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Experimental study on thermal performance of water-based nano-PCM emulsion flow in multichannel heat sinks with parallel and divergent rectangular mini-channels
International Journal of Heat and Mass Transfer 146 (2020) 118861
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Experimental study on thermal performance of water-based nano-PCM emulsion flow in multichannel heat sinks with parallel and divergent rectangular mini-channels C.J. Ho a,⇑, Shao-Teng Hsu a, Jer-Huan Jang b, Seyyede Fatemeh Hosseini c, Wei-Mon Yan d,e,⇑ a
Department of Mechanical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan Department of Mechanical Engineering, Ming Chi University of Technology, New Taipei City 24352, Taiwan Department of Chemistry, Faculty of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran d Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan e Research Center of Energy Conservation for New Generation of Residential, Commercial, and Industrial Sectors, National Taipei University of Technology, Taipei 10608, Taiwan b c
a r t i c l e
i n f o
Article history: Received 26 May 2019 Received in revised form 6 October 2019 Accepted 7 October 2019
Keywords: Nano-PCM emulsion Mini-channel heat sink Parallel and divergent channels Thermal performance
a b s t r a c t In this work, an experimental study is arranged to investigate the cooling efficacies of water-based nano-PCM emulsion flow in the multi-channel heat sinks with parallel and divergent rectangular mini-channels. N-eicosane particles with size of 130 nm are considered as the phase change material (PCM) nanoparticles. Two multi-channel heat sinks with eight parallel and divergent mini-channels are fabricated. The divergent channel has a divergent angle of 2.06°. The effects of different parameters including volumetric flow rate of working fluid (60 cm3/min < Q_ < 600 cm3/min), heat flux (3.2 W/cm2 < q00h < 4.8 W/cm2), Reynolds number (100 < Re < 1000), and mass fraction of PCM nanoparticles (0% < xPCM < 10%) on the dimensionless wall temperature, the Nusselt number, the cost of performance (COP), and the pressure drop are investigated. The experimental results show that the nano-PCM emulsion can improve heat transfer in both parallel and divergent mini-channel heat sinks as compared with the pure water. At Rebf = 965 and q00h = 3.21 W/cm2, the average Nusselt number in the parallel mini-channel heat sink improves about 15.2% by adding the PCM nanoparticles with mass fraction of 10% to the base fluid. This enhancement is up to 13.8% in the divergent mini-channel heat sink at Rebf = 295 and q00h = 3.21 W/cm2. Moreover, the divergent mini-channel heat sinks provide a higher Nusselt number along with lower pressure drop as compared with the parallel ones. Accordingly, the value of COP increases by diverging the mini-channel. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction With the fast development of IT technologies and microchips industries, it is momentous to remove a large value of thermal energy from a finite surface to cool the electronic components used in these technologies and industries. Channel heat sinks with micro or mini sizes can be nominated to achieve this purpose. Generally, they have a high heat transfer efficiency, small geometric size and volume per heat load. Moreover, they require a lower coolant and impose less operational cost as compared with the regular heat sinks [1–3].
⇑ Corresponding authors at: Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan (W.-M. Yan). E-mail addresses: [email protected] (C.J. Ho), [email protected] (W.-M. Yan). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118861 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
Some researchers have focused on the channel heat sinks with mini or micro sizes. Ghasemi et al. [4] investigated the effects of diameter of the circular mini-channel heat sink on the heat transfer and pressure drop of this device. They found that the pressure drop decreases by increasing the channel diameter of the heat sink. In addition, the mini-channel heat sink with the diameter of 4 mm provides a much smaller thermal resistance as compared with the mini-channel heat sinks with the diameters of 6 mm and 8 mm. Kumar and Singh [5] studied the influences of flow inlet angle on flow maldistribution and thermal efficiency of the mini-channel heat sink. They focused on three flow inlet angles including 90°, 105°, and 120°. They concluded that the flow inlet angle of 105° has the best thermal efficiency among other flow inlet angles considered in their study. Xie et al. [6] performed a numerical simulation to investigate the heat transfer and fluid flow through a water-cooled mini-channel heat sink for the turbulent regime. They concluded that using a narrow and deep channel with thin
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Nomenclature A Abase Cp DH f hpcm H k ks L N Nuitd Pw qo,corr qo,eff Q_ Re Rmax Sb*
base area of the heat sink (m2) total base area of the heat sink (m2) specific heat (J/kg K) hydraulic diameter of channel (m) fanning friction factor (–) latent heat of melting (J/kg) height (m) thermal conductivity of the coolant (W/m K) thermal conductivity of the substrate material (W/m K) length (m) number of channels (–) average Nusselt number (–) pumping power (W) corrected electric power due to wall heat conduction losses effective heat input carried by the working fluid volume flow rate (cm3/min) Reynolds number (–) overall thermal resistance (K/W) modified inlet subcooling parameter (Tm Tin)/DTref
thickness can enhance the thermal efficiency with an acceptable pressure drop. In other research, Xie et al. [7] simulated a watercooled mini-channel heat sink with various chip arrangements. They showed that a good cooling efficiency can be achieved for the electronic systems by using a proper chip arrangement. Other techniques have been employed by some researchers to enhance the thermal efficiencies of the channel heat sinks [8]. Khoshvaght-Aliabadi and Nozan [9] evaluated the influences of corrugation shapes of a corrugated mini-channel heat sink on the heat transfer and pressure drop of this device. They considered four cases including three corrugated mini-channel heat sinks with the triangular, trapezoidal, and sinusoidal shapes and straight minichannel heat sink. It was found that the largest ratio of the heat transfer rate to the pumping power is related to the sinusoidal mini-channel heat sinks. In a numerical work, Hung et al. [10] used the nanofluids to improve the thermal efficiency of the microchannel heat sinks. They used water based Al2O3 and water based diamond nanofluids as the coolant in this system. Their results showed that the thermal efficiency of the system can be improved about 21.6% by using these nanofluids as compared with the pure water. In addition, the thermal efficiency is usually higher by using a nanofluid with small value of dynamic viscosity as compared with the nanofluid with large value of dynamic viscosity. Ho and Chen [11] performed an experimental work to investigate the thermal efficiency of water based Al2O3 nanofluid in the mini-channel heat sink. They found that the heat sink cooled with nanofluid provides considerably larger average heat transfer coefficients and accordingly, works better in comparison with the heat sink cooled with the pure water. Tullius et al. [12] used micro pin fins in the mini-channels. They employed the pin fins with different shapes including square, circle, triangle, diamond, ellipse, and hexagon. They concluded that triangular pin fin heat sink with larger height, smaller width, and spacing double the fin width provides a better efficiency. Bi et al. [13] improved the thermal efficiency of the mini-channel heat sinks with dimples and cylindrical grooves. Their results showed that the efficiency of cylindrical groove surface is somewhat lower as compared with the dimple surface. Phase change material particles are suspended in the thermal fluid to transport and/or save thermal energy. They were widely used for applications of forced convective heat transfer improvement [14–16]. Sivasamy et al. [17] reviewed the heat transfer
Stebf T DTref u W Wrib
Stefan number temperature (K) reference temperature difference (K) velocity of fluid (m/s) width (m) rib width (m)
Greek symbols l dynamic viscosity (kg/m s) q coolant density (kg/m3) X pumping power (W) Subscripts bf base fluid ch channel eff effective in inlet itd inlet temperature difference m mean w wall
improvement techniques used in the phase change materials. They reported that the extended surface, multiple PCMs, composite PCMs, and encapsulation are some techniques use to accelerate the solidification and melting processes in the phase change materials. Aziz et al. [18] used the pins and copper plating to improve the performance of an encapsulated PCM in sphere used in a thermal energy storage system. Their results showed that the usage of pins can decrease the phase change time in the PCM about 27%, while the usage of copper coating and embedded pins decreases the phase change time up to 37% as compared with a plain sphere. Ho et al. [19] investigated the thermal characteristics of hybrid water-based suspension of aluminium oxide nanoparticles and microencapsulated phase change material particles. They concluded that the dispersion of aluminium oxide nanoparticles can considerably recover the low thermal conductivity of the pure phase change material suspensions. The heat transfer efficiency of water-based suspensions of aluminium oxide nanoparticles and microencapsulated phase change material particles in the mini-channel heat sink was experimentally performed by Ho et al. [20]. Their results showed that the heat transfer effectiveness of the mini-channel heat sink can improve about 56% by using this hybrid water-based suspensions. Later, Ho et al. [21] investigated the potentials of hybrid aluminium oxide-water based nanofluid and phase change material suspension for improving the thermal efficiency of coolant in the mini-channel heat sink. It was observed that the efficiency of the hybrid suspension is significantly related to the Reynolds number. For example, the pure nanofluid acts better as compared with the hybrid suspension at larger value of Reynolds number. Recently, Ho et al. [22] enhanced the thermal efficiency of the mini-channel heat sink by diverging the minichannel. It was found that the divergent mini-channel heat sink can provide higher values of heat transfer coefficient and cost of performance as well as smaller value of pressure drop penalty as compared with the parallel one, especially for the larger flow rates. The literature review showed that the thermal efficiencies of mini-channel heat sinks can be improved by using Nano-PCM emulsion or diverging the mini-channel as two different techniques. These two techniques are used in this study, simultaneously in the mini-channel heat sink to achieve the larger thermal efficiencies. This paper arranges an experimental study to investigate the convective heat transfer of Nano-PCM emulsion flow
