transfer coefficient

Nusselt number

2.45%

2.62%

Table 5 Comparison the present results with the 3D results of Fusegi et al. [39]and Wakashima and Saitoh [40] for heated cubic cavity at Pr = 0.71. Ra

Investigators

ψz (center)

ωz (center)

Vxmax (y)

Vymax (y)

Nuav

104

Present work Fusegi et al. [39] Wakashima and Saitoh [40] Present work Fusegi et al. [39] Wakashima and Saitoh [40] Present work Fusegi et al. [39] Wakashima and Saitoh [40]

0.05347 – 0.05492 0.0343 – 0.03403 0.01972 – 0.01976

1.1021 – 1.1018 0.2588 – 0.2573 0.1339 – 0.1366

0.196 (0.813) 0.201 (0.817) 0.198 (0.825) 0.151 (0.560) 0.147 (0.855) 0.147 (0.85) 0.0867 (0.853) 0.0841 (0.856) 0.0811 (0.86)

0.211 (0.117) 0.225 (0.117) 0.222 (0.117) 0.245 (0.067) 0.247 (0.065) 0.246 (0.068) 0.261 (0.033) 0.259 (0.033) 0.2583 (0.032)

2.081 2.1 2.062 4.360 4.361 4.366 8.73 8.77 8.6097

105

106

346


Table 6 Grid independence study (Ra=5.29×108 and φ=0.2 vol%). Mesh size Nu

10 × 20 × 20 73.843

20 × 40 × 40 74.349

30 × 60 × 60 75.569

In present work, the uncertainties for the parameters are listed in Table 4. 4. Numerical study 4.1. Physical model A numerical study has been carried out as a complementary of the measurements and understanding of the natural convection phenomena in details. The thermal boundary conditions are completely similar to experimental setup including left hot wall (Th), right cold wall (Tc) and other walls are adiabatic. Height, length and depth of the enclosure are represented by H, L and D, respectively. 4.2. Governing equations By introducing the following dimensionless parameters: x0 y0 ; y¼ ; H H pH2 ¼ ρnf αnf 2

x¼

z¼

z0 ; H

U¼

uH vH ; V¼ ; αnf αnf

W¼

wH ; αnf

P

Fig. 7. Effective dynamic viscosity at different temperature as a function of solid volume fractions.

40 × 80 × 80 75.721

50 × 100 × 100 75.722

60 × 120 × 120 75.711

νnf gβ H3 ΔT ; Ra ¼ nf where ΔT νnf αnf αnf TH þ TC ¼ TH −To and T0 ¼ 2

θ¼

T−Tc ; ΔT

Pr ¼

Here x′, y′ and z′ are the distances along the width, height and depth of the enclosure, respectively; u, v and w are the velocity components in the directions of x′, y′ and z′, respectively; T shows the temperature, νnf and αnf are kinematic viscosity and thermal diffusivity of nanofluid. Moreover, p is the pressure and ρnf is the density of nanofluid, Th and TC are the temperature of hot and cold walls, respectively; H is the height of the enclosure, g and β denote the gravity acceleration and volume expansion coefficient. It should be noted that x, y and z are dimensionless coordinates; U, V and W are dimensionless velocity components. Ra and Pr present the Rayleigh number and Prandtl number. The dimensionless continuous equation is written as follows: ∂U ∂V ∂W þ þ ¼0 ∂x ∂y ∂z

ð21Þ

Fig. 8. Effective thermal conductivity at different temperature as a function of solid volume fractions.

