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Effects of different geometric structures on fluid flow and heat transfer performance in microchannel heat sinks
International Journal of Heat and Mass Transfer 80 (2015) 439–447
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effects of different geometric structures on fluid flow and heat transfer performance in microchannel heat sinks G.D. Xia ⇑, J. Jiang, J. Wang, Y.L. Zhai, D.D. Ma Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, College of Environmental and Energy Engineering, Beijing University of Technology, Beijing 100124, China
a r t i c l e
i n f o
Article history: Received 21 May 2014 Received in revised form 11 August 2014 Accepted 24 August 2014
Keywords: Microchannel heat sink Flow distribution Inlet/outlet location Header shape Microchannel cross-section shape Geometric parameter
a b s t r a c t In the present study, fluid flow and heat transfer in microchannel heat sinks with different inlet/outlet locations (I, C and Z-type), header shapes (triangular, trapezoidal and rectangular) and microchannel cross-section shapes (the conventional rectangular microchannel, the microchannel with offset fanshaped reentrant cavities and the microchannel with triangular reentrant cavities) are numerically studied with computational domain including the entire microchannel heat sink. Detailed three-dimensional numerical simulations are useful in identifying the optimal geometric parameters that provide better heat transfer and flow distribution in a microchannel heat sink. Results highlight that flow velocity uniformity is comparatively better for I-type and poor for Z-type. The flow distribution is found to be symmetrical for I-type. It is seen from the header shapes analysis that the rectangular header shapes provides better flow velocity uniformity than the trapezoidal and triangular headers. The fluid flow mechanism can be attributed to the interaction of the branching of fluid and the friction offered by the walls of the header. Effects of microchannel cross-section shapes emphasize that the microchannel with offset fan-shaped reentrant cavities and the microchannel with triangular reentrant cavities of the heat sinks enhance the heat transfer compared to the conventional rectangular microchannel. The heat transfer mechanism can be attributed to the jetting and throttling effect, the additional flow disturbance near the wall of the reentrant cavities and the form drag of the reentrant cavities. The heat sink C has better heat transfer characteristic for qv = 150 ml/min and is able to prolong the life of the microelectronic devices. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction With the rapid development of ULSIC (Ultra-Large-Scale-Integrated-Circuit) and MEMS (Micro-Electro-Mechanical-Systems), the application of microchannel heat sinks has attracted much attention in the field of advanced energy and power engineering, microelectronics, military and nuclear energy, aerospace, biochemistry, etc. As one of the most promising high efficiency heat exchange technologies, the microchannel heat sinks are used in a lot of devices for cooling down the miniature systems. According to the International Technology Roadmap for Semiconductors (ITRS), the peak power consumption of high performance desktops will rise by 96% (147 W–288 W) in 2016, and by 95% (91 W–158 W) in lower-end desktops in 2016 [1]. With the increase of the heat load and the intensity of the heat exchange systems, the traditional straight microchannel heat sink cooling ⇑ Corresponding author. Tel.: +86 1067392176; fax: +86 1067391983. E-mail address: [email protected] (G.D. Xia). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.08.095 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
systems have been unable to meet the requirements and impose limits on product design if no action is taken to propose more effective cooling methods. Since Tuckerman and Pease [2] first proposed the microchannel heat sink cooling concept for electronic cooling in the early 1980s, there have been a variety of interests in the study of fluid flow and heat transfer characteristic in microchannel. It combines two ways of heat transfer: increasing the convective heat transfer coefficient by decreasing the hydraulic diameter of the microchannel and the heat conduction through the microchannel walls. Gunnasegaran et al. [3] studied the effects of geometrical parameters on heat transfer and fluid flow in microchannel heat sink. It is found that the temperature distribution is much uniform for the smallest hydraulic diameter of the microchannel heat sinks, and pressure drop and friction factor are larger. Eun et al. [4] investigated the cooling performance of microchannel heat sinks with different geometric structures, which is straight and diverging channels under various heat flux conditions. The straight microchannels show less sensitivity of the temperature distributions on the variation of the header shape than diverging
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Nomenclature cp Dh f h H kf ks L Nu Dp Po qm qw Q Re
special heat capacity kJ/(kg K) hydrodynamic diameter mm friction factor heat transfer coefficient W/(m2 K) height mm thermal conductivity of fluid W/(m K) thermal conductivity of solid W/(m K) length mm Nusselt number pressure drop Pa Poiseuille number volume flow rate m3/s heat flux W/m2 total heat input W Reynolds number
micro channels. The pressure drop in the straight channels is higher than that in the diverging microchannels. Facing the challenge of increasing the heat load and the intensity of the heat exchange systems, a significant amount of innovative cooling techniques have the potential to remove high heat flux for some microelectronic applications. Enhancement of microscale heat transfer can be attributed to better flow distribution. Chein and Chen [5] investigated the inlet/outlet arrangement effects on the fluid flow and heat transfer inside the heat sinks. The focus of their research is inlet/outlet arrangement effects on the flow distribution. They indicated that the low heat sink temperature takes place at the entrance zones of microchannels because high heat transfer coefficient and the highest heat sink temperature occur at the edge of the heat sink, where there is no heat dissipation by fluid convection. Kumaran et al. [6] revealed the effects of header design on flow mal-distribution in a microchannel heat sink by experiment and numerical simulation. The emphasis of their research is inlet/outlet arrangement and header design effects on flow mal-distribution. It is reported that the flow distribution is better for C-type, and the triangular inlet header and the trapezoidal outlet header provide better flow distribution. Lu and Wang [7] presented the effect of inlet location on the performance of parallel-channel cold-plate. The focus of their research is inlet location effects on velocity mal-distribution and nonuniformity of temperature. They found that the I-arrangement shows the best heat transfer performance because of the impingement configurations and the Z-arrangement gives the lowest heat transfer performance due to the dramatic flow recirculation and maldistribution. Manoj et al. [8] carried out an experimental study to investigate the effect of flow maldistribution on the thermal performance of parallel microchannel cooling systems. The emphasis of their research is inlet/outlet arrangement effects on the thermal performance. It is found that the average temperature and the peak temperature of the device trend to a considerable reduction with the decreasing of channel diameter and the heat sinks have better temperature distribution. Liu et al. [9] studied the effect of flow maldistribution on the thermal performance of parallel microchannel cooling systems. The results showed that the flow distribution of the heat sink is better for UC-type. Enhancement of microscale heat transfer can be attributed to providing more surface area and interrupting the boundary layer formation. Hong and Cheng [10] employed a three-dimensional numerical simulation to analyze the heat transfer enhancement
m W x
mean velocity m/s width mm length of header mm
Greek symbols q density kg/m3 l dynamic viscosity kg/(m s) Subscript ave in max min m out
average inlet maximum minimum mean outlet
mechanism in offset strip-fin microchannel. Foong et al. [11] numerically studied the heat transfer and fluid flow characteristics in a square microchannel with four longitudinal internal fins. Danish et al. [12] studied and optimized the shape of the microchannel heat sink with a grooved structure. The result implied the microchannel heat sink with grooved structure is better compared to the smooth microchannel both fluid flow and heat transfer characteristics, which can improve the heat transfer performance. Chai et al. [13] revealed the effects of fluid flow and heat transfer characteristics of interrupted microchannel heat sink with rectangular ribs in the transverse microchambers. The heat transfer enhancement mechanism can be attributed to the interaction of the mainstream flow separation, recirculation, vortex and interrupted boundary layer. Xia et al. [14–17] studied and optimized the structural parameters of the microchannel with offset fan-shaped reentrant cavities, triangular reentrant cavities and aligned fan-shaped reentrant cavities by numerical simulation of flow and heat transfer mechanism. They analyzed the effect of geometric parameters on fluid flow and heat transfer characteristics and obtained the optimal geometric parameters for the heat transfer enhancement of microchannel heat sinks. The heat transfer enhancement mechanism can be attributed to the interaction of increasing the heat transfer surface area, interrupting the boundary layers, redeveloping the hydraulic and thermal boundary layers, throttling effects and slipping over the reentrant cavities. These innovative cooling techniques are sufficient for cooling requirements in some applications. From the literature review, many researchers have investigated the fluid flow and heat transfer characteristics of the microchannel heat sinks. However, it is clear that few studies (both numerical and experimental) are investigated the effects of the inlet/outlet locations, header design (shape and size) and the shape of microchannel on heat transfer and fluid flow of the entire heat sink. Therefore, in the present study, fluid flow and heat transfer in microchannel heat sinks with different inlet/outlet locations (I, C and Z-type), header shapes (triangular, trapezoidal and rectangular) and microchannel shapes (the conventional rectangular microchannel, the microchannel with offset fan-shaped reentrant cavities and the microchannel with triangular reentrant cavities) are numerically studied with computational domain including the entire microchannel heat sink. Detailed three-dimensional numerical simulations are useful in identifying the optimal geometric parameters that provide better heat transfer and flow distribution in a microchannel heat sink.