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
through the parallel and divergent rectangular mini-channels. The effects of different parameters including the volumetric flow rate of working fluid, the heat flux, the Reynolds number, and the mass fraction of PCM nanoparticles on the Nusselt number, the cost of performance, and the pressure drop are investigated. 2. Experimental 2.1. Experimental setup The schematic view of the present experimental setup is depicted in Fig. 1. As it is seen in this figure, the experimental setup has a closed circuit. The main components of this setup are a tank, DC power supply, a data acquisition system, the heat exchangers (cooling and heating exchangers), and a centrifugal pump. The working fluid enters the centrifugal pump from the tank. The centrifugal pump is employed for circulating the working fluid within the circuit. By adjusting the pump speed, the desired flow rate can be achieved. To maintain the inlet working fluid at a constant temperature, the fluid enters a heating heat exchanger, consists of constant temperature bath, at the inlet section of the test section. In addition, the fluid enters the cooling heat exchanger for resetting its temperature before backing to the tank at the outlet section of the test section. Indeed, the cooling heat exchanger is employed for cooling down the heated coolant before entering the tank for recirculation. It has a plate heat exchanger and a fabricated water bath. The water bath is employed for supplying the cooling fluid for the plate heat exchanger. A DC power supply is installed to provide the homogeneous wall heat flux. The amount of the desired heat flux can be achieved by adjusting the current and voltage used for the heater. A flow meter is used for adjusting the volumetric flow rate. Two pressure taps are located at two ends of the minichannels to determine the pressure drop along the heat sink. In this study, two T-type thermocouples are placed at two ends of the mini-channels to measure the temperatures at these regions. In addition, the wall temperature is measured employing seven T-type thermocouples placed in small holes at a distance of 3 mm under the base surface along the centerline of the minichannel heat sink. In the experimental setup, insulating material is used to reduce the heat loss from the test section. 2.2. Experimental procedure details The working fluid (coolant) of this experiment is the waterbased phase change material (PCM) emulsions. N-eicosane and
3
SLS are considered as the PCM and the surfactant, respectively. In the present investigation, two different configurations for the multi-channels are used. These configurations are two mini-channel heat sinks with eight parallel and eight divergent mini-channels, respectively. Divergent mini-channels have divergence angle of 2.06° and the length of 50 mm. Figs. 2 and 3 show the three-dimensional schematic and the detailed schematic of the mini-channel heat sink configurations, respectively. Moreover, more details about the mini-channel heat sink are summarized in Table 1. The photographs of parallel and divergent flow channels are shown in Fig. 4. It should be noted that the divergent mini-channels have the same geometry with the parallel one at the inlet cross-section. However, the channel width is linearly expanded from the inlet, leading to a width of 2.8 mm at the outlet section for the divergent minichannels. Each mini-channel has been fabricated from oxygenfree copper with an inlet cross-sectional area of 1 mm in width by 1.5 mm in height. The test section also has two plate heaters that are powered by a DC power supply. In Fig. 2, the material used for the top surface is acrylic. It should be also noted that the acrylic has good thermal insulation effect. Moreover, it has a transparent appearance, which is convenient for directly observing the flow field condition in the minichannel. Due to these reasons, this material is selected as the top surface. For the middle and bottom sections, that mainly cover the oxygen-free copper flow path and the main and auxiliary heating sheets, the polyether ether ketone plastic material is selected. The polyether ether ketone plastic material has the high values of temperature resistance, mechanical strength, and chemical resistance. Note that in Table 1, Wch, Hch, Wrib, DH, Ar, and Hc are the channel inlet and outlet widths, the channel height, the fin width, the hydraulic diameter, the aspect ratio, and the heat sink bottom thickness, respectively. In this study, some techniques are used when preparing the nano-PCM emulsion to ensure about the stability of the nanofluids. The details of these techniques can be found at Ho et al. [23]. Fig. 5 shows the results of the SEM and TEM analyses. These analyses are employed for approximating the size of the MEPCM employing JEOL JEM-1400 device. It can be seen that the MEPCM particles have approximately spherical shape with the particle size distribution in the range of 5–10 lm. A DSC with the Flash DSC 1 of Mettler-Toledo is employed in this study. The results of detailed DSC measurement for the nano-PCM powder are displayed in Fig. 6. For DSC measurements, the cooling/heating rate is 5 K/min and temperature is varied in the range of 15–50 °C [23].
Fig. 1. The schematic of the experimental setup.
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Temperature port
Outlet PMMA plate cover
Inlet
Pressure port
PEEK plate Mini-channel heat sink Main heater Asbestos Compensative heater
PEEK dock Fig. 2. Three-dimensional schematic of the oxygen-free copper heat sink.
3. Theoretical consideration 3.1. Parameters definitions Before defining the parameters, it must be noted that the following assumptions are consummated: The parallel and divergent mini-channels have similar sizes at the inlet section and wall roughness. The flow rates and the heat flux are assumed to be same in each mini-channel. The required parameters in this study are defined in this section. The Reynolds number, based on the properties of the base fluid, is defined by:
Rebf ¼
qbf um DH lbf
ð1Þ
where qbf and lbf are the density and dynamic viscosity of the base fluid, respectively; DH is the hydraulic diameter of the minichannel; and um is the bulk fluid velocity, which can be defined by:
Q_ um ¼ NAch
ð2Þ
where Q_ is the volumetric flow rate, N is the number of channels, and Ach is the cross-sectional of a mini-channel. The divergent and parallel channels have the same inlet cross-sectional areas. Accordingly, the flow velocity and the hydraulic diameter are calculated based on the inlet cross-sectional areas. Therefore, the Reynolds number at the inlet from Eq. (1) can be calculated as follows:
Rebf ;in ¼
qbf ;in uin DH;in lbf ;in
ð3Þ
The friction factor can be determined as follows [24]:
f ¼
1 DH Dp 2 Lch qu2
ð4Þ
Fig. 3. The geometries of mini-channel heat sink configurations: (a) Parallel flow path mini-channel heat sink; (b) Divergent flow path mini-channel heat sink.
where Lch is the length of the mini-channel. Moreover, Dp indicates the pressure drop between inlet and outlet of the mini channel, which can be determined by [24]:
Dp ¼ Dpm ðkc þ ke Þ
qu2 2
ð5Þ
Here, Dpm is the measured pressure drop by the instrument in the inlet and outlet sections of the mini-channel and kc and ke indicate the contraction and expansion coefficients, respectively. For the parallel mini-channel, the contraction and expansion coefficients are equal to 0.937271 and 0.4499492, respectively, while for the divergent one, kc = 0.829478 and the expansion coefficient is the same with the parallel mini-channel.
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C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861 Table 1 Details about the dimensions of parallel and divergent mini-channel heat sinks. Type of MCHS
Wch (mm)
Hch (mm)
Wrib (mm)
DH (mm)
Ar (mm)
Hc (mm)
Parallel Divergent
1.0 2.8
1.5 1.5
2.1 0.3
1.2 1.95
1.5 0.54
5 5
Parallel flow channel
D i v e r g e n t f l o w ch a n n e l
Fig. 4. Photographs of parallel and divergent flow channels.
SEM image
TEM image Fig. 5. SEM and TEM images.
Fig. 6. DSC chart for nano-PCM powders.
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C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
The non-dimensional wall temperature employed in this study can be determined by:
hw ¼
T w T in DT ref ;bf
ð6Þ
where Tw and Tin are the wall and input temperatures, respectively. The following equation can be used to calculate the wall temperature:
T w ¼ T tc
q00 h Hc kc
ð7Þ
where Ttc indicates the measured local wall temperature. kc and Hc are the base material thermal conductivity and the heat sink bottom thickness, respectively. q00h can be determined by:
q00h ¼
qh qh ¼ Abase NðW ch þ W rib ÞLch
ð8Þ
where qh and Abase are the heat input carried by the working fluid and the total base area of the heat sink, respectively. In Eq. (6), the reference temperature of base fluid, DT ref ;bf , can be calculated by:
DT ref ;bf ¼
qh
ð9Þ
qbf cp;bf Q_
where cpbf is the heat capacity of base fluid. The average Nusselt number is defined by:
Nuitd ¼
hitd DH km
The thermophysical properties of the mixture water-PCM nanoparticles can be found at Ho et al. [23]. 3.2. Validation part In order to validate the experimental data, the current results are compared with the experimental results for the average Nusselt number variation against the Reynolds number. The validation is performed for the case of pure water. The results of this comparison are shown in Fig. 4. It should be noted that these results are given for the parallel mini-channel heat sink. Lee et al. [26] have examined the hydrothermal characteristics of flow through a mini-channel with the hydraulic diameter in the range of 0.318– 0.903 mm and Reynolds number in the range of 300–3500. Moreover, Rao et al. [27] and Ho et al. [11] examined the effectiveness of PCMs and nanofluids on the hydrothermal characteristics of flow inside a mini-channel heat sink with different hydraulic diameters, respectively. Notice that the aspect ratios of mini-channels considered by Ho et al. [11], Lee et al. [26], and Rao et al. [27] are 1.5, 5.45, and 2.1, respectively. Fig. 7 shows that there are good agreements between the current results and the results presented by Ho et al. [26], Lee et al. [14], and Rao et al. [27] for the average Nusselt number at different Reynolds numbers with pure water fluid. To perform more validation, the friction factor obtained by the present experiment is compared with that of Ho et al. [11]. This comparison can be seen in Fig. 8. As shown in this figure, the good agreement between the current results and the results presented by Ho et al. [11] can be observed for the friction factor at different Reynolds numbers.