Table 7 Correlations of effective dynamic viscosity based on temperature for different nanoparticle concentrations. Solid volume fraction

Correlations

R-squared

φ = 0.01% φ = 0.02% φ = 0.05% φ = 0.1% φ = 0.2% φ = 0.4%

μnf/μw = − 3.933 + 1.012T − 0.428T0.8427Ln(T) μnf/μw = 1.657 + 0.5732T − 2738T0.8249Ln(T) μnf/μw = − 3.432 + 0.9931T − 0.4213T0.8424Ln(T) μnf/μw = − 299.3 + 0.03763T + 174.6T−0.2168Ln(T) μnf/μw = − 2.929 + 0.9499T − 0.4046T0.8418Ln(T) μnf/μw = 219.3 − 23.26T + 8.941T0.8568Ln(T)

R-squared = 0.9821 R-squared = 0.9949 R-squared = 0.9975 R-squared = 0.9975 R-squared = 0.9902 R-squared = 0.9995


347

Table 8 Correlations of effective thermal conductivity based on temperature for different nanoparticle concentrations. Solid volume fraction

Correlations

R-squared

φ = 0.01% φ = 0.02% φ = 0.05% φ = 0.1% φ = 0.2% φ = 0.4%

knf/kw = 116.3 − 0.01001T − 62.31T−0.202Ln(T) knf/kw = − 1.988 + 0.0004053T + 1.734T−0.2169Ln(T) knf/kw = − 405.4 + 0.03705T + 221T−0.2033Ln(T) knf/kw = − 1156 + 0.101T + 625.5T−0.202Ln(T) knf/kw = 596 − 0.05347T − 323.3T−0.2031Ln(T) knf/kw = 631 − 0.07067T − 323.3T−0.2031Ln(T)

R-squared = 0.9977 R-squared = 0.9923 R-squared = 0.9989 R-squared = 0.9988 R-squared = 0.9938 R-squared = 0.9968

The dimensionless momentum equation is written as follows:

! 2 2 2 ∂W ∂W ∂W ∂P ∂ W ∂ W ∂ W þ þ þV þW ¼ − þ Pr U ∂x ∂y ∂z ∂z ∂x2 ∂y2 ∂z2

! 2 2 2 ∂U ∂U ∂U ∂P ∂ U ∂ U ∂ U U þ þ þV þW ¼ − þ Pr ∂x ∂y ∂z ∂x ∂X2 ∂y2 ∂z2

ð22Þ

! 2 2 2 ∂V ∂V ∂V ∂P ∂ V ∂ V ∂ V þ þ þV þW ¼ − þ Pr þ RaPrθ U ∂x ∂y ∂z ∂y ∂x2 ∂y2 ∂z2

ð23Þ

ð24Þ

The dimensionless energy equation is written as follows: 2

U

2

2

∂θ ∂θ ∂θ ∂ θ ∂ θ ∂ θ þ V þ W ¼ 2 þ 2 þ 2 ð4Þ ∂x ∂y ∂z ∂x ∂y ∂z

Fig. 9. Isothermal surfaces for different temperature differences and φ=0.1%.

ð25Þ

348


performed with different grid sizes. The grid independency analysis is presented in Table 6. The values average Nusselt number ðNuÞ at different grid sizes are calculated. It can be observed that the grid distribution of (50 × 100 × 100) must be selected due to close value with its before and after grid distribution. 5. Results and discussion 5.1. Dynamic viscosity analysis

Fig. 10. Repeatability evaluation of the data measured by PT100 thermocouples.

4.3. Numerical code validation The finite volume approach and SIMPLE algorithm are utilized in order to solve the governing equations and coupling the velocity with pressure. The present simulation is validated with the threedimensional results of the works performed by Fusegi et al. [39] and Wakashima and Saitoh [40]. The comparisons are presented in Table 5. It can be concluded that there are close agreements between the value of different parameters of the present work and the selected ones. In order to verify that the results are independent from the mesh sizes and choose the best grid size, the grid size independency analysis is