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2. Numerical modeling of microchannel heat sink A three-dimensional model has been created using Gambit 2.1 and the numerical simulation has been performed using Fluent 6.3. In practical application, it is difficult to arrange the inlet/outlet locations on the side walls because the microchannel heat sink is too thin, so we arrange the inlet/outlet on the heat sinks. Three different inlet/outlet configurations (C, Z and I-type) have been selected on the heat sinks in Fig. 1. The different geometries header shapes (rectangular, trapezoidal and triangular) and microchannel shapes (the conventional rectangular microchannel, the microchannel with offset fan-shaped reentrant cavities and the microchannel with triangular reentrant cavities) are presented in Figs. 2 and 3, respectively. The geometric configurations of I-type heat sink are shown in Fig. 4. The geometrical dimensions of header and microchannels using for the simulation are summarized in Table 1. The I-type heat sink is 10 mm in length, 10 mm in width, 0.9 mm in thickness, respectively. The whole length of the parallel microchannels in longitudinal direction is 4 mm, the total width covering the thirty microchannels is 6 mm, and the depth of the microchannel is 0.3 mm. The number of microchannels is 30, and the hydraulic diameter is 0.15 mm, and the aspect ratio is 0.333.
(2) The fluid is in single phase and flow is incompressible, laminar. (3) The effects of gravity and other forms of body forces are negligible. (4) The viscous dissipation is considered. (5) The fluid properties are set as piecewise-linear function of water temperature. (6) Multi-channel effect is taken into account. Based on above assumptions, the governing equations for fluid and energy transport can be expressed as follows: Fluid flow:
r V ¼ 0q
ð1Þ 2
qðV rVÞ ¼ rp þ lr V
ð2Þ
Energy in fluid flow:
qcp ðV rTÞ ¼ kf r2 T
ð3Þ
Energy in heat sink solid part:
ks r2 T s ¼ 0
ð4Þ
The boundary conditions for these equations are given as:
3. Governing equations To focus on the effects of inlet/outlet locations, header shapes and microchannel cross-sections shapes on the heat sink performance, the Navier–Stokes and energy equations are used to model the convective heat transfer process. The following assumptions are made: (1) The fluid flow and heat transfer are in steady-state and three-dimensional.
Inlet:
V ¼ V in ;
T ¼ T in
ð5aÞ
Outlet:
p ¼ pout
ð5bÞ
Fluid–solid interface:
V ¼ 0;
T ¼ Ts;
ks ð@T S =@nÞ ¼ kf ð@T=@nÞ
Fig. 1. Schematic diagram of different inlet/outlet locations.
Fig. 2. Schematic diagram of microchannel heat sinks header design.
ð5cÞ
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Fig. 3. Geometry of the different microchannels.
Fig. 4. Geometric configuration of I-type microchannel heat sink.
Table 2 Thermophysical properties of water.
Table 1 Parameters considered for the numerical study. No.
Parameters
1 2
Inlet/outlet configurations Header shape
3
Microchannel shape
4 5
Number of microchannels Heat sink
Values C, Z and I Rectangular Symmetry trapezoidal Triangular A (L1/W3 = 40) B (W4/W3 = 0.5, R/W3 = 1, L5/W3 = 2.5) C (L4/W3 = 2, W5/W3 = 2) 30 W/W3 = L/W3 = 100, D/W3 = 10, H/W3 = 9
At the base plate:
qw ¼ 200 W=cm2
ð5dÞ
In Eq. (5), Vin and Tin are the fluid velocity and temperature at the inlet, respectively, pout is the outlet pressure, n is the local coordinate normal to the wall, and qw is the heat flux applied at the heat sink bottom surface. The pressure drop is defined as Dp = pinpout.
T (K)
q (kg/m3)
cp (J kg1 K1)
kf (W m1 K1)
l (Pa s)
298 308 318 328 338 348
996.6 994.2 990.2 985.6 980.5 974.8
4178 4174 4174 4176 4183 4191
0.609 0.627 0.642 0.653 0.664 0.671
0.0009027 0.0007274 0.0006014 0.0005096 0.0004380 0.0003806
water temperature is 298 K at the inlet. The heat flux qw applied at the heat sink bottom surface is fixed at 200 W/cm2. The microchannels wall surface of the heat sink are no-slip and no-penetration. The properties of solid used in the numerical simulation are ks = 148 W/(m K), cps = 712 J/(kg K), qs = 2329 kg/m3, respectively. When the water temperature is 298 K, the properties of water in kf = 0.609 W/(m K), q = 996.6 kg/m3, cp = 4178 J/(kg K). The properties of water are assumed piecewise-linear functions of temperature in Table 2 [18]. 4.1. Grid independence
4. Numerical parameters and procedures Before the numerical simulations, many parameters considered for the numerical study must be given in advance. The working fluid is deionized water and the heat sink material is silicon. The
The sensitivity of the grid with the heat sink A has been tested by three different grids, coarse grids with total of 1.30 106 cells, fine grids with total of 2.39 106 cells and very fine grids with total of 3.61 106 cells. Finer grids have been used within the microchannels in order to obtain the fluid flow and heat transfer
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Table 3 Validation of grid independence.
DP/kPa Tave/°C Tmax/°C
Coarse grids (1.30 106)
E%
Fine grids (2.39 106)
E%
Very fine grids (3.61 106)
38.477 44.70 49.69
2.90 2.52 2.25
39.287 43.90 48.85
0.86 0.69 0.51
39.627 43.60 48.60
Fig. 6. Comparison between numerical and theoretical local Nusselt number variation.
Re ¼
qum Dh l
Nux;3 ¼ Nux;4 ðNufd;3 =Nufd;4 Þ Fig. 5. Comparison of friction factor f vs. Re number.