ð10Þ 3.3. Uncertainty analysis
where km is the thermal conductivity of the mixture. The average
convection coefficient, hitd ;is calculated as follows:
hitd ¼
q00 h
ð11Þ
ðT w T in Þ
The cost of performance (COP) shows the heat carried by the coolant per unit required pumping power. This parameter is defined by:
COP ¼
qh P
Since the measurements of physical parameters of the experiment and the measuring instruments have some errors, the influences of these errors should be considered on the results. In order to understand the impact of experimental error on the experimental data processing, an uncertainty analysis is required. This analysis is provided in this section. According to Taylor’s theorem, the mathematical expression for the function f can be presented as follows:
ð12Þ
20
where P is the required pumping power calculated by:
18
P ¼ Dp Q
ð13Þ
16
The friction of the flow through the rectangular mini-channel heat sink, proposed by Kandlikar [25], has been employed. The proposed equation for the rectangular mini-channel in fully developed flow is presented as follows:
0:2537a5 Þ
3
4
ð14Þ
where a is the aspect ratio of the cross-sectional area of the minichannel. In this experiment, the value for a is 0.667, and the value of fRe is 14.71 by using Eq. (14). The Stefan number is defined by:
Stebf ¼
cp;bf DT ref ;bf hpcm
14
Nu mtd
f Re ¼ 24ð1 1:3553a þ 1:9467a 1:7012a þ 0:9564a 2
Present Work (DH=1.2 mm) Ho et al. (2013) (DH=1.2 mm) Lee et al. (2005) (DH=0.9 mm) Rao et al. (2007) (DH=2.71 mm)
12
10
8
6
4
ð15Þ
where cp,bf, DTref,bf, hpcm are the heat capacity of the base fluid, reference temperature difference of base fluid, and latent heat of melting of PCM, respectively.
0
500
1000
1500
2000
Rebf Fig. 7. The comparison between the present experimental results and the results presented by Lee et al. [26], Rao et al. [27] and Ho et al. [11] for the average Nusselt number at different Reynolds numbers in the parallel mini-channel heat sink.
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C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
100
4. Results and discussion Present work Ho et al.(2013)
10-1
The experimental results are presented in this section. The effects of different parameters including the volumetric flow rate of working fluid (60 cm3/min < Q_ < 600 cm3/min), the heat flux (3.2 W/cm2 < q00h < 4.8 W/cm2), the Reynolds number (100 < Re < 1000), and the mass fraction of PCM nanoparticles (0% < xPCM < 10%) on the Nusselt number, the cost of performance, and the pressure drop are investigated. 4.1. Dimensionless wall temperature
14.71/Re 10
-2
500 Rebf
1500
Fig. 8. The comparison between the present experimental results and the results presented by Ho et al. [11] for the friction factor at different Reynolds numbers.
f ðx1 þ Dx1 ;x2 þ Dx2 ; ;xn þ Dxn Þ ¼ @f þ high order f ðx1 ;x2 ; xn Þ þ Dx1 @x@f1 þ Dx2 @x@f2 þ þ Dxn @x n
ð16Þ The error of this function can be calculated by:
df ðx1 ; x2 ; xn Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 @f @f @f D x1 þ Dx2 þ þ D xn ¼ @x1 @x2 @xn
ð17Þ
The uncertainties of the physical parameters and the measuring instruments used in the experiment are summarized in Table 2.
The effects of heat fluxes and mass fraction of PCM nanoparticles on the dimensionless wall temperatures of divergent minichannel heat sink are shown in Fig. 9. As can be seen in this figure, the dimensionless wall temperature has reduction trend at the end sections of the divergent mini-channels. This trend can be justified by occurring the post heating at the end sections of the minichannel due to the axial wall conductive heat transfer. Furthermore, the cooling effect improves and the dimensionless wall temperature decreases by adding the PCM nanoparticles to the base fluid and increasing the mass fraction of nanoparticles. For example, at the end of mini-channel, the dimensionless wall temperature reduces about 12% by adding the PCM nanoparticles with mass fraction of 10% to the base fluid at q00h ¼ 3:21 W=cm2 . The thermal conductivity of the base fluid enhances by adding the PCM nanoparticles with larger mass fractions. The increment in the thermal conductivity leads to increasing the heat transfer rate and subsequently, the dimensionless wall temperature decreases. Finally, this figure shows that the dimensionless wall temperature reduces by increasing the heat flux. Fig. 10 discloses the dimensionless wall temperature of pure water flow in divergent mini-channel heat sink for two values of volumetric flow rate. As shown in this figure, the dimensionless wall temperature increases by increasing the volumetric flow rate. For example, at the end of the mini-channel, the dimensionless wall temperature of pure water flow in divergent mini-channel heat sink increases about 211% by increasing the volumetric flow
Table 2 The uncertainties of the physical parameters and the measuring instruments in the experiment for the parallel and divergent mini-channels. Item
Symbols
Ranges
Uncertainties
Input parameters Electrical voltage (Volt) Electrical current (A) Length of mini-channel (mm) Hydraulic diameter (mm)
V I Lch DH
75 to 95 0.522 to 0.653 50 1.20 to1.68
±0.5 (V) ±0.0005 (A) 0.01 (mm) 1.3 to 0.9 (%)
Q_ Dp Ttc DT
60 to 600
0.5 to 5 (%)
20 to 5100 311.4 to 337.4 1.0 to 14.9
±5 (pa) ±0.3 (K) ±0.3 (K)
qh
40.2 to 60.1
0.5 to 0.7 (%)
hw Rebf Rebf P f
1.46 to 6.56 138 to 1381 102 to 1015 1.541e05 to 0.046 0.018 to 0.164 2005 to 5935
3.1 1.9 1.4 0.5 5.7 2.4
Measured parameters Volume flow rate (cm3/min) Pressure drop (pa) Temperature (K) Temperature difference between the inlet and outlet section of mini-channel Power (W) Output parameters Dimensionless temperature Reynolds number for parallel mini-channel Reynolds number for divergent mini-channel Pumping power Friction factor Average heat transfer coefficient (W/m2 K) Average Nusselt number Maximum thermal resistance (K/W) Average thermal resistance (K/W) Peclet number Stefan number
hitd
Nuitd Rmax Ravg Pebf Stebf
to to to to to to
11.2 (%) 5.3 (%) 5.2 (%) 25.5 (%) 28.6 (%) 7.9 (%)
4.0 to 11.8
3.2 to 8.2 (%)
0.16 to 0.47 0.13 to 0.45 507 to 6902 0.0164 to 0.2444
2.5 2.6 1.9 0.8
to to to to
6.6 (%) 8.5 (%) 5.2 (%) 28.6 (%)
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C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
Symbols
3
0% 2% 5% 10%
2.2
Pebf=484.77
Q=60 cm /min
pcm
" h
q =3.21 W/ cm
2
Symbols
* bf
Ste =0.1638
3
Q=60 cm /min
pcm
" h
0% 2% 5% 10%
*
Sbbf=0.2103
q =4.79 W/ cm
Pebf=482.15 2
Ste*bf=0.2444 *
Sbbf=0.1460
w
2
1.8
1.6
1.4
0
0.01
0.02
0.03
0.04
0.05
+
x /(DHPebf )
0
0.01
0.02
0.03
0.04
0.05
+
x /(DHPebf )
Fig. 9. The dimensionless wall temperature of divergent mini-channel heat sinks for different values of heat flux and mass fraction of PCM nanoparticles atQ_ = 60 cm3/min.
Q =60 cm3/min
Q =600 cm3/min
Fig. 10. The dimensionless wall temperature of pure water flow in divergent mini-channel heat sink for two values of volumetric flow rate.
rate in the range of 60–600 cm3/min at q00h ¼ 3:21 W=cm2 . Note that for the flow with high values of volumetric flow rate, the effective heat exchange duration cannot be achieved as the time spent for heat transfer in the heat exchanger is too short. This causes the increment in the dimensionless wall temperature. Also, it should be noted that the coolant velocity within the mini-channel heat sink increases as the volumetric flow rate increases. However, the time spent for the heat transfer in the system decreases by increasing the coolant velocity. The dimensionless wall temperature distributions of pure water flow in parallel and divergent mini-channel heat sinks are disclosed in Fig. 11. It can be dedicated that using the divergent
mini-channel significantly decreases the dimensionless wall temperature as compared with the parallel one. Moreover, this figure demonstrates that the maximum dimensionless wall temperatures occur in the vicinity of the mid-sections of both configurations. The difference between the dimensionless wall temperatures of parallel and divergent mini-channel heat sinks is smaller at the end section of the mini-channel. 4.2. Heat transfer characteristics Fig. 12(a) and (b) show the variations of average Nusselt number versus the Reynolds numbers for different values of mass fraction of
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
7 pcm
6.5
=0%
Symbols
Channel
Rebf,in=690 " hh
qq =3.20 W/cm
6
9
par ( =0 ) div ( =2.06 )
2
5.5 5 w
4.5 4 3.5 3 2.5 2
0
5
10
15
20 + x /DH,in
25
30
35
40
Fig. 11. The dimensionless wall temperature distribution for pure water in parallel and divergent mini-channel heat sinks.