Influences of two main parameters namely solid volume fraction and temperature of nanofluid on the dynamic viscosity of DWCNTswater nanofluid have been studied. The dynamic viscosity is analyzed at six different solid volume fractions (φ = 0.01, 0.02, 0.05, 0.1, 0.2, and 0.4 vol%) and a temperature range of 300 to 340 K. The relative value of dynamic viscosity (μnf/μw) variation with respect to temperature as a function of solid volume fraction is depicted in Fig. 7. As it can be seen in Fig. 7, the dynamic viscosity of nanofluid reduces with increasing of temperature. It is due to the fact that the intermolecular forces reduce with augmenting of temperature in the fluid. As such, different layer of nanofluid can move easier as temperature increasing with respect to lower temperature because of lower shear stress between two layers. As it is mentioned before, the empirical thermophysical properties of DWCNTs-water nanofluid are utilized in the numerical simulation. As such it is needed to identify the relationship between the dynamic viscosities with temperature at different solid volume fractions. In this context, the correlations between dynamic viscosity of nanofluid and temperature at all six different solid volume fractions are presented in Table 7. 5.2. Thermal conductivity analysis Influences of a temperature range of 300 to 340 K and six cases of solid volume fractions of nanofluid (φ = 0.01, 0.02, 0.05, 0.1, 0.2, and 0.4 vol%) on the thermal conductivity are presented. The relative value of thermal conductivity (knf/kw) with respect to temperature as a

Table 9 Repeatability evaluation of the data measured by LM-35 sensors. Type

Sensor num. 1

Sensor num. 2

Sensor num. 3

Sensor num. 4

Sensor num. 5

Sensor num. 6

Sensor num. 7

Sensor num. 8

Sensor num. 9

Hot wall Error Cold wall Error

70.4 °C +0.4 °C 20 °C 0 °C

69.9 °C −0.1 °C 20.3 °C +0.3 °C

70.6 °C +0.6 °C 19.9 °C −0.1 °C

70.2 °C +0.2 °C 20.5 °C +0.5 °C

70.2 °C +0.2 °C 19.7 °C −0.3 °C

69.7 °C −0.3 °C 20.6 °C +0.6 °C

70.4 °C +0.4 °C 20.3 °C +0.3 °C

70.5 °C +0.5 °C 20.4 °C +0.4 °C

69.8 °C −0.2 °C 19.7 °C −0.3 °C

Fig. 11. Comparison of experimental and numerical results at ΔT=20°C and ΔT=50°C, φ=0.4 vol%.


349

Fig. 12. Temperature distribution for different temperature differences and constant solid volume fraction (φ=0.2 vol%).

Fig. 13. Temperature distribution for different solid volume fractions and constant temperature difference ΔT=30°C.

function of solid volume fraction is depicted in Fig. 8. It can be observed that there are no significant differences at the effective thermal conductivity at low concentration of solid particles. On the contrary, the effective thermal conductivity increases considerably at high solid volume fractions. It is due to the fact that the number of collision between the solid particles augments, as a result of greater number of solid particles in a specific volume of base fluid and Brownian motion. On the other hand, the temperature increment boosts the kinetic energy of solid particles which has resulted in significant motions of solid particles and according collisions with other particles including base fluid and solid particles. As such, the temperature increment has more significant influence on the enhancing of effective thermal conductivity at high concentration. The empirical thermo-physical properties of DWCNTs-water nanofluid are utilized in the numerical simulation. As such it is needed to identify the relationship between the thermal conductivity with temperature at different solid volume fractions. In this context, the correlations between thermal conductivity of nanofluid and temperature at all six different solid volume fractions are presented in Table 8.

transferred by the convective flow to the top region of the enclosure at the adjacent of hot wall. Because of this matter, it can be seen that the temperature of nanofluid at the top region of the enclosure is higher than the bottom region where the cold stream is available there. 5.4. Repeatability analysis of temperature measurements The repeatability analysis regarding the temperature measuring with PT100 thermocouples and LM-35 temperature sensors is performed to verify the experimental results and show the range of error at each thermocouple. A sample of temperature distribution at Ra = 5.96 × 108 and φ= 0.4 vol% for expressing the repeatability of the measured temperature by PT100 thermocouples is presented in Fig. 10. As it was mentioned before, the temperature of each point within the enclosure using PT100 thermocouples is measured three times. The temperature differences in total of three experiments measured