characteristics accurately. The deviation between very fine grids (f1) and other grids (f2) can be defined as [19]:
f f 1 100 E% ¼ 2 f1
ð6Þ
The structures of the grid include structured and unstructured. The number of nodes for axial length of microchannel is 200. There are locally refined grids. For the area of microchannel, the interval size is 0.02. In Table 3, the pressure, maximum temperature and averaged temperature of the heat sink bottom surface are presented for these three grids. According to Table 3, the deviations of the pressure drop, the averaged temperature and the maximum temperature using the fine grids with total of 2.39 106 cells from that of the very fine grids with total of 3.61 106 cells are 0.86%, 0.69% and 0.51%, respectively. The deviations between these two grids are less than 1%, so the result shows that the calculation is accurate. Due to the large amount of calculations, the long computing time, the limited computer memory and the accuracy of the calculation, a fine grid with 2.39 106 cells has been adopted as the optimum grid system for further simulations. Simulations have been carried out until the normalized residual values were less than 107 for all the flow variables but 108 only for the energy equation, during the iterative solution procedure. 4.2. Verification of smooth microchannel
Po Re Po ¼ 96ð1 1:3553ac þ 1:9467a2c 1:7012a3c þ 0:9564a4c 0:2537a5c Þ
ð10Þ
where, Po is Poiseuille number, which based on the aspect ratio ac of the rectangular microchannel. Re is the Reynolds number, which is related to the Dh. Nux,3 and Nux,4 stand for the Nusselt number at a distance x in the heated length for the three-sided and four-sided heating cases respectively. Nufd,3 and Nufd,4 refer to the Nusselt numbers for the three-sided and four-sided heating cases in fully developed laminar respectively. Figs. 5 and 6 indicate the comparison of the numerical and theoretical data of the friction factor f and Nusselt number Nux,3, respectively. It is seen that the numerical and theoretical results are in good agreement with each other with the difference being less than 4.5% for friction factor f and 7.8% for Nusselt number Nux,3, respectively. Therefore, the present numerical code can be able to ensure accuracy of the computation. 5. Results and discussion In order to obtain the optimal geometric parameters of microchannel heat sinks, the effects of the different inlet/outlet configurations (C, Z and I-type), different geometries header shapes (rectangular, symmetry trapezoidal and triangular) and microchannel shapes (the conventional rectangular microchannel, the microchannel with offset fan-shaped reentrant cavities and the microchannel with triangular reentrant cavities) have been analyzed by numerical simulations. 5.1. Effect of inlet/outlet locations on flow distribution
In this section, in order to verify the accuracy and reliability of the code, simulations of fluid flow and heat transfer are carried out to predict the results in terms of friction factor f and Nusselt number Nux,3, which are compared with the theoretical correlation given by Refs. [20,21] with three-side heating correction. Comparisons between the numerical data and the theoretical data for the heat sink A about the Reynolds number are shown in Figs. 5 and 6, respectively. The friction factor f and Nusselt number Nux,3 can be computed with the following equations:
f ¼
ð9Þ
ð7Þ
ð8Þ
Fig. 7 shows the average velocity distribution in microchannel heat sinks with different inlet/outlet locations when qv = 150 ml/ min. It is seen that different inlet/outlet configurations have great influence on the characteristic of flow distribution for the heat sink. When the fluid flow into the inlet of the heat sink, the direction of velocity is vertical to the bottom wall of the header (effect of flow impingement), which enhances the uniformity of fluid distribution in each microchannel. The flow velocity uniformity is comparatively better for I-type arrangement among all other configurations considered in this study; whereas, the flow velocity uniformity is worse for Z-type configuration. In C-type configuration, the fluid has to travel from one end to the dead end of the inlet header, which results in poor velocity distribution with intense flow separation. In the case of Z-type configuration, the
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Fig. 7. Average velocity in each channel of microchannel heat sinks with different inlet/outlet locations.
Table 4 Mal-distribution for three inlet/outlet parameters.
Fig. 8. Average velocity in each channel of microchannel heat sinks with different header shapes.
Table 5 Mal-distribution for three header shapes parameters.
Parameters
I-type
C-type
Z-type
Parameters
Rectangular
Symmetry trapezoidal
Triangular
VSTD/Vave
0.156
0.471
0.551
VSTD/Vave
0.156
0.203
0.214
velocity of the channel number 1 is relatively higher than nearby channels because of the Coanda effect [9]. The inlet locates near the side wall of the channel number 1, which makes the velocity of the channel number1 is relatively higher. The large flow velocity mal-distribution can be attributed to the interaction of the effect of flow impingement and entering/exiting of flow from opposite ends, which brings the intense flow separation. Due to geometric symmetry, the average velocity distribution in the I-type flow arrangement is found to be symmetrical with respect to the centerline of the heat sink located between channel number 15 and 16. The flow separation is relatively lesser which leads to better velocity distribution in I-type flow arrangement. For three inlet/outlet geometric configurations considered in the study, a mal-distribution factor, which is defined as VSTD/Vave [7], is employed to identify the flow velocity distribution in the multi-channel heat sink. The lower mal-distribution is, the better uniformity is. The mal-distribution factor is calculated and summarized in Table 4. Here, the subscripts STD and ave denote the standard deviation and average values, respectively. Table 4 indicates that I-type flow exhibits lower mal-distribution (VSTD/ Vave = 0.156) and higher value (VSTD/Vave = 0.551) for the Z-type configuration.
5.2. Effect of header shapes on flow distribution In the following parts of the present work, I-type has been selected to study the effect of header shapes on flow velocity distribution in that the flow distribution has an significant impact on the temperature distribution. Fig. 8 indicates the average velocity distribution in microchannel heat sinks with different header shapes when qv = 150 ml/min. The flow distribution is found to be symmetrical because both inlet and outlet are located at the center. It is observed from Fig. 8 that better velocity distribution is noticed for the rectangular header and poor velocity distribution for the triangular header. The variation of the velocity distribution for the symmetry trapezoidal header is similar to the rectangular header except for the discrepancy at the initial few channels (1–7) and the last few channels (24–30). The reason for this can be analyzed as follows: It is seen that the flow velocity
peaks are found at the inlet portion and at edges of the coldplate, whereas channels with the lowest velocity locate between inlet and edge region for rectangular and symmetry trapezoidal header heat sinks. For triangular header, the locations of the lowest velocity occur at edges of the coldplate because the fluid flow is very small. Due to the flow impingement configuration where major part of impinging flow follows the shortest path length toward outlet, the maximum flow velocity appears at the entrance region. However, part of the impinging flow is directed along the wall of the header in y-direction to the edge. Finally, this flow stream is guided by the wall of the header in x-direction through the channels, leading to the second flow velocity peak nearby the edge. The fluid is distributed through the channels in the flow direction and the flow decrease due to the branching of fluid. In the case of rectangular header, when the fluid is distributed through the channels, flow decelerates because of the branching of fluid, so the static pressure increase. Simultaneously, the wall friction effect of header also tends to reduce the static pressure in the flow direction, which results in relatively uniform velocity distribution. For the case of the triangular header, the velocity is relatively larger than others at the entrance because the cross section of header decreases (the minimum header volume) in the flow direction. The flow decreases because of the branching of fluid and the decreasing the velocity, which in turn enhances the static pressure. At the same time, the wall friction effect of header trends to decrease the static pressure which leads to relatively poor velocity distribution. In a word, the rectangular header heat sink obtains lower mal-distribution than others. For three header shapes geometric configurations considered in the study, the mal-distribution is calculated and summarized in Table 5. It indicates that rectangular header shape configuration assumes lower mal-distribution (VSTD/Vave = 0.156) and strong mal-distribution can be observed (VSTD/Vave = 0.214) in the triangular header shape configuration. In real applications, the temperature of the electronic chips cannot exceed certain temperature values, above which great damage might be caused to the devices. Particularly, local hot must be avoided because the performance of the electronic device strongly depends on the working temperature. The thermal performance of the heat sinks is usually characterized based on the average
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temperature, maximum temperature and the deviation of the heat sinks bottom surface temperature. The flow distribution, which can be characterized based on the flow velocity distribution in the multiple channels, has an significant impact on the heat sinks bottom surface temperature distribution. It is obvious that the more uniform the flow velocity distribution is, the less the deviation of the heat sinks bottom surface temperature is. 5.3. Effect of microchannel cross-section shapes on fluid flow and heat transfer In this section, I-type heat sink with rectangular header has been selected to study the effect of microchannel shapes on the flow and heat transfer. The following three types of microchannel shapes are studied: microchannel A (the conventional rectangular microchannel), microchannel B (the microchannel with offset fanshaped reentrant cavities) and microchannel C (the microchannel with triangular reentrant cavities). Fluid flow performance of the microchannel heat sink is characterized based on the pressure drop. The heat transfer performance of the heat sink is characterized based on the temperature of the bottom surface, including maximum temperature, average temperature and the deviation of the temperature DT = Tmax Tmin. Fig. 9 shows the comparison of pressure drop for different microchannel heat sinks with different flow rates. It is seen that the total pressure drop increases with increasing flow rate for the three different heat sinks, but the pressure drops of the heat sinks B and C are larger than that of the heat sink A. For the heat sink B or C, the pressure drop consists of not only the term along the microchannel, but also term in the reentrant cavities. In the case of heat sink C, when the water flows into the expansion cross-section region, the velocity decreases and the pressure drop increases, and when the water flows into the constriction crosssection region and impinging the constriction wall, the throttling effect at the constriction wall outlet forms and the laminar flow boundary layer is interrupted, which also leads to a high pressure drop. The flow mechanism can be attributed to the throttling effect at the constriction wall outlet and the second flow from the reentrant cavities. For the heat sink B, the pressure drop increases due to the jetting and throttling effect of the offset fan-shaped reentrant cavities. When the fluid flow increases from 100 ml/min to 200 ml/min, the increasing tendency of the pressure drop of the heat sinks A, B and C become fast, respectively. This means the pressure drop increases rapidly with the increasing of fluid flow when the fluid flow exceeds a certain value, which is bad for the heat sink. Figs. 10 and 11 indicate the average temperature and maximum temperature on the heat sinks bottom surface versus qv, respec-
Fig. 10. Comparison of average temperature on the heat sinks bottom surface.