PCM nanoparticles in the parallel and divergent mini-channel heat sinks, respectively. As can be seen in these figures, the average Nusselt number increases with increasing the Reynolds number for both mini-channel heat sinks. It is noticed that the velocity of working fluid and subsequently, the convective heat transfer rate increase as the Reynolds number increases. Moreover, the thermal boundary layer thickness decreases as the Reynolds number increases and this causes the increment in the convective heat transfer rate. For example, the average Nusselt number of waterbased Nano-PCM emulsion flow in the parallel mini-channel heat sink enhances up to 193% by increasing the Reynolds number in the range of 136 to 1380 at q00h ¼ 3:21 W=cm2 and xPCM = 10%. The heat transfer rate and Nusselt numbers are improved by adding the PCM nanoparticles to the base fluid and increasing the mass fraction of nanoparticles for both channels. For example, the average Nusselt number in the parallel mini-channel heat sink improves about 15.2% by adding the PCM nanoparticles with mass fraction of 10% to the base fluid at Rebf = 965 and q00h ¼ 3:21 W=cm2 . This enhancement is up to 13.8% in the divergent mini-channel heat sink at Rebf = 295 and q00h ¼ 3:21 W=cm2 . Finally, it can be concluded by comparing the results presented in Fig. 12(a) and (b) that the Nusselt number for the divergent mini-channel heat sink is larger as compared with the parallel one. Note that the reduction in the coolant velocity within divergent mini-channel leads to the higher resistance time of the working flow. Accordingly, the working fluid can absorb larger amount of thermal energy that provides higher heat transfer rate. Fig. 13 discloses the variations of average Nusselt number versus Reynolds number for different values of mass fraction of PCM nanoparticles in the divergent mini-channel heat sink under different heat fluxes. It can be seen that the average Nusselt number enhances with increasing the Reynolds number and mass fraction of PCM nanoparticles in the divergent mini-channel heat sink. In addition, the heat flux has a minor effect on the average Nusselt number for most cases.
As shown in this figure, the pressure drop increases as the Reynolds number increases for both mini-channels. In addition, the pressure drop increases by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles for both minichannels. This is due to the increase in the viscosity of the fluid phase by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles. Finally, with comparing two configurations of mini-channel heat sinks, it can be dedicated that the pressure drop reduces when the divergent mini-channel heat sink is used. This reduction is more obvious at larger Reynolds numbers. For example, the pressure drop decreases about 72.9% by diverging the mini-channel at Rebf = 1376 and xPCM = 10%. As a result, a lower pumping power is required for divergent mini-channels.
4.3. Pressure drop
4.4. Cost of performance
The variations of pressure drop versus Reynolds numbers for different values of mass fraction of PCM nanoparticles in the parallel and divergent mini-channel heat sinks are disclosed in Fig. 14.
In order to evaluate the conditions and effectiveness of the changes made in the system and to achieve the best results, it is important to consider the heat transfer improvement and the pres-
Fig. 12. The variations of average Nusselt number versus Reynolds number for different values of mass fraction of PCM nanoparticles in (a) the parallel minichannel heat sink; (b) the divergent mini-channel heat sink.
10
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
24
Symbols
=2.06
pcm
qh"h=3.21 W/cm2
0% 2% 5% 10%
22 20
Symbols
=2.06
pcm
2 " qqhh=4.79 W/cm
0% 2% 5% 10%
18
Nu itd
16 14 12 10 8 6 4 2
200
400
600
800
1000
200
Rebf
400
600
800
1000
Rebf
Fig. 13. The variations of average Nusselt number versus Reynolds number for different values of mass fraction of PCM nanoparticles in the divergent mini-channel heat sink under different heat fluxes.
=0
=2.06
nanoparticles especially at high mass fraction, leading to the increase in friction and required pumping power. Finally, by comparing the results obtained for the parallel and divergent minichannel heat sinks, it can be concluded that the value of COP increases by diverging the mini-channel. In addition, the results of this study showed that the divergent mini-channel heat sinks are more suitable for the practical applications in comparison with the parallel ones. The results obtained from the investigations of the average Nusselt number and the pressure drop also confirm this claim. In other words, the divergent mini-channel heat sinks have the higher Nusselt number along with lower pressure drop as compared with the parallel ones.
pcm
0% 2% 5% 10%
p
4000
2000
5. Conclusions
0
0
500
Rebf,in
1000
1500
Fig. 14. The variations of pressure drop versus Reynolds number for different values of mass fraction of PCM nanoparticles in the parallel and divergent minichannel heat sinks.
sure drop, simultaneously. The cost of performance (COP) is a criteria used to express the concept of whether the increase in heat transfer is dominant over the produced pressure drop. COP can be estimated by Eq. (13) at different volumetric flow rates and heat fluxes. Fig. 15(a) and (b) disclose the variations of COPs with the Reynolds number for different values of mass fraction of PCM nanoparticles in the parallel and divergent mini-channel heat sinks, respectively. As can be seen in these figures, COP decreases as the Reynolds number increases for both channels. Moreover, by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles, COPs decrease due to larger viscosity of the PCM
In this study, the cooling efficacies of water-based nano-PCM emulsion flow in the multi-channel heat sinks with parallel and divergent rectangular mini-channels were investigated experimentally. The effects of different parameters including the volumetric flow rate of working fluid, the heat flux, the Reynolds number, and the mass fraction of PCM nanoparticles on the dimensionless wall temperature, the Nusselt number, the cost of performance, and the pressure drop are studied. The main findings of this study are listed as follows: The heat transfer rate and Nusselt number are improved and the dimensionless wall temperature decreases by adding the PCM nanoparticles to the base fluid and increasing the mass fraction of nanoparticles for both channels. The divergent mini-channel significantly decreases the dimensionless wall temperature as compared with the parallel one. In addition, the Nusselt number for the divergent minichannel heat sink is higher as compared with the parallel one. The pressure drop increases by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles for both mini-channels. However, the pressure drop reduces when the divergent mini-channel heat sink is used.
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
(a) 10
7
Symbols
=0 " 2 qhh =4.78 W/cm
COP
10
0% 2% 5% 10%
6
10
5
10
4
10
3
400
pcm
800
1200
1600
Rebf
(b) 10
7
Symbols
=2.06 " hh
q =4.79 W/cm
COP
10
2
6
10
5
10
4
10
3
400
pcm
0% 2% 5% 10%
800
1200 1600
Rebf Fig. 15. The variations of COP with the Reynolds number for different values of mass fraction of PCM nanoparticles in (a) the parallel mini-channel heat sink; (b) the divergent mini-channel heat sink.
The value of COP decreases as the Reynolds number increases for both channels. Moreover, by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles, COPs decrease due to larger viscosity of the PCM nanoparticles especially at high mass fraction, leading to the increase in friction and required pumping power.
Declaration of Competing Interest The author declare that there is no conflict of interest. Acknowledgements The authors appreciate the financial support from Ministry of Science and Technology, Taiwan, under grant number MOST 1062221-E-027-103. The authors also acknowledge the financially supported by the ‘‘Research Center of Energy Conservation for New Generation of Residential, Commercial, and Industrial
11
Sectors” from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan. References [1] A. Cavallini, D.D. Col, L. Rossetto, Micro-channel heat sink with slurry of water with micro-encapsulated phase change material: 3D-numerical study, Int. J. Refrig. 36 (2013) 287–300. [2] Z. Wu, B. Sundén, On further enhancement of single-phase and flow boiling heat transfer in micro/minichannels, Renew. Sust. Energ. Rev. 40 (2014) 11–12. [3] T. Dixit, I. Ghosh, Review of micro- and mini-channel heat sinks and heat exchangers for single phase fluids, Renew. Sust. Energ. Rev. 41 (2015) 1298–1311. [4] S.E. Ghasemi, A.A. Ranjbar, M.J. Hosseini, Experimental and numerical investigation of circular minichannel heat sinks with various hydraulic diameter for electronic cooling application, Microelectron. Reliab. 73 (2017) 97–105. [5] S. Kumar, P.K. Singh, Effects of flow inlet angle on flow maldistribution and thermal performance of water cooled mini-channel heat sink, Int. J. Therm. Sci. 138 (2019) 504–511. [6] X.L. Xie, W.Q. Tao, Y.L. He, Numerical study of turbulent heat transfer and pressure drop characteristics in a water-cooled minichannel heat sink, J. Electron. Packag. 129 (2007) 247–255. [7] G. Xie, S. Li, B. Sunden, W. Zhang, Computational fluid dynamics for thermal performance of a water-cooled minichannel heat sink with different chip arrangements, Int. J. Numer. Methods Heat Fluid Flow 24 (2014) 797–810. [8] A.A. Hussien, M.Z. Abdullah, M.A. Al-Nimr, Single-phase heat transfer enhancement in micro/minichannels using nanofluids: theory and applications, Appl. Energy 164 (2016) 733–755. [9] M. Khoshvaght-Aliabadi, F. Nozan, Water cooled corrugated minichannel heat sink for electronic devices: effect of corrugation shape, Int. Commun. Heat Mass Transf. 76 (2016) 188–196. [10] T.C. Hung, W.M. Yan, X.D. Wang, C.Y. Chang, Heat transfer enhancement in microchannel heat sinks using nanofluids, Int. J. Heat Mass Transf. 55 (2012) 2559–2570. [11] C.J. Ho, W.C. Chen, An experimental study on thermal performance of Al2O3/water nanofluid in a minichannel heat sink, Appl. Therm. Eng. 50 (2013) 516–522. [12] J.F. Tullius, T.K. Tullius, Y. Bayazitoglu, Optimization of short micro pin fins in minichannels, Int. J. Heat Mass Transf. 