5.3. Three-dimensional temperature field The Three-dimensional temperature distributions for different temperature differences between hot and cold walls of setup and one constant solid volume fraction of (φ =0.1 vol%) are depicted graphically in Fig. 9. These figures can give a comprehensive view of the temperature filed and effect of convective flow on the temperature distribution which is not possible, or at least very hard to achieve, by experimental investigations. To understand the temperature field, the flow structure of inside fluid must be identified. As the temperature of nanofluid at the adjacent of hot enhances, the gravity of nanofluid reduces which has resulted in ascending due to buoyancy forces occurring in the presence of gravity acceleration. Afterwards, the nanoparticles and fluid particles travel along the hot wall and top adiabatic wall. As the nanofluid stream reaches to the cold wall, the gravity of nanofluid augments due to lower temperature which has been obtained by the cold wall. As a result, the nanofluid stream descending along the cold wall and travel along bottom adiabatic wall due its velocity magnitude to reach the hot wall again. This process continues again and again which makes a clock-wise three-dimensional flow structure. The heat energy is

Fig. 14. Effect of DWCNT nanoparticle concentration on the average heat transfer coefficient.

350


5.6. Temperature distribution The temperature distribution of nanofluid within the enclosure measured by PT100 thermocouples at the mid-height of the enclosure at different temperature differences (Rayleigh number) and specific solid volume fraction is presented in Fig. 12. Nine points at the inside of the enclosure are measured with the PT100 thermocouples. It can be observed that the temperature value of nanofluid augments with enhancing the temperature difference. The Rayleigh numbers, presented in Fig. 12, are equal to temperature differences of: • • • •

Fig. 15. Effect of DWCNT nanoparticle concentration on the average Nusselt number.

by PT100 sensors are in range of −0.25 to +0.55 °C. At similar Rayleigh number and solid volume fraction, the repeatability of LM-35 sensors is presented in Table 9. As it is observed in Table 9, the temperature measured by LM35 at the back of the heater has a slight difference in each measuring process in range of −0.3 to +0.6 °C.

5.5. Comparison of temperature distribution (experimental vs. numerical) The comparison between the experimental and numerical results for the temperature distribution at the mid-height of the enclosure measured by PT100 thermocouples is presented in Fig. 11. Two experimental cases with constant solid volume fraction (φ = 0.4 vol%) and Rayleigh numbers of Ra = 2.39 × 108 (equal to Δ T = 20°C) and Ra = 5.96 × 108 (equal to ΔT = 50°C) are compared with the numerical results with similar boundary conditions and operating fluid. It can be observed that the experimental and numerical results are in close agreements with each other. As such, it can be concluded that the experimental results can be verified properly.

Ra =2.64× 108 is equal to ΔT = 20°C Ra =3.96× 108 is equal to ΔT = 30°C Ra =5.26× 108 is equal to ΔT = 40°C Ra =6.61× 108 is equal to ΔT = 50°C.

It can be observed that the temperature differences between the side heated and cooled walls and the center of the enclosure become greater as Rayleigh number increases. Also, to draw a comprehensive view, the influence of different solid volume fractions at a constant temperature difference is presented in Fig. 13. It can be seen that there are no considerable changes at the temperature at each point. It is due to the fact that the nanoparticles influences become stronger at high velocity magnitude. As the velocity magnitude and according kinetic energy increases, the Brownian motion effects become stronger and play more important role in changing the thermal characteristics of a thermal system. In this context, it can be observed that the temperature difference at the adjacent of side walls are more clear that the core region of the enclosure where the velocity components magnitudes are no significant. 5.7. Average heat transfer coefficient It follows from Fig. 14, the effects of solid volume fraction of DWCNTs-water nanofluid on the average heat transfer coefficient. It can be observed that the average heat transfer coefficient enhances with increasing of solid volume fraction until φ = 0.05 vol%. It is due to the fact that the thermal performances of the pure water are improved by adding nanoparticles. After this solid volume fraction, the

Table 10 Correlations of average Nusselt number based on Rayleigh number for different nanoparticle concentrations. Solid volume fraction φ = 0.01%