Fig. 11. Comparison of maximum temperature on the heat sinks bottom surface.
Fig. 12. Comparison of deviation of the heat sinks bottom surface temperature.
Fig. 9. Comparison of pressure drop for different microchannel heat sinks.
tively. It is observed that the average temperature and maximum temperature decrease with increasing flow rate for all the three different heat sinks, but the average temperature and maximum temperature of the heat sink B and C are lower than that of the heat sink A, respectively. This means the reentrant cavities provide a significant enhancement on the temperature distribution. The reason can be analyzed as follows: (1) the structure of the reentrant cavities increases owning the heat transfer area and enhances the heat transfer effect; (2) for the heat sink C, the expansion–constriction cross-sections can induce better fluid mixing between the wall and the core flow regions, the jetting effect at the expansion
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Fig. 13. The temperature distribution of the three heat sinks bottom surface.
wall entrance and the throttling effect at the constriction wall outlet, the second flow from the triangular reentrant cavities and the additional flow disturbance near the wall of the reentrant cavities, which make the laminar flow boundary layer interrupted and redeveloped, so the heat transfer can be enhanced. For the heat sink B, the enhancement of the heat transfer is attributed to the jetting and throttling effects of the offset fan-shaped reentrant cavities and the additional flow disturbance near the wall of the reentrant cavities and the form drag of the reentrant cavities. The bottom temperature distribution of the heat sink is more uniform and the life of the microelectronic devices is expected to be prolonged. When the fluid flow increases from 100 ml/min to 200 ml/min, the decreasing tendencies of the average temperature and maximum temperature of the heat sink A, B and C become flat, respectively. This means the increasing of fluid flow cannot reduce the bottom surface temperature effectively when the fluid flow exceeds a certain value, which is bad for enhancement of the heat transfer. As shown in Fig. 12, with an increase of fluid flow rate, the deviation of the heat sinks bottom surface temperature (DT = Tmax Tmin) reduces and the deviation of the heat sink B and C are lower than that of the heat sink A, and the deviation of the heat sink C is lower than that of the heat sink B. The values of maximum temperature and average temperature are close to each other while the deviation keeps minimum. When the fluid flow increases from 100 ml/min to 200 ml/min, the decreasing tendencies of the deviation of temperature of the heat sink A, B and C become flat, respectively. As a result, when the fluid flow exceeds a certain value, the increasing of fluid flow cannot decrease the bottom surface temperature effectively, which is bad for enhancement of the heat transfer. Isaev et al. [22] investigated the unsteady-state heat transfer under conditions of laminar transverse flow past a circular cylinder. It has been found that the averaged value of total heat transfer from the cylinder increases by only 8.3% compared to the case of steady-state flow past the cylinder. Silva et al. [23] investigated the flow structure and heat transfer in channel with dimpled surfaces by numerical and experimental studies. The result shows there is a positive improvement (twofold on average) in Nusselt number when dimpled surfaces are compared to flat plates. Compared to the channel with dimpled surfaces, we find that the structure of the reentrant cavities increases owning the heat transfer area and enhances the heat transfer effect. Fig. 13 plots the temperature distribution of the three heat sinks bottom surface for qv = 150 ml/min. It is worth noting that, the maximum temperature appear near the outlet of microchannel region due to the heat conduction in the lateral parts of channels. The maximum temperature, average temperature and the deviation of the heat sink C with triangular reentrant cavities are lower than that of the heat sink B with offset fan-shaped reentrant
cavities and the heat sink A. The triangular reentrant cavities increase the heat transfer area and enhance the heat transfer effect. The pressure drop of the heat sink C is lower than that of the heat sink B. Therefore, the heat sink C has better heat transfer characteristic and is able to prolong the life of the microelectronic devices.
6. Conclusions Numerical investigation has been performed to study the effects of the inlet/outlet locations, header shapes and microchannel shapes on fluid flow and heat transfer, and obtain the optimal geometric parameters. The following conclusions might be drawn from the present study: (1) Effects of inlet/outlet configurations highlight that flow velocity uniformity is comparatively better for I-type and poor for Z-type. The flow distribution is found to be symmetrical for I-type. (2) It is seen from the header shapes analysis that the rectangular head shape provides the better flow velocity uniformity than the symmetry trapezoidal and triangular headers. The fluid flow mechanism can be attributed to the interaction of the branching of fluid and the friction offered by the walls of the header. (3) Effects of microchannel shapes emphasize that the microchannel with offset fan-shaped reentrant cavities and with triangular reentrant cavities of the heat sinks enhance the heat transfer than the conventional rectangular microchannel of the heat sink. The heat transfer mechanism can be attributed to the jetting and throttling effect, the additional flow disturbance near the wall of the reentrant cavities and the form drag of the reentrant cavities. (4) The maximum temperature appears near the outlet of microchannel region due to the heat conduction in the lateral parts of channels. The heat sink C has better heat transfer characteristic for qv = 150 ml/min and is able to prolong the life of the microelectronic devices. Conflict of interest None declared. Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 51176002), the National Basic Research Program
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of China (2011CB710704) and the Beijing Natural Science Foundation (3142004). References [1] 2003 International Technology Roadmap for Semiconductors (ITRS), Executive Summary, vol. 57, 2003. [2] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking for VLSI, IEEE Electron. Dev. Lett. EDL-2 (1981) 126–129. [3] P. Gunnasegaran, H.A. Mohammed, R. Saidur, The effect of geometrical parameters on heat transfer characteristics of microchannels heat sink with different shapes, Int. Commun. Heat Mass Transfer 37 (2010) 1078–1086. [4] S.C. Eun, S.Y. Jae, S.K. Min, Experimental study on microchannel heat sinks considering mass flow distribution with non-uniform heat flux conditions, Int. J. Heat Mass Transfer 53 (2010) 2159–2168. [5] R.Y. Chein, J.H. Chen, Numerical study of the inlet/outlet arrangement effect on microchannel heat sink performance, Int. J. Therm. Sci. 48 (2009) 1627–1638. [6] R. Kumaran, G. Kumaraguruparan, T. Sornakumar, Experimental and numerical studies of header design and inlet/outlet configurations on flow maldistribution in parallel micro-channels, Appl. Therm. Eng. 58 (2013) 205–216. [7] M.C. Lu, C.C. Wang, Effect of the location on the performance of parallelchannel coldplate, IEEE Trans. CPT 29 (2006) 30–38. [8] S.V. Manoj, P. Arvind, K.D. Sarit, Effect of flow maldistribution on the thermal performance of parallel microchannel cooling systems, Int. J. Heat Mass Transfer 73 (2014) 424–428. [9] D. Liu, B. Jiang, M.H. Liu, Effect of inlet/outlet types on the flow distribution and heat transfer in mini-channels, Chin. J. Lasers 39 (2012) 1003005. [10] F. Hong, P. Cheng, Three dimensional numerical analyses and optimization of offset strip-fin microchannel heat sinks, Int. Commun. Heat Mass Transfer 36 (2009) 651–656. [11] A.J. Foong, N. Ramesh, T.T. Chandratilleke, Laminar convective heat transfer in a microchannel with internal longitudinal fins, Int. J. Therm. Sci. 48 (2009) 1908–1913.