55 (2012) 3921–3932. [13] C. Bi, G.H. Tang, W.Q. Tao, Heat transfer enhancement in mini-channel heat sinks with dimples and cylindrical grooves, Appl. Therm. Eng. 55 (2013) 121– 132. [14] X. Wang, J. Niu, Y. Li, X. Wang, B. Chen, R. Zeng, Q. Song, Y. Zhang, Flow and heat transfer behaviors of phase change material slurries in a horizontal circular tube, Int. J. Heat Mass Transfer 50 (2007) 2480–2491. [15] B. Chen, X. Wang, R. Zeng, Y. Zhang, X. Wang, J. Niu, Y. Li, H. Di, An experimental study of convective heat transfer with microencapsulated phase change material suspension: laminar flow in a circular tube under constant heat flux, Exp. Therm. Fluid Sci. 32 (2008) 1638–6146. [16] X. Wang, J. Niu, Y. Li, Y. Zhang, X. Wang, B. Chen, R. Zeng, Q. Song, Heat transfer of microencapsulated PCM slurry flow in a circular tube, AIChE J. 54 (2008) 1110–1120. [17] P. Sivasamy, A. Devaraju, S. Harikrishnan, Review on heat transfer enhancement of phase change materials (PCMs), Mater. Today: Proc. 5 (2018) 14423–14431. [18] S. Aziz, N.A.M. Amin, M.S. Abdul Majid, M. Belusko, F. Bruno, CFD simulation of a TES tank comprising a PCM encapsulated in sphere with heat transfer enhancement, Appl. Therm. Eng. 143 (2018) 1085–1092. [19] C.J. Ho, J.B. Huang, P.S. Tsai, Y.M. Yang, Preparation and properties of hybrid water-based suspension of Al2O3 nanoparticles and MEPCM particles as functional forced convection fluid, Int. Commun. Heat Mass Transf. 37 (2010) 490–494. [20] C.J. Ho, W.C. Chen, W.M. Yan, Experiment on thermal performance of waterbased suspensions of Al2O3 nanoparticles and MEPCM particles in a minichannel heat sink, Int. J. Heat Mass Transf. 69 (2014) 276–284. [21] C.J. Ho, W.C. Chen, W.M. Yan, P. Amani, Contribution of hybrid Al2O3-water nanofluid and PCM suspension to augment thermal performance of coolant in a minichannel heat sink, Int. J. Heat Mass Transf. 122 (2018) 651–659. [22] C.J. Ho, P.C. Chang, W.C. Chen, P. Amani, Thermal and hydrodynamic characteristics of divergent rectangular minichannel heat sinks, Int. J. Heat Mass Transf. 122 (2018) 264–274. [23] C.J. Ho, P.C. Chang, W.M. Yan, M. Amani, ‘Microencapsulated n-eicosane PCM suspensions: thermophysical properties measurement and modelling’, Int. J. Heat Mass Transf. 125 (2018) 792–800. [24] C.J. Ho, W.C. Chen, W.M. Yan, P. Amani, Comparative study on thermal performance of MEPCM suspensions in parallel and divergent minichannel heat sinks, Int. Commun. Heat Mass Transf. 94 (2018) 96–105. [25] S. Kandlikar, S. Garimella, D. Li, S. Colin, M.R. King, Heat Transfer and Fluid Flow in Minichannels and Microchannels, Elsevier, New York, 2006. [26] P.S. Lee, S.V. Garimella, D. Liu, Investigation of heat transfer in rectangular microchannels, Int. J. Heat Mass Transf. 48 (2005) 1688–1704. [27] Y. Rao, F. Dammel, P. Stephan, G. Lin, Convective heat transfer characteristics of microencapsulated phase change material suspensions in minichannels, Heat Mass Transf. 44 (2007) 175–186.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental study on thermal performance of water-based nano-PCM emulsion flow in multichannel heat sinks with parallel and divergent rectangular mini-channels C.J. Ho a,⇑, Shao-Teng Hsu a, Jer-Huan Jang b, Seyyede Fatemeh Hosseini c, Wei-Mon Yan d,e,⇑ a
Department of Mechanical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan Department of Mechanical Engineering, Ming Chi University of Technology, New Taipei City 24352, Taiwan Department of Chemistry, Faculty of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran d Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan e Research Center of Energy Conservation for New Generation of Residential, Commercial, and Industrial Sectors, National Taipei University of Technology, Taipei 10608, Taiwan b c
a r t i c l e
i n f o
Article history: Received 26 May 2019 Received in revised form 6 October 2019 Accepted 7 October 2019
Keywords: Nano-PCM emulsion Mini-channel heat sink Parallel and divergent channels Thermal performance
a b s t r a c t In this work, an experimental study is arranged to investigate the cooling efficacies of water-based nano-PCM emulsion flow in the multi-channel heat sinks with parallel and divergent rectangular mini-channels. N-eicosane particles with size of 130 nm are considered as the phase change material (PCM) nanoparticles. Two multi-channel heat sinks with eight parallel and divergent mini-channels are fabricated. The divergent channel has a divergent angle of 2.06°. The effects of different parameters including volumetric flow rate of working fluid (60 cm3/min < Q_ < 600 cm3/min), heat flux (3.2 W/cm2 < q00h < 4.8 W/cm2), Reynolds number (100 < Re < 1000), and mass fraction of PCM nanoparticles (0% < xPCM < 10%) on the dimensionless wall temperature, the Nusselt number, the cost of performance (COP), and the pressure drop are investigated. The experimental results show that the nano-PCM emulsion can improve heat transfer in both parallel and divergent mini-channel heat sinks as compared with the pure water. At Rebf = 965 and q00h = 3.21 W/cm2, the average Nusselt number in the parallel mini-channel heat sink improves about 15.2% by adding the PCM nanoparticles with mass fraction of 10% to the base fluid. This enhancement is up to 13.8% in the divergent mini-channel heat sink at Rebf = 295 and q00h = 3.21 W/cm2. Moreover, the divergent mini-channel heat sinks provide a higher Nusselt number along with lower pressure drop as compared with the parallel ones. Accordingly, the value of COP increases by diverging the mini-channel. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction With the fast development of IT technologies and microchips industries, it is momentous to remove a large value of thermal energy from a finite surface to cool the electronic components used in these technologies and industries. Channel heat sinks with micro or mini sizes can be nominated to achieve this purpose. Generally, they have a high heat transfer efficiency, small geometric size and volume per heat load. Moreover, they require a lower coolant and impose less operational cost as compared with the regular heat sinks [1–3].
⇑ Corresponding authors at: Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan (W.-M. Yan). E-mail addresses: [email protected] (C.J. Ho), [email protected] (W.-M. Yan). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118861 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
Some researchers have focused on the channel heat sinks with mini or micro sizes. Ghasemi et al. [4] investigated the effects of diameter of the circular mini-channel heat sink on the heat transfer and pressure drop of this device. They found that the pressure drop decreases by increasing the channel diameter of the heat sink. In addition, the mini-channel heat sink with the diameter of 4 mm provides a much smaller thermal resistance as compared with the mini-channel heat sinks with the diameters of 6 mm and 8 mm. Kumar and Singh [5] studied the influences of flow inlet angle on flow maldistribution and thermal efficiency of the mini-channel heat sink. They focused on three flow inlet angles including 90°, 105°, and 120°. They concluded that the flow inlet angle of 105° has the best thermal efficiency among other flow inlet angles considered in their study. Xie et al. [6] performed a numerical simulation to investigate the heat transfer and fluid flow through a water-cooled mini-channel heat sink for the turbulent regime. They concluded that using a narrow and deep channel with thin
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C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
Nomenclature A Abase Cp DH f hpcm H k ks L N Nuitd Pw qo,corr qo,eff Q_ Re Rmax Sb*
base area of the heat sink (m2) total base area of the heat sink (m2) specific heat (J/kg K) hydraulic diameter of channel (m) fanning friction factor (–) latent heat of melting (J/kg) height (m) thermal conductivity of the coolant (W/m K) thermal conductivity of the substrate material (W/m K) length (m) number of channels (–) average Nusselt number (–) pumping power (W) corrected electric power due to wall heat conduction losses effective heat input carried by the working fluid volume flow rate (cm3/min) Reynolds number (–) overall thermal resistance (K/W) modified inlet subcooling parameter (Tm Tin)/DTref
thickness can enhance the thermal efficiency with an acceptable pressure drop. In other research, Xie et al. [7] simulated a watercooled mini-channel heat sink with various chip arrangements. They showed that a good cooling efficiency can be achieved for the electronic systems by using a proper chip arrangement. Other techniques have been employed by some researchers to enhance the thermal efficiencies of the channel heat sinks [8]. Khoshvaght-Aliabadi and Nozan [9] evaluated the influences of corrugation shapes of a corrugated mini-channel heat sink on the heat transfer and pressure drop of this device. They considered four cases including three corrugated mini-channel heat sinks with the triangular, trapezoidal, and sinusoidal shapes and straight minichannel heat sink. It was found that the largest ratio of the heat transfer rate to the pumping power is related to the sinusoidal mini-channel heat sinks. In a numerical work, Hung et al. [10] used the nanofluids to improve the thermal efficiency of the microchannel heat sinks. They used water based Al2O3 and water based diamond nanofluids as the coolant in this system. Their results showed that the thermal efficiency of the system can be improved about 21.6% by using these nanofluids as compared with the pure water. In addition, the thermal efficiency is usually higher by using a nanofluid with small value of dynamic viscosity as compared with the nanofluid with large value of dynamic viscosity. Ho and Chen [11] performed an experimental work to investigate the thermal efficiency of water based Al2O3 nanofluid in the mini-channel heat sink. They found that the heat sink cooled with nanofluid provides considerably larger average heat transfer coefficients and accordingly, works better in comparison with the heat sink cooled with the pure water. Tullius et al. [12] used micro pin fins in the mini-channels. They employed the pin fins with different shapes including square, circle, triangle, diamond, ellipse, and hexagon. They concluded that triangular pin fin heat sink with larger height, smaller width, and spacing double the fin width provides a better efficiency. Bi et al. [13] improved the thermal efficiency of the mini-channel heat sinks with dimples and cylindrical grooves. Their results showed that the efficiency of cylindrical groove surface is somewhat lower as compared with the dimple surface. Phase change material particles are suspended in the thermal fluid to transport and/or save thermal energy. They were widely used for applications of forced convective heat transfer improvement [14–16]. Sivasamy et al. [17] reviewed the heat transfer