φ = 0.02%

φ = 0.05%

φ = 0.1%

φ = 0.2%

φ = 0.01%

Correlations

R-squared

Nu ¼ 370:5−4:709 108 Ra−747:1

Nu ¼ 26:7−4:9 108 Ra−751:1

R-squared = 0.9950

Ra0:2

LnðRaÞ

Nu ¼ 375:7−4:9 108 Ra−753:8

Nu ¼ 375−6:18 108 Ra−729:3

LnðRaÞ

R-squared = 0.9949

Ra0:2 LnðRaÞ

R-squared = 0.9948

Ra0:2 LnðRaÞ

Nu ¼ 366:3−5:45 108 Ra−722:1

R-squared = 0.9946

Ra0:2 LnðRaÞ

Nu ¼ 353:1−5:828 108 Ra−686:7

R-squared = 0.9954

Ra0:2 LnðRaÞ Ra0:2

R-squared = 0.9960


average heat transfer performance deteriorates because of dominant influence of viscosity compared with the thermal properties.

p P

351

pressure, Pa dimensionless pressure

5.8. Average Nusselt number The values of average Nusselt number with respect to Rayleigh number as a function of solid volume fractions are presented in Fig. 15. As it can be observed in this figure, the average Nusselt number augments with increasing of Rayleigh number. It is due to the fact that the velocity magnitude of the nanofluid stream enhances as the Rayleigh number increases. Moreover, the kinetic energy increases which causes that the Brownian effects becomes more effective. Also, in a same condition with the average heat transfer coefficient, the Nusselt number enhances with increasing of solid volume fraction till =0.05 vol%. In a curve fitting to the experimental data, the following correlations are developed to connect the average Nusselt number to solid volume fraction and Rayleigh number as presented in Table 10.

Greek letters

α μ ν ρ β θ

thermal diffusivity, m2 s−1(k/ρCp) dynamic viscosity, N s m−2 kinematic viscosity, m2 s−1(μ/ρ) density, kg m−3 thermal expansion coefficient of fluid, 1/K dimensionless temperature

Subscripts

6. Conclusion An experimental and numerical investigation on the natural convection heat transfer performance in a cuboid enclosure filled with DWCNTs-water nanofluid is carried out. The experiments are conducted for four different temperature differences between side hot and cold walls (ΔT = 20 °C, 30 °C, 40 °C and 50 °C) and four six different solid volume fractions of nanofluid (φ = 0.01, 0.02, 0.05, 0.1, 0.2, and 0.4 vol%). Moreover, the thermo-physical properties of obtained DWCNTs-water nanofluid are measured empirically. The numerical simulation has been performed to verify the experimental results and draw a comprehensive view of three-dimensional temperature field. Changing the temperature difference has considerable influences on the temperature distribution. On the contrary, increasing of solid volume fraction has no significant effect on the temperature distribution, especially at the core region of the enclosure. Increasing of temperature difference causes enhancing average heat transfer coefficient and Nusselt number. The optimum value of solid volume fraction for highest value of average heat transfer coefficient and Nusselt number is 0.05 vol% which after this point the both parameters will be deteriorated. Nomenclature g gravitation acceleration, m s−2 H height of cavity, m L width of cavity, m D depth of cavity, m q_ heat generation rate in water channel _ m mass flux in water channel Cp specific heat capacity, J∙ kg−1 · K−1 Th average temperature of hot wall, K Tc average temperature of cold wall, K Tih temperature of points of hot wall, K T temperature of points of cold wall, K ΔTEn temperature difference of side walls ΔTEx temperature difference of water channel Tinlet temperature of inlet in water channel, K Toutlet temperature of outlet in water channel, K A area of side walls, m2 h Nu Ra x′, y′, z′ x, y, z u,v,w U, V,W

average heat transfer coefficient, W/m2·K Averaged Nusselt number Rayleigh number, Ra = gβnf(TH −TC)H3/να Cartesian coordinates, m 0 0 0 dimensionless coordinates (x H , y H , z H ) velocity components (m =s ) dimensionless velocity components

h c nf w

hot cold nanofluid water

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