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[12] A. Danish, H. Afzal, K. Kwang-Yong, Multi-objective optimization of a grooved micro-channel heat sink, IEEE Trans. CPT 33 (2010) 767–776. [13] L. Chai, G.D. Xia, M.Z. Zhou, Optimum thermal design of interrupted microchannel heat sink with rectangular ribs in the transverse microchambers, Appl. Therm. Eng. 51 (2013) 880–889. [14] G.D. Xia, L. Chai, M.Z. Zhou, Effects of structural parameters on fluid flow and heat transfer in a microchannel with aligned fan-shaped reentrant cavities, Int. J. Therm. Sci. 50 (2011) 411–419. [15] G.D. Xia, L. Chai, H.Y. Wang, Optimum thermal design of microchannel heat sink with triangular reentrant cavities, Appl. Therm. Eng. 31 (2011) 1208– 1219. [16] G.D. Xia, L. Chai, M.Z. Zhou, Numerical simulation of fluid flow and heat transfer in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall, Int. Commun. Heat Mass Transfer 38 (2011) 577–584. [17] G.D. Xia, L. Chai, L. Wang, M.Z. Zhou, Z.Z. Cui, Heat transfer enhancement in microchannel heat sinks with periodic expansion–constriction cross-sections, Int. J. Heat Mass Transfer 62 (2013) 741–751. [18] S.M. Yang, W.Q. Tao, Heat Transfer, third ed., Higher Education Press, Beijing, 1998. [19] J.F. Guo, M.T. Xu, L. Cheng, Second law analysis of curved rectangular channel, Int. J. Therm. Sci. 50 (2011) 760–768. [20] M.E. Steinke, S.G. Kandlikar, Single-phase liquid friction factors in microchannels, Int. J. Therm. Sci. 45 (2006) 1073–1083. [21] Z.G. Li, X.L. Huai, Y.J. Tao, H.Z. Chen, Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks, Appl. Therm. Eng. 27 (2007) 2803–2814. [22] S.A. Isaev, A.I. Leontiev, N.A. Kudryavtsev, T.A. Baranova, D.A. Lysenko, Numerical simulation of unsteady-state heat transfer under conditions of laminar transverse flow past a circular cylinder, Heat Mass Transfer Phys. Gasdyn. High Temp. 43 (2005) 746–759. [23] C. Silva, E. Marotta, L. Fletcher, Flow structure and enhanced heat transfer in channel flow with dimpled surfaces: application to heat sinks in microelectronic cooling, J. Electron. Packag. 2 (2007) 157–166.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effects of different geometric structures on fluid flow and heat transfer performance in microchannel heat sinks G.D. Xia ⇑, J. Jiang, J. Wang, Y.L. Zhai, D.D. Ma Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, College of Environmental and Energy Engineering, Beijing University of Technology, Beijing 100124, China
a r t i c l e
i n f o
Article history: Received 21 May 2014 Received in revised form 11 August 2014 Accepted 24 August 2014
Keywords: Microchannel heat sink Flow distribution Inlet/outlet location Header shape Microchannel cross-section shape Geometric parameter
a b s t r a c t In the present study, fluid flow and heat transfer in microchannel heat sinks with different inlet/outlet locations (I, C and Z-type), header shapes (triangular, trapezoidal and rectangular) and microchannel cross-section shapes (the conventional rectangular microchannel, the microchannel with offset fanshaped reentrant cavities and the microchannel with triangular reentrant cavities) are numerically studied with computational domain including the entire microchannel heat sink. Detailed three-dimensional numerical simulations are useful in identifying the optimal geometric parameters that provide better heat transfer and flow distribution in a microchannel heat sink. Results highlight that flow velocity uniformity is comparatively better for I-type and poor for Z-type. The flow distribution is found to be symmetrical for I-type. It is seen from the header shapes analysis that the rectangular header shapes provides better flow velocity uniformity than the trapezoidal and triangular headers. The fluid flow mechanism can be attributed to the interaction of the branching of fluid and the friction offered by the walls of the header. Effects of microchannel cross-section shapes emphasize that the microchannel with offset fan-shaped reentrant cavities and the microchannel with triangular reentrant cavities of the heat sinks enhance the heat transfer compared to the conventional rectangular microchannel. The heat transfer mechanism can be attributed to the jetting and throttling effect, the additional flow disturbance near the wall of the reentrant cavities and the form drag of the reentrant cavities. The heat sink C has better heat transfer characteristic for qv = 150 ml/min and is able to prolong the life of the microelectronic devices. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction With the rapid development of ULSIC (Ultra-Large-Scale-Integrated-Circuit) and MEMS (Micro-Electro-Mechanical-Systems), the application of microchannel heat sinks has attracted much attention in the field of advanced energy and power engineering, microelectronics, military and nuclear energy, aerospace, biochemistry, etc. As one of the most promising high efficiency heat exchange technologies, the microchannel heat sinks are used in a lot of devices for cooling down the miniature systems. According to the International Technology Roadmap for Semiconductors (ITRS), the peak power consumption of high performance desktops will rise by 96% (147 W–288 W) in 2016, and by 95% (91 W–158 W) in lower-end desktops in 2016 [1]. With the increase of the heat load and the intensity of the heat exchange systems, the traditional straight microchannel heat sink cooling ⇑ Corresponding author. Tel.: +86 1067392176; fax: +86 1067391983. E-mail address: [email protected] (G.D. Xia). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.08.095 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
systems have been unable to meet the requirements and impose limits on product design if no action is taken to propose more effective cooling methods. Since Tuckerman and Pease [2] first proposed the microchannel heat sink cooling concept for electronic cooling in the early 1980s, there have been a variety of interests in the study of fluid flow and heat transfer characteristic in microchannel. It combines two ways of heat transfer: increasing the convective heat transfer coefficient by decreasing the hydraulic diameter of the microchannel and the heat conduction through the microchannel walls. Gunnasegaran et al. [3] studied the effects of geometrical parameters on heat transfer and fluid flow in microchannel heat sink. It is found that the temperature distribution is much uniform for the smallest hydraulic diameter of the microchannel heat sinks, and pressure drop and friction factor are larger. Eun et al. [4] investigated the cooling performance of microchannel heat sinks with different geometric structures, which is straight and diverging channels under various heat flux conditions. The straight microchannels show less sensitivity of the temperature distributions on the variation of the header shape than diverging
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Nomenclature cp Dh f h H kf ks L Nu Dp Po qm qw Q Re
special heat capacity kJ/(kg K) hydrodynamic diameter mm friction factor heat transfer coefficient W/(m2 K) height mm thermal conductivity of fluid W/(m K) thermal conductivity of solid W/(m K) length mm Nusselt number pressure drop Pa Poiseuille number volume flow rate m3/s heat flux W/m2 total heat input W Reynolds number
micro channels. The pressure drop in the straight channels is higher than that in the diverging microchannels. Facing the challenge of increasing the heat load and the intensity of the heat exchange systems, a significant amount of innovative cooling techniques have the potential to remove high heat flux for some microelectronic applications. Enhancement of microscale heat transfer can be attributed to better flow distribution. Chein and Chen [5] investigated the inlet/outlet arrangement effects on the fluid flow and heat transfer inside the heat sinks. The focus of their research is inlet/outlet arrangement effects on the flow distribution. They indicated that the low heat sink temperature takes place at the entrance zones of microchannels because high heat transfer coefficient and the highest heat sink temperature occur at the edge of the heat sink, where there is no heat dissipation by fluid convection. Kumaran et al. [6] revealed the effects of header design on flow mal-distribution in a microchannel heat sink by experiment and numerical simulation. The emphasis of their research is inlet/outlet arrangement and header design effects on flow mal-distribution. It is reported that the flow distribution is better for C-type, and the triangular inlet header and the trapezoidal outlet header provide better flow distribution. Lu and Wang [7] presented the effect of inlet location on the performance of parallel-channel cold-plate. The focus of their research is inlet location effects on velocity mal-distribution and nonuniformity of temperature. They found that the I-arrangement shows the best heat transfer performance because of the impingement configurations and the Z-arrangement gives the lowest heat transfer performance due to the dramatic flow recirculation and maldistribution. Manoj et al. [8] carried out an experimental study to investigate the effect of flow maldistribution on the thermal performance of parallel microchannel cooling systems. The emphasis of their research is inlet/outlet arrangement effects on the thermal performance. It is found that the average temperature and the peak temperature of the device trend to a considerable reduction with the decreasing of channel diameter and the heat sinks have better temperature distribution. Liu et al. [9] studied the effect of flow maldistribution on the thermal performance of parallel microchannel cooling systems. The results showed that the flow distribution of the heat sink is better for UC-type. Enhancement of microscale heat transfer can be attributed to providing more surface area and interrupting the boundary layer formation. Hong and Cheng [10] employed a three-dimensional numerical simulation to analyze the heat transfer enhancement