Stebf T DTref u W Wrib
Stefan number temperature (K) reference temperature difference (K) velocity of fluid (m/s) width (m) rib width (m)
Greek symbols l dynamic viscosity (kg/m s) q coolant density (kg/m3) X pumping power (W) Subscripts bf base fluid ch channel eff effective in inlet itd inlet temperature difference m mean w wall
improvement techniques used in the phase change materials. They reported that the extended surface, multiple PCMs, composite PCMs, and encapsulation are some techniques use to accelerate the solidification and melting processes in the phase change materials. Aziz et al. [18] used the pins and copper plating to improve the performance of an encapsulated PCM in sphere used in a thermal energy storage system. Their results showed that the usage of pins can decrease the phase change time in the PCM about 27%, while the usage of copper coating and embedded pins decreases the phase change time up to 37% as compared with a plain sphere. Ho et al. [19] investigated the thermal characteristics of hybrid water-based suspension of aluminium oxide nanoparticles and microencapsulated phase change material particles. They concluded that the dispersion of aluminium oxide nanoparticles can considerably recover the low thermal conductivity of the pure phase change material suspensions. The heat transfer efficiency of water-based suspensions of aluminium oxide nanoparticles and microencapsulated phase change material particles in the mini-channel heat sink was experimentally performed by Ho et al. [20]. Their results showed that the heat transfer effectiveness of the mini-channel heat sink can improve about 56% by using this hybrid water-based suspensions. Later, Ho et al. [21] investigated the potentials of hybrid aluminium oxide-water based nanofluid and phase change material suspension for improving the thermal efficiency of coolant in the mini-channel heat sink. It was observed that the efficiency of the hybrid suspension is significantly related to the Reynolds number. For example, the pure nanofluid acts better as compared with the hybrid suspension at larger value of Reynolds number. Recently, Ho et al. [22] enhanced the thermal efficiency of the mini-channel heat sink by diverging the minichannel. It was found that the divergent mini-channel heat sink can provide higher values of heat transfer coefficient and cost of performance as well as smaller value of pressure drop penalty as compared with the parallel one, especially for the larger flow rates. The literature review showed that the thermal efficiencies of mini-channel heat sinks can be improved by using Nano-PCM emulsion or diverging the mini-channel as two different techniques. These two techniques are used in this study, simultaneously in the mini-channel heat sink to achieve the larger thermal efficiencies. This paper arranges an experimental study to investigate the convective heat transfer of Nano-PCM emulsion flow
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
through the parallel and divergent rectangular mini-channels. The effects of different parameters including the volumetric flow rate of working fluid, the heat flux, the Reynolds number, and the mass fraction of PCM nanoparticles on the Nusselt number, the cost of performance, and the pressure drop are investigated. 2. Experimental 2.1. Experimental setup The schematic view of the present experimental setup is depicted in Fig. 1. As it is seen in this figure, the experimental setup has a closed circuit. The main components of this setup are a tank, DC power supply, a data acquisition system, the heat exchangers (cooling and heating exchangers), and a centrifugal pump. The working fluid enters the centrifugal pump from the tank. The centrifugal pump is employed for circulating the working fluid within the circuit. By adjusting the pump speed, the desired flow rate can be achieved. To maintain the inlet working fluid at a constant temperature, the fluid enters a heating heat exchanger, consists of constant temperature bath, at the inlet section of the test section. In addition, the fluid enters the cooling heat exchanger for resetting its temperature before backing to the tank at the outlet section of the test section. Indeed, the cooling heat exchanger is employed for cooling down the heated coolant before entering the tank for recirculation. It has a plate heat exchanger and a fabricated water bath. The water bath is employed for supplying the cooling fluid for the plate heat exchanger. A DC power supply is installed to provide the homogeneous wall heat flux. The amount of the desired heat flux can be achieved by adjusting the current and voltage used for the heater. A flow meter is used for adjusting the volumetric flow rate. Two pressure taps are located at two ends of the minichannels to determine the pressure drop along the heat sink. In this study, two T-type thermocouples are placed at two ends of the mini-channels to measure the temperatures at these regions. In addition, the wall temperature is measured employing seven T-type thermocouples placed in small holes at a distance of 3 mm under the base surface along the centerline of the minichannel heat sink. In the experimental setup, insulating material is used to reduce the heat loss from the test section. 2.2. Experimental procedure details The working fluid (coolant) of this experiment is the waterbased phase change material (PCM) emulsions. N-eicosane and
3
SLS are considered as the PCM and the surfactant, respectively. In the present investigation, two different configurations for the multi-channels are used. These configurations are two mini-channel heat sinks with eight parallel and eight divergent mini-channels, respectively. Divergent mini-channels have divergence angle of 2.06° and the length of 50 mm. Figs. 2 and 3 show the three-dimensional schematic and the detailed schematic of the mini-channel heat sink configurations, respectively. Moreover, more details about the mini-channel heat sink are summarized in Table 1. The photographs of parallel and divergent flow channels are shown in Fig. 4. It should be noted that the divergent mini-channels have the same geometry with the parallel one at the inlet cross-section. However, the channel width is linearly expanded from the inlet, leading to a width of 2.8 mm at the outlet section for the divergent minichannels. Each mini-channel has been fabricated from oxygenfree copper with an inlet cross-sectional area of 1 mm in width by 1.5 mm in height. The test section also has two plate heaters that are powered by a DC power supply. In Fig. 2, the material used for the top surface is acrylic. It should be also noted that the acrylic has good thermal insulation effect. Moreover, it has a transparent appearance, which is convenient for directly observing the flow field condition in the minichannel. Due to these reasons, this material is selected as the top surface. For the middle and bottom sections, that mainly cover the oxygen-free copper flow path and the main and auxiliary heating sheets, the polyether ether ketone plastic material is selected. The polyether ether ketone plastic material has the high values of temperature resistance, mechanical strength, and chemical resistance. Note that in Table 1, Wch, Hch, Wrib, DH, Ar, and Hc are the channel inlet and outlet widths, the channel height, the fin width, the hydraulic diameter, the aspect ratio, and the heat sink bottom thickness, respectively. In this study, some techniques are used when preparing the nano-PCM emulsion to ensure about the stability of the nanofluids. The details of these techniques can be found at Ho et al. [23]. Fig. 5 shows the results of the SEM and TEM analyses. These analyses are employed for approximating the size of the MEPCM employing JEOL JEM-1400 device. It can be seen that the MEPCM particles have approximately spherical shape with the particle size distribution in the range of 5–10 lm. A DSC with the Flash DSC 1 of Mettler-Toledo is employed in this study. The results of detailed DSC measurement for the nano-PCM powder are displayed in Fig. 6. For DSC measurements, the cooling/heating rate is 5 K/min and temperature is varied in the range of 15–50 °C [23].
Fig. 1. The schematic of the experimental setup.
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C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
Temperature port
Outlet PMMA plate cover
Inlet
Pressure port
PEEK plate Mini-channel heat sink Main heater Asbestos Compensative heater
PEEK dock Fig. 2. Three-dimensional schematic of the oxygen-free copper heat sink.
3. Theoretical consideration 3.1. Parameters definitions Before defining the parameters, it must be noted that the following assumptions are consummated: The parallel and divergent mini-channels have similar sizes at the inlet section and wall roughness. The flow rates and the heat flux are assumed to be same in each mini-channel. The required parameters in this study are defined in this section. The Reynolds number, based on the properties of the base fluid, is defined by:
Rebf ¼
qbf um DH lbf
ð1Þ
where qbf and lbf are the density and dynamic viscosity of the base fluid, respectively; DH is the hydraulic diameter of the minichannel; and um is the bulk fluid velocity, which can be defined by:
Q_ um ¼ NAch
ð2Þ
where Q_ is the volumetric flow rate, N is the number of channels, and Ach is the cross-sectional of a mini-channel. The divergent and parallel channels have the same inlet cross-sectional areas. Accordingly, the flow velocity and the hydraulic diameter are calculated based on the inlet cross-sectional areas. Therefore, the Reynolds number at the inlet from Eq. (1) can be calculated as follows:
Rebf ;in ¼
qbf ;in uin DH;in lbf ;in
ð3Þ
The friction factor can be determined as follows [24]:
f ¼
1 DH Dp 2 Lch qu2
ð4Þ
Fig. 3. The geometries of mini-channel heat sink configurations: (a) Parallel flow path mini-channel heat sink; (b) Divergent flow path mini-channel heat sink.
where Lch is the length of the mini-channel. Moreover, Dp indicates the pressure drop between inlet and outlet of the mini channel, which can be determined by [24]:
Dp ¼ Dpm ðkc þ ke Þ
qu2 2
ð5Þ
Here, Dpm is the measured pressure drop by the instrument in the inlet and outlet sections of the mini-channel and kc and ke indicate the contraction and expansion coefficients, respectively. For the parallel mini-channel, the contraction and expansion coefficients are equal to 0.937271 and 0.4499492, respectively, while for the divergent one, kc = 0.829478 and the expansion coefficient is the same with the parallel mini-channel.