m W x
mean velocity m/s width mm length of header mm
Greek symbols q density kg/m3 l dynamic viscosity kg/(m s) Subscript ave in max min m out
average inlet maximum minimum mean outlet
mechanism in offset strip-fin microchannel. Foong et al. [11] numerically studied the heat transfer and fluid flow characteristics in a square microchannel with four longitudinal internal fins. Danish et al. [12] studied and optimized the shape of the microchannel heat sink with a grooved structure. The result implied the microchannel heat sink with grooved structure is better compared to the smooth microchannel both fluid flow and heat transfer characteristics, which can improve the heat transfer performance. Chai et al. [13] revealed the effects of fluid flow and heat transfer characteristics of interrupted microchannel heat sink with rectangular ribs in the transverse microchambers. The heat transfer enhancement mechanism can be attributed to the interaction of the mainstream flow separation, recirculation, vortex and interrupted boundary layer. Xia et al. [14–17] studied and optimized the structural parameters of the microchannel with offset fan-shaped reentrant cavities, triangular reentrant cavities and aligned fan-shaped reentrant cavities by numerical simulation of flow and heat transfer mechanism. They analyzed the effect of geometric parameters on fluid flow and heat transfer characteristics and obtained the optimal geometric parameters for the heat transfer enhancement of microchannel heat sinks. The heat transfer enhancement mechanism can be attributed to the interaction of increasing the heat transfer surface area, interrupting the boundary layers, redeveloping the hydraulic and thermal boundary layers, throttling effects and slipping over the reentrant cavities. These innovative cooling techniques are sufficient for cooling requirements in some applications. From the literature review, many researchers have investigated the fluid flow and heat transfer characteristics of the microchannel heat sinks. However, it is clear that few studies (both numerical and experimental) are investigated the effects of the inlet/outlet locations, header design (shape and size) and the shape of microchannel on heat transfer and fluid flow of the entire heat sink. Therefore, in the present study, fluid flow and heat transfer in microchannel heat sinks with different inlet/outlet locations (I, C and Z-type), header shapes (triangular, trapezoidal and rectangular) and microchannel shapes (the conventional rectangular microchannel, the microchannel with offset fan-shaped reentrant cavities and the microchannel with triangular reentrant cavities) are numerically studied with computational domain including the entire microchannel heat sink. Detailed three-dimensional numerical simulations are useful in identifying the optimal geometric parameters that provide better heat transfer and flow distribution in a microchannel heat sink.
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2. Numerical modeling of microchannel heat sink A three-dimensional model has been created using Gambit 2.1 and the numerical simulation has been performed using Fluent 6.3. In practical application, it is difficult to arrange the inlet/outlet locations on the side walls because the microchannel heat sink is too thin, so we arrange the inlet/outlet on the heat sinks. Three different inlet/outlet configurations (C, Z and I-type) have been selected on the heat sinks in Fig. 1. The different geometries header shapes (rectangular, trapezoidal and triangular) and microchannel shapes (the conventional rectangular microchannel, the microchannel with offset fan-shaped reentrant cavities and the microchannel with triangular reentrant cavities) are presented in Figs. 2 and 3, respectively. The geometric configurations of I-type heat sink are shown in Fig. 4. The geometrical dimensions of header and microchannels using for the simulation are summarized in Table 1. The I-type heat sink is 10 mm in length, 10 mm in width, 0.9 mm in thickness, respectively. The whole length of the parallel microchannels in longitudinal direction is 4 mm, the total width covering the thirty microchannels is 6 mm, and the depth of the microchannel is 0.3 mm. The number of microchannels is 30, and the hydraulic diameter is 0.15 mm, and the aspect ratio is 0.333.
(2) The fluid is in single phase and flow is incompressible, laminar. (3) The effects of gravity and other forms of body forces are negligible. (4) The viscous dissipation is considered. (5) The fluid properties are set as piecewise-linear function of water temperature. (6) Multi-channel effect is taken into account. Based on above assumptions, the governing equations for fluid and energy transport can be expressed as follows: Fluid flow:
r V ¼ 0q
ð1Þ 2
qðV rVÞ ¼ rp þ lr V
ð2Þ
Energy in fluid flow:
qcp ðV rTÞ ¼ kf r2 T
ð3Þ
Energy in heat sink solid part:
ks r2 T s ¼ 0
ð4Þ
The boundary conditions for these equations are given as:
3. Governing equations To focus on the effects of inlet/outlet locations, header shapes and microchannel cross-sections shapes on the heat sink performance, the Navier–Stokes and energy equations are used to model the convective heat transfer process. The following assumptions are made: (1) The fluid flow and heat transfer are in steady-state and three-dimensional.
Inlet:
V ¼ V in ;
T ¼ T in
ð5aÞ
Outlet:
p ¼ pout
ð5bÞ
Fluid–solid interface:
V ¼ 0;
T ¼ Ts;
ks ð@T S =@nÞ ¼ kf ð@T=@nÞ
Fig. 1. Schematic diagram of different inlet/outlet locations.
Fig. 2. Schematic diagram of microchannel heat sinks header design.
ð5cÞ
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Fig. 3. Geometry of the different microchannels.
Fig. 4. Geometric configuration of I-type microchannel heat sink.
Table 2 Thermophysical properties of water.
Table 1 Parameters considered for the numerical study. No.
Parameters
1 2
Inlet/outlet configurations Header shape
3
Microchannel shape
4 5
Number of microchannels Heat sink
Values C, Z and I Rectangular Symmetry trapezoidal Triangular A (L1/W3 = 40) B (W4/W3 = 0.5, R/W3 = 1, L5/W3 = 2.5) C (L4/W3 = 2, W5/W3 = 2) 30 W/W3 = L/W3 = 100, D/W3 = 10, H/W3 = 9
At the base plate:
qw ¼ 200 W=cm2
ð5dÞ
In Eq. (5), Vin and Tin are the fluid velocity and temperature at the inlet, respectively, pout is the outlet pressure, n is the local coordinate normal to the wall, and qw is the heat flux applied at the heat sink bottom surface. The pressure drop is defined as Dp = pinpout.
T (K)
q (kg/m3)
cp (J kg1 K1)
kf (W m1 K1)
l (Pa s)
298 308 318 328 338 348
996.6 994.2 990.2 985.6 980.5 974.8
4178 4174 4174 4176 4183 4191
0.609 0.627 0.642 0.653 0.664 0.671
0.0009027 0.0007274 0.0006014 0.0005096 0.0004380 0.0003806
water temperature is 298 K at the inlet. The heat flux qw applied at the heat sink bottom surface is fixed at 200 W/cm2. The microchannels wall surface of the heat sink are no-slip and no-penetration. The properties of solid used in the numerical simulation are ks = 148 W/(m K), cps = 712 J/(kg K), qs = 2329 kg/m3, respectively. When the water temperature is 298 K, the properties of water in kf = 0.609 W/(m K), q = 996.6 kg/m3, cp = 4178 J/(kg K). The properties of water are assumed piecewise-linear functions of temperature in Table 2 [18]. 4.1. Grid independence
4. Numerical parameters and procedures Before the numerical simulations, many parameters considered for the numerical study must be given in advance. The working fluid is deionized water and the heat sink material is silicon. The
The sensitivity of the grid with the heat sink A has been tested by three different grids, coarse grids with total of 1.30 106 cells, fine grids with total of 2.39 106 cells and very fine grids with total of 3.61 106 cells. Finer grids have been used within the microchannels in order to obtain the fluid flow and heat transfer
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Table 3 Validation of grid independence.