5
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861 Table 1 Details about the dimensions of parallel and divergent mini-channel heat sinks. Type of MCHS
Wch (mm)
Hch (mm)
Wrib (mm)
DH (mm)
Ar (mm)
Hc (mm)
Parallel Divergent
1.0 2.8
1.5 1.5
2.1 0.3
1.2 1.95
1.5 0.54
5 5
Parallel flow channel
D i v e r g e n t f l o w ch a n n e l
Fig. 4. Photographs of parallel and divergent flow channels.
SEM image
TEM image Fig. 5. SEM and TEM images.
Fig. 6. DSC chart for nano-PCM powders.
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C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
The non-dimensional wall temperature employed in this study can be determined by:
hw ¼
T w T in DT ref ;bf
ð6Þ
where Tw and Tin are the wall and input temperatures, respectively. The following equation can be used to calculate the wall temperature:
T w ¼ T tc
q00 h Hc kc
ð7Þ
where Ttc indicates the measured local wall temperature. kc and Hc are the base material thermal conductivity and the heat sink bottom thickness, respectively. q00h can be determined by:
q00h ¼
qh qh ¼ Abase NðW ch þ W rib ÞLch
ð8Þ
where qh and Abase are the heat input carried by the working fluid and the total base area of the heat sink, respectively. In Eq. (6), the reference temperature of base fluid, DT ref ;bf , can be calculated by:
DT ref ;bf ¼
qh
ð9Þ
qbf cp;bf Q_
where cpbf is the heat capacity of base fluid. The average Nusselt number is defined by:
Nuitd ¼
hitd DH km
The thermophysical properties of the mixture water-PCM nanoparticles can be found at Ho et al. [23]. 3.2. Validation part In order to validate the experimental data, the current results are compared with the experimental results for the average Nusselt number variation against the Reynolds number. The validation is performed for the case of pure water. The results of this comparison are shown in Fig. 4. It should be noted that these results are given for the parallel mini-channel heat sink. Lee et al. [26] have examined the hydrothermal characteristics of flow through a mini-channel with the hydraulic diameter in the range of 0.318– 0.903 mm and Reynolds number in the range of 300–3500. Moreover, Rao et al. [27] and Ho et al. [11] examined the effectiveness of PCMs and nanofluids on the hydrothermal characteristics of flow inside a mini-channel heat sink with different hydraulic diameters, respectively. Notice that the aspect ratios of mini-channels considered by Ho et al. [11], Lee et al. [26], and Rao et al. [27] are 1.5, 5.45, and 2.1, respectively. Fig. 7 shows that there are good agreements between the current results and the results presented by Ho et al. [26], Lee et al. [14], and Rao et al. [27] for the average Nusselt number at different Reynolds numbers with pure water fluid. To perform more validation, the friction factor obtained by the present experiment is compared with that of Ho et al. [11]. This comparison can be seen in Fig. 8. As shown in this figure, the good agreement between the current results and the results presented by Ho et al. [11] can be observed for the friction factor at different Reynolds numbers.
ð10Þ 3.3. Uncertainty analysis
where km is the thermal conductivity of the mixture. The average
convection coefficient, hitd ;is calculated as follows:
hitd ¼
q00 h
ð11Þ
ðT w T in Þ
The cost of performance (COP) shows the heat carried by the coolant per unit required pumping power. This parameter is defined by:
COP ¼
qh P
Since the measurements of physical parameters of the experiment and the measuring instruments have some errors, the influences of these errors should be considered on the results. In order to understand the impact of experimental error on the experimental data processing, an uncertainty analysis is required. This analysis is provided in this section. According to Taylor’s theorem, the mathematical expression for the function f can be presented as follows:
ð12Þ
20
where P is the required pumping power calculated by:
18
P ¼ Dp Q
ð13Þ
16
The friction of the flow through the rectangular mini-channel heat sink, proposed by Kandlikar [25], has been employed. The proposed equation for the rectangular mini-channel in fully developed flow is presented as follows:
0:2537a5 Þ
3
4
ð14Þ
where a is the aspect ratio of the cross-sectional area of the minichannel. In this experiment, the value for a is 0.667, and the value of fRe is 14.71 by using Eq. (14). The Stefan number is defined by:
Stebf ¼
cp;bf DT ref ;bf hpcm
14
Nu mtd
f Re ¼ 24ð1 1:3553a þ 1:9467a 1:7012a þ 0:9564a 2
Present Work (DH=1.2 mm) Ho et al. (2013) (DH=1.2 mm) Lee et al. (2005) (DH=0.9 mm) Rao et al. (2007) (DH=2.71 mm)
12
10
8
6
4
ð15Þ
where cp,bf, DTref,bf, hpcm are the heat capacity of the base fluid, reference temperature difference of base fluid, and latent heat of melting of PCM, respectively.
0
500
1000
1500
2000
Rebf Fig. 7. The comparison between the present experimental results and the results presented by Lee et al. [26], Rao et al. [27] and Ho et al. [11] for the average Nusselt number at different Reynolds numbers in the parallel mini-channel heat sink.
7
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
100
4. Results and discussion Present work Ho et al.(2013)
10-1
The experimental results are presented in this section. The effects of different parameters including the volumetric flow rate of working fluid (60 cm3/min < Q_ < 600 cm3/min), the heat flux (3.2 W/cm2 < q00h < 4.8 W/cm2), the Reynolds number (100 < Re < 1000), and the mass fraction of PCM nanoparticles (0% < xPCM < 10%) on the Nusselt number, the cost of performance, and the pressure drop are investigated. 4.1. Dimensionless wall temperature
14.71/Re 10
-2
500 Rebf
1500
Fig. 8. The comparison between the present experimental results and the results presented by Ho et al. [11] for the friction factor at different Reynolds numbers.
f ðx1 þ Dx1 ;x2 þ Dx2 ; ;xn þ Dxn Þ ¼ @f þ high order f ðx1 ;x2 ; xn Þ þ Dx1 @x@f1 þ Dx2 @x@f2 þ þ Dxn @x n
ð16Þ The error of this function can be calculated by:
df ðx1 ; x2 ; xn Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 @f @f @f D x1 þ Dx2 þ þ D xn ¼ @x1 @x2 @xn
ð17Þ
The uncertainties of the physical parameters and the measuring instruments used in the experiment are summarized in Table 2.
The effects of heat fluxes and mass fraction of PCM nanoparticles on the dimensionless wall temperatures of divergent minichannel heat sink are shown in Fig. 9. As can be seen in this figure, the dimensionless wall temperature has reduction trend at the end sections of the divergent mini-channels. This trend can be justified by occurring the post heating at the end sections of the minichannel due to the axial wall conductive heat transfer. Furthermore, the cooling effect improves and the dimensionless wall temperature decreases by adding the PCM nanoparticles to the base fluid and increasing the mass fraction of nanoparticles. For example, at the end of mini-channel, the dimensionless wall temperature reduces about 12% by adding the PCM nanoparticles with mass fraction of 10% to the base fluid at q00h ¼ 3:21 W=cm2 . The thermal conductivity of the base fluid enhances by adding the PCM nanoparticles with larger mass fractions. The increment in the thermal conductivity leads to increasing the heat transfer rate and subsequently, the dimensionless wall temperature decreases. Finally, this figure shows that the dimensionless wall temperature reduces by increasing the heat flux. Fig. 10 discloses the dimensionless wall temperature of pure water flow in divergent mini-channel heat sink for two values of volumetric flow rate. As shown in this figure, the dimensionless wall temperature increases by increasing the volumetric flow rate. For example, at the end of the mini-channel, the dimensionless wall temperature of pure water flow in divergent mini-channel heat sink increases about 211% by increasing the volumetric flow
Table 2 The uncertainties of the physical parameters and the measuring instruments in the experiment for the parallel and divergent mini-channels. Item
Symbols
Ranges
Uncertainties
Input parameters Electrical voltage (Volt) Electrical current (A) Length of mini-channel (mm) Hydraulic diameter (mm)
V I Lch DH
75 to 95 0.522 to 0.653 50 1.20 to1.68
±0.5 (V) ±0.0005 (A) 0.01 (mm) 1.3 to 0.9 (%)
Q_ Dp Ttc DT
60 to 600
0.5 to 5 (%)
20 to 5100 311.4 to 337.4 1.0 to 14.9
±5 (pa) ±0.3 (K) ±0.3 (K)
qh
40.2 to 60.1
0.5 to 0.7 (%)
hw Rebf Rebf P f
1.46 to 6.56 138 to 1381 102 to 1015 1.541e05 to 0.046 0.018 to 0.164 2005 to 5935
3.1 1.9 1.4 0.5 5.7 2.4
Measured parameters Volume flow rate (cm3/min) Pressure drop (pa) Temperature (K) Temperature difference between the inlet and outlet section of mini-channel Power (W) Output parameters Dimensionless temperature Reynolds number for parallel mini-channel Reynolds number for divergent mini-channel Pumping power Friction factor Average heat transfer coefficient (W/m2 K) Average Nusselt number Maximum thermal resistance (K/W) Average thermal resistance (K/W) Peclet number Stefan number
hitd
Nuitd Rmax Ravg Pebf Stebf
to to to to to to
11.2 (%) 5.3 (%) 5.2 (%) 25.5 (%) 28.6 (%) 7.9 (%)
4.0 to 11.8
3.2 to 8.2 (%)
0.16 to 0.47 0.13 to 0.45 507 to 6902 0.0164 to 0.2444
2.5 2.6 1.9 0.8
to to to to
6.6 (%) 8.5 (%) 5.2 (%) 28.6 (%)
8
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
Symbols
3
0% 2% 5% 10%
2.2
Pebf=484.77
Q=60 cm /min
pcm
" h
q =3.21 W/ cm
2
Symbols
* bf
Ste =0.1638
3
Q=60 cm /min
pcm
" h
0% 2% 5% 10%
*
Sbbf=0.2103
q =4.79 W/ cm
Pebf=482.15 2
Ste*bf=0.2444 *
Sbbf=0.1460
w
2
1.8
1.6
1.4
0
0.01
0.02
0.03
0.04
0.05
+
x /(DHPebf )
0
0.01
0.02
0.03
0.04
0.05
+
x /(DHPebf )
Fig. 9. The dimensionless wall temperature of divergent mini-channel heat sinks for different values of heat flux and mass fraction of PCM nanoparticles atQ_ = 60 cm3/min.