DP/kPa Tave/°C Tmax/°C
Coarse grids (1.30 106)
E%
Fine grids (2.39 106)
E%
Very fine grids (3.61 106)
38.477 44.70 49.69
2.90 2.52 2.25
39.287 43.90 48.85
0.86 0.69 0.51
39.627 43.60 48.60
Fig. 6. Comparison between numerical and theoretical local Nusselt number variation.
Re ¼
qum Dh l
Nux;3 ¼ Nux;4 ðNufd;3 =Nufd;4 Þ Fig. 5. Comparison of friction factor f vs. Re number.
characteristics accurately. The deviation between very fine grids (f1) and other grids (f2) can be defined as [19]:
f f 1 100 E% ¼ 2 f1
ð6Þ
The structures of the grid include structured and unstructured. The number of nodes for axial length of microchannel is 200. There are locally refined grids. For the area of microchannel, the interval size is 0.02. In Table 3, the pressure, maximum temperature and averaged temperature of the heat sink bottom surface are presented for these three grids. According to Table 3, the deviations of the pressure drop, the averaged temperature and the maximum temperature using the fine grids with total of 2.39 106 cells from that of the very fine grids with total of 3.61 106 cells are 0.86%, 0.69% and 0.51%, respectively. The deviations between these two grids are less than 1%, so the result shows that the calculation is accurate. Due to the large amount of calculations, the long computing time, the limited computer memory and the accuracy of the calculation, a fine grid with 2.39 106 cells has been adopted as the optimum grid system for further simulations. Simulations have been carried out until the normalized residual values were less than 107 for all the flow variables but 108 only for the energy equation, during the iterative solution procedure. 4.2. Verification of smooth microchannel
Po Re Po ¼ 96ð1 1:3553ac þ 1:9467a2c 1:7012a3c þ 0:9564a4c 0:2537a5c Þ
ð10Þ
where, Po is Poiseuille number, which based on the aspect ratio ac of the rectangular microchannel. Re is the Reynolds number, which is related to the Dh. Nux,3 and Nux,4 stand for the Nusselt number at a distance x in the heated length for the three-sided and four-sided heating cases respectively. Nufd,3 and Nufd,4 refer to the Nusselt numbers for the three-sided and four-sided heating cases in fully developed laminar respectively. Figs. 5 and 6 indicate the comparison of the numerical and theoretical data of the friction factor f and Nusselt number Nux,3, respectively. It is seen that the numerical and theoretical results are in good agreement with each other with the difference being less than 4.5% for friction factor f and 7.8% for Nusselt number Nux,3, respectively. Therefore, the present numerical code can be able to ensure accuracy of the computation. 5. Results and discussion In order to obtain the optimal geometric parameters of microchannel heat sinks, the effects of the different inlet/outlet configurations (C, Z and I-type), different geometries header shapes (rectangular, symmetry trapezoidal and triangular) and microchannel shapes (the conventional rectangular microchannel, the microchannel with offset fan-shaped reentrant cavities and the microchannel with triangular reentrant cavities) have been analyzed by numerical simulations. 5.1. Effect of inlet/outlet locations on flow distribution
In this section, in order to verify the accuracy and reliability of the code, simulations of fluid flow and heat transfer are carried out to predict the results in terms of friction factor f and Nusselt number Nux,3, which are compared with the theoretical correlation given by Refs. [20,21] with three-side heating correction. Comparisons between the numerical data and the theoretical data for the heat sink A about the Reynolds number are shown in Figs. 5 and 6, respectively. The friction factor f and Nusselt number Nux,3 can be computed with the following equations:
f ¼
ð9Þ
ð7Þ
ð8Þ
Fig. 7 shows the average velocity distribution in microchannel heat sinks with different inlet/outlet locations when qv = 150 ml/ min. It is seen that different inlet/outlet configurations have great influence on the characteristic of flow distribution for the heat sink. When the fluid flow into the inlet of the heat sink, the direction of velocity is vertical to the bottom wall of the header (effect of flow impingement), which enhances the uniformity of fluid distribution in each microchannel. The flow velocity uniformity is comparatively better for I-type arrangement among all other configurations considered in this study; whereas, the flow velocity uniformity is worse for Z-type configuration. In C-type configuration, the fluid has to travel from one end to the dead end of the inlet header, which results in poor velocity distribution with intense flow separation. In the case of Z-type configuration, the
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Fig. 7. Average velocity in each channel of microchannel heat sinks with different inlet/outlet locations.
Table 4 Mal-distribution for three inlet/outlet parameters.
Fig. 8. Average velocity in each channel of microchannel heat sinks with different header shapes.
Table 5 Mal-distribution for three header shapes parameters.
Parameters
I-type
C-type
Z-type
Parameters
Rectangular
Symmetry trapezoidal
Triangular
VSTD/Vave
0.156
0.471
0.551
VSTD/Vave
0.156
0.203
0.214
velocity of the channel number 1 is relatively higher than nearby channels because of the Coanda effect [9]. The inlet locates near the side wall of the channel number 1, which makes the velocity of the channel number1 is relatively higher. The large flow velocity mal-distribution can be attributed to the interaction of the effect of flow impingement and entering/exiting of flow from opposite ends, which brings the intense flow separation. Due to geometric symmetry, the average velocity distribution in the I-type flow arrangement is found to be symmetrical with respect to the centerline of the heat sink located between channel number 15 and 16. The flow separation is relatively lesser which leads to better velocity distribution in I-type flow arrangement. For three inlet/outlet geometric configurations considered in the study, a mal-distribution factor, which is defined as VSTD/Vave [7], is employed to identify the flow velocity distribution in the multi-channel heat sink. The lower mal-distribution is, the better uniformity is. The mal-distribution factor is calculated and summarized in Table 4. Here, the subscripts STD and ave denote the standard deviation and average values, respectively. Table 4 indicates that I-type flow exhibits lower mal-distribution (VSTD/ Vave = 0.156) and higher value (VSTD/Vave = 0.551) for the Z-type configuration.