Q =60 cm3/min
Q =600 cm3/min
Fig. 10. The dimensionless wall temperature of pure water flow in divergent mini-channel heat sink for two values of volumetric flow rate.
rate in the range of 60–600 cm3/min at q00h ¼ 3:21 W=cm2 . Note that for the flow with high values of volumetric flow rate, the effective heat exchange duration cannot be achieved as the time spent for heat transfer in the heat exchanger is too short. This causes the increment in the dimensionless wall temperature. Also, it should be noted that the coolant velocity within the mini-channel heat sink increases as the volumetric flow rate increases. However, the time spent for the heat transfer in the system decreases by increasing the coolant velocity. The dimensionless wall temperature distributions of pure water flow in parallel and divergent mini-channel heat sinks are disclosed in Fig. 11. It can be dedicated that using the divergent
mini-channel significantly decreases the dimensionless wall temperature as compared with the parallel one. Moreover, this figure demonstrates that the maximum dimensionless wall temperatures occur in the vicinity of the mid-sections of both configurations. The difference between the dimensionless wall temperatures of parallel and divergent mini-channel heat sinks is smaller at the end section of the mini-channel. 4.2. Heat transfer characteristics Fig. 12(a) and (b) show the variations of average Nusselt number versus the Reynolds numbers for different values of mass fraction of
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
7 pcm
6.5
=0%
Symbols
Channel
Rebf,in=690 " hh
qq =3.20 W/cm
6
9
par ( =0 ) div ( =2.06 )
2
5.5 5 w
4.5 4 3.5 3 2.5 2
0
5
10
15
20 + x /DH,in
25
30
35
40
Fig. 11. The dimensionless wall temperature distribution for pure water in parallel and divergent mini-channel heat sinks.
PCM nanoparticles in the parallel and divergent mini-channel heat sinks, respectively. As can be seen in these figures, the average Nusselt number increases with increasing the Reynolds number for both mini-channel heat sinks. It is noticed that the velocity of working fluid and subsequently, the convective heat transfer rate increase as the Reynolds number increases. Moreover, the thermal boundary layer thickness decreases as the Reynolds number increases and this causes the increment in the convective heat transfer rate. For example, the average Nusselt number of waterbased Nano-PCM emulsion flow in the parallel mini-channel heat sink enhances up to 193% by increasing the Reynolds number in the range of 136 to 1380 at q00h ¼ 3:21 W=cm2 and xPCM = 10%. The heat transfer rate and Nusselt numbers are improved by adding the PCM nanoparticles to the base fluid and increasing the mass fraction of nanoparticles for both channels. For example, the average Nusselt number in the parallel mini-channel heat sink improves about 15.2% by adding the PCM nanoparticles with mass fraction of 10% to the base fluid at Rebf = 965 and q00h ¼ 3:21 W=cm2 . This enhancement is up to 13.8% in the divergent mini-channel heat sink at Rebf = 295 and q00h ¼ 3:21 W=cm2 . Finally, it can be concluded by comparing the results presented in Fig. 12(a) and (b) that the Nusselt number for the divergent mini-channel heat sink is larger as compared with the parallel one. Note that the reduction in the coolant velocity within divergent mini-channel leads to the higher resistance time of the working flow. Accordingly, the working fluid can absorb larger amount of thermal energy that provides higher heat transfer rate. Fig. 13 discloses the variations of average Nusselt number versus Reynolds number for different values of mass fraction of PCM nanoparticles in the divergent mini-channel heat sink under different heat fluxes. It can be seen that the average Nusselt number enhances with increasing the Reynolds number and mass fraction of PCM nanoparticles in the divergent mini-channel heat sink. In addition, the heat flux has a minor effect on the average Nusselt number for most cases.
As shown in this figure, the pressure drop increases as the Reynolds number increases for both mini-channels. In addition, the pressure drop increases by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles for both minichannels. This is due to the increase in the viscosity of the fluid phase by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles. Finally, with comparing two configurations of mini-channel heat sinks, it can be dedicated that the pressure drop reduces when the divergent mini-channel heat sink is used. This reduction is more obvious at larger Reynolds numbers. For example, the pressure drop decreases about 72.9% by diverging the mini-channel at Rebf = 1376 and xPCM = 10%. As a result, a lower pumping power is required for divergent mini-channels.
4.3. Pressure drop
4.4. Cost of performance
The variations of pressure drop versus Reynolds numbers for different values of mass fraction of PCM nanoparticles in the parallel and divergent mini-channel heat sinks are disclosed in Fig. 14.
In order to evaluate the conditions and effectiveness of the changes made in the system and to achieve the best results, it is important to consider the heat transfer improvement and the pres-
Fig. 12. The variations of average Nusselt number versus Reynolds number for different values of mass fraction of PCM nanoparticles in (a) the parallel minichannel heat sink; (b) the divergent mini-channel heat sink.
10
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
24
Symbols
=2.06
pcm
qh"h=3.21 W/cm2
0% 2% 5% 10%
22 20
Symbols
=2.06
pcm
2 " qqhh=4.79 W/cm
0% 2% 5% 10%
18
Nu itd
16 14 12 10 8 6 4 2
200
400
600
800
1000
200
Rebf
400
600
800
1000
Rebf
Fig. 13. The variations of average Nusselt number versus Reynolds number for different values of mass fraction of PCM nanoparticles in the divergent mini-channel heat sink under different heat fluxes.
=0
=2.06
nanoparticles especially at high mass fraction, leading to the increase in friction and required pumping power. Finally, by comparing the results obtained for the parallel and divergent minichannel heat sinks, it can be concluded that the value of COP increases by diverging the mini-channel. In addition, the results of this study showed that the divergent mini-channel heat sinks are more suitable for the practical applications in comparison with the parallel ones. The results obtained from the investigations of the average Nusselt number and the pressure drop also confirm this claim. In other words, the divergent mini-channel heat sinks have the higher Nusselt number along with lower pressure drop as compared with the parallel ones.
pcm
0% 2% 5% 10%
p
4000
2000
5. Conclusions
0
0
500
Rebf,in
1000
1500
Fig. 14. The variations of pressure drop versus Reynolds number for different values of mass fraction of PCM nanoparticles in the parallel and divergent minichannel heat sinks.
sure drop, simultaneously. The cost of performance (COP) is a criteria used to express the concept of whether the increase in heat transfer is dominant over the produced pressure drop. COP can be estimated by Eq. (13) at different volumetric flow rates and heat fluxes. Fig. 15(a) and (b) disclose the variations of COPs with the Reynolds number for different values of mass fraction of PCM nanoparticles in the parallel and divergent mini-channel heat sinks, respectively. As can be seen in these figures, COP decreases as the Reynolds number increases for both channels. Moreover, by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles, COPs decrease due to larger viscosity of the PCM
In this study, the cooling efficacies of water-based nano-PCM emulsion flow in the multi-channel heat sinks with parallel and divergent rectangular mini-channels were investigated experimentally. The effects of different parameters including the volumetric flow rate of working fluid, the heat flux, the Reynolds number, and the mass fraction of PCM nanoparticles on the dimensionless wall temperature, the Nusselt number, the cost of performance, and the pressure drop are studied. The main findings of this study are listed as follows: The heat transfer rate and Nusselt number are improved and the dimensionless wall temperature decreases by adding the PCM nanoparticles to the base fluid and increasing the mass fraction of nanoparticles for both channels. The divergent mini-channel significantly decreases the dimensionless wall temperature as compared with the parallel one. In addition, the Nusselt number for the divergent minichannel heat sink is higher as compared with the parallel one. The pressure drop increases by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles for both mini-channels. However, the pressure drop reduces when the divergent mini-channel heat sink is used.
C.J. Ho et al. / International Journal of Heat and Mass Transfer 146 (2020) 118861
(a) 10
7
Symbols
=0 " 2 qhh =4.78 W/cm
COP
10
0% 2% 5% 10%
6
10
5
10
4
10
3
400
pcm
800
1200
1600
Rebf
(b) 10
7
Symbols
=2.06 " hh
q =4.79 W/cm
COP
10
2
6
10
5
10
4
10
3
400
pcm
0% 2% 5% 10%
800
1200 1600
Rebf Fig. 15. The variations of COP with the Reynolds number for different values of mass fraction of PCM nanoparticles in (a) the parallel mini-channel heat sink; (b) the divergent mini-channel heat sink.
The value of COP decreases as the Reynolds number increases for both channels. Moreover, by adding the PCM nanoparticles and increasing the mass fraction of nanoparticles, COPs decrease due to larger viscosity of the PCM nanoparticles especially at high mass fraction, leading to the increase in friction and required pumping power.
Declaration of Competing Interest The author declare that there is no conflict of interest. Acknowledgements The authors appreciate the financial support from Ministry of Science and Technology, Taiwan, under grant number MOST 1062221-E-027-103. The authors also acknowledge the financially supported by the ‘‘Research Center of Energy Conservation for New Generation of Residential, Commercial, and Industrial
11
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