5.2. Effect of header shapes on flow distribution In the following parts of the present work, I-type has been selected to study the effect of header shapes on flow velocity distribution in that the flow distribution has an significant impact on the temperature distribution. Fig. 8 indicates the average velocity distribution in microchannel heat sinks with different header shapes when qv = 150 ml/min. The flow distribution is found to be symmetrical because both inlet and outlet are located at the center. It is observed from Fig. 8 that better velocity distribution is noticed for the rectangular header and poor velocity distribution for the triangular header. The variation of the velocity distribution for the symmetry trapezoidal header is similar to the rectangular header except for the discrepancy at the initial few channels (1–7) and the last few channels (24–30). The reason for this can be analyzed as follows: It is seen that the flow velocity
peaks are found at the inlet portion and at edges of the coldplate, whereas channels with the lowest velocity locate between inlet and edge region for rectangular and symmetry trapezoidal header heat sinks. For triangular header, the locations of the lowest velocity occur at edges of the coldplate because the fluid flow is very small. Due to the flow impingement configuration where major part of impinging flow follows the shortest path length toward outlet, the maximum flow velocity appears at the entrance region. However, part of the impinging flow is directed along the wall of the header in y-direction to the edge. Finally, this flow stream is guided by the wall of the header in x-direction through the channels, leading to the second flow velocity peak nearby the edge. The fluid is distributed through the channels in the flow direction and the flow decrease due to the branching of fluid. In the case of rectangular header, when the fluid is distributed through the channels, flow decelerates because of the branching of fluid, so the static pressure increase. Simultaneously, the wall friction effect of header also tends to reduce the static pressure in the flow direction, which results in relatively uniform velocity distribution. For the case of the triangular header, the velocity is relatively larger than others at the entrance because the cross section of header decreases (the minimum header volume) in the flow direction. The flow decreases because of the branching of fluid and the decreasing the velocity, which in turn enhances the static pressure. At the same time, the wall friction effect of header trends to decrease the static pressure which leads to relatively poor velocity distribution. In a word, the rectangular header heat sink obtains lower mal-distribution than others. For three header shapes geometric configurations considered in the study, the mal-distribution is calculated and summarized in Table 5. It indicates that rectangular header shape configuration assumes lower mal-distribution (VSTD/Vave = 0.156) and strong mal-distribution can be observed (VSTD/Vave = 0.214) in the triangular header shape configuration. In real applications, the temperature of the electronic chips cannot exceed certain temperature values, above which great damage might be caused to the devices. Particularly, local hot must be avoided because the performance of the electronic device strongly depends on the working temperature. The thermal performance of the heat sinks is usually characterized based on the average
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temperature, maximum temperature and the deviation of the heat sinks bottom surface temperature. The flow distribution, which can be characterized based on the flow velocity distribution in the multiple channels, has an significant impact on the heat sinks bottom surface temperature distribution. It is obvious that the more uniform the flow velocity distribution is, the less the deviation of the heat sinks bottom surface temperature is. 5.3. Effect of microchannel cross-section shapes on fluid flow and heat transfer In this section, I-type heat sink with rectangular header has been selected to study the effect of microchannel shapes on the flow and heat transfer. The following three types of microchannel shapes are studied: microchannel A (the conventional rectangular microchannel), microchannel B (the microchannel with offset fanshaped reentrant cavities) and microchannel C (the microchannel with triangular reentrant cavities). Fluid flow performance of the microchannel heat sink is characterized based on the pressure drop. The heat transfer performance of the heat sink is characterized based on the temperature of the bottom surface, including maximum temperature, average temperature and the deviation of the temperature DT = Tmax Tmin. Fig. 9 shows the comparison of pressure drop for different microchannel heat sinks with different flow rates. It is seen that the total pressure drop increases with increasing flow rate for the three different heat sinks, but the pressure drops of the heat sinks B and C are larger than that of the heat sink A. For the heat sink B or C, the pressure drop consists of not only the term along the microchannel, but also term in the reentrant cavities. In the case of heat sink C, when the water flows into the expansion cross-section region, the velocity decreases and the pressure drop increases, and when the water flows into the constriction crosssection region and impinging the constriction wall, the throttling effect at the constriction wall outlet forms and the laminar flow boundary layer is interrupted, which also leads to a high pressure drop. The flow mechanism can be attributed to the throttling effect at the constriction wall outlet and the second flow from the reentrant cavities. For the heat sink B, the pressure drop increases due to the jetting and throttling effect of the offset fan-shaped reentrant cavities. When the fluid flow increases from 100 ml/min to 200 ml/min, the increasing tendency of the pressure drop of the heat sinks A, B and C become fast, respectively. This means the pressure drop increases rapidly with the increasing of fluid flow when the fluid flow exceeds a certain value, which is bad for the heat sink. Figs. 10 and 11 indicate the average temperature and maximum temperature on the heat sinks bottom surface versus qv, respec-
Fig. 10. Comparison of average temperature on the heat sinks bottom surface.
Fig. 11. Comparison of maximum temperature on the heat sinks bottom surface.
Fig. 12. Comparison of deviation of the heat sinks bottom surface temperature.
Fig. 9. Comparison of pressure drop for different microchannel heat sinks.
tively. It is observed that the average temperature and maximum temperature decrease with increasing flow rate for all the three different heat sinks, but the average temperature and maximum temperature of the heat sink B and C are lower than that of the heat sink A, respectively. This means the reentrant cavities provide a significant enhancement on the temperature distribution. The reason can be analyzed as follows: (1) the structure of the reentrant cavities increases owning the heat transfer area and enhances the heat transfer effect; (2) for the heat sink C, the expansion–constriction cross-sections can induce better fluid mixing between the wall and the core flow regions, the jetting effect at the expansion
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Fig. 13. The temperature distribution of the three heat sinks bottom surface.
wall entrance and the throttling effect at the constriction wall outlet, the second flow from the triangular reentrant cavities and the additional flow disturbance near the wall of the reentrant cavities, which make the laminar flow boundary layer interrupted and redeveloped, so the heat transfer can be enhanced. For the heat sink B, the enhancement of the heat transfer is attributed to the jetting and throttling effects of the offset fan-shaped reentrant cavities and the additional flow disturbance near the wall of the reentrant cavities and the form drag of the reentrant cavities. The bottom temperature distribution of the heat sink is more uniform and the life of the microelectronic devices is expected to be prolonged. When the fluid flow increases from 100 ml/min to 200 ml/min, the decreasing tendencies of the average temperature and maximum temperature of the heat sink A, B and C become flat, respectively. This means the increasing of fluid flow cannot reduce the bottom surface temperature effectively when the fluid flow exceeds a certain value, which is bad for enhancement of the heat transfer. As shown in Fig. 12, with an increase of fluid flow rate, the deviation of the heat sinks bottom surface temperature (DT = Tmax Tmin) reduces and the deviation of the heat sink B and C are lower than that of the heat sink A, and the deviation of the heat sink C is lower than that of the heat sink B. The values of maximum temperature and average temperature are close to each other while the deviation keeps minimum. When the fluid flow increases from 100 ml/min to 200 ml/min, the decreasing tendencies of the deviation of temperature of the heat sink A, B and C become flat, respectively. As a result, when the fluid flow exceeds a certain value, the increasing of fluid flow cannot decrease the bottom surface temperature effectively, which is bad for enhancement of the heat transfer. Isaev et al. [22] investigated the unsteady-state heat transfer under conditions of laminar transverse flow past a circular cylinder. It has been found that the averaged value of total heat transfer from the cylinder increases by only 8.3% compared to the case of steady-state flow past the cylinder. Silva et al. [23] investigated the flow structure and heat transfer in channel with dimpled surfaces by numerical and experimental studies. The result shows there is a positive improvement (twofold on average) in Nusselt number when dimpled surfaces are compared to flat plates. Compared to the channel with dimpled surfaces, we find that the structure of the reentrant cavities increases owning the heat transfer area and enhances the heat transfer effect. Fig. 13 plots the temperature distribution of the three heat sinks bottom surface for qv = 150 ml/min. It is worth noting that, the maximum temperature appear near the outlet of microchannel region due to the heat conduction in the lateral parts of channels. The maximum temperature, average temperature and the deviation of the heat sink C with triangular reentrant cavities are lower than that of the heat sink B with offset fan-shaped reentrant
cavities and the heat sink A. The triangular reentrant cavities increase the heat transfer area and enhance the heat transfer effect. The pressure drop of the heat sink C is lower than that of the heat sink B. Therefore, the heat sink C has better heat transfer characteristic and is able to prolong the life of the microelectronic devices.
6. Conclusions Numerical investigation has been performed to study the effects of the inlet/outlet locations, header shapes and microchannel shapes on fluid flow and heat transfer, and obtain the optimal geometric parameters. The following conclusions might be drawn from the present study: (1) Effects of inlet/outlet configurations highlight that flow velocity uniformity is comparatively better for I-type and poor for Z-type. The flow distribution is found to be symmetrical for I-type. (2) It is seen from the header shapes analysis that the rectangular head shape provides the better flow velocity uniformity than the symmetry trapezoidal and triangular headers. The fluid flow mechanism can be attributed to the interaction of the branching of fluid and the friction offered by the walls of the header. (3) Effects of microchannel shapes emphasize that the microchannel with offset fan-shaped reentrant cavities and with triangular reentrant cavities of the heat sinks enhance the heat transfer than the conventional rectangular microchannel of the heat sink. The heat transfer mechanism can be attributed to the jetting and throttling effect, the additional flow disturbance near the wall of the reentrant cavities and the form drag of the reentrant cavities. (4) The maximum temperature appears near the outlet of microchannel region due to the heat conduction in the lateral parts of channels. The heat sink C has better heat transfer characteristic for qv = 150 ml/min and is able to prolong the life of the microelectronic devices. Conflict of interest None declared. Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 51176002), the National Basic Research Program
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