a numerica1 study of fluid flow and heat transfer in different ......four different microchannel...

Journal of Mechanical Science and Technology 26 (4) (2012) 1257~1263

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-012-0209-x

A numerica1 study of fluid flow and heat transfer in different microchannel

heat sinks for electronic chip cooling† Shanglong Xu1,*, Guangxin Hu1, Jie Qin1 and Yue Yang2

1Department of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu, China 2School of Mechanical & Vehicle Engineering, Beijing Institute of Technology, Beijing, China

(Manuscript Received March 20, 2011; Revised July 23, 2011; Accepted December 14, 2011)

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Abstract Four different microchannel heat sinks are designed to study the effects of structures in microchannel heat sinks for electronic chips

cooling. Based on the theoretic analysis and numerical computation of flow and heat exchange characteristics, the electronic chip’s tem-perature and flow rate distributions are obtained. The correspondence between flow pressure drop and chip’s temperature in the four microchannel heat sinks is also studied and analyzed. Numerically analyzed results indicate that the topological structure in microchannel heat sink has a significant influence on electronic chips cooling. This study shows various thermal properties in the four microchannel heat sinks.

Keywords: Microchannel; Heat sink; Heat dissipation; Heat-flow coupling; Structure ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

The research of the microchannel heat sink started in the early 1980s, and it was first introduced by Tuckerman and Pease [1] in 1981, who discussed the heat transfer characteris-tics. In the study, the fully developed flow was considered and the capacity of dissipating heat flux could be promoted to 103

W/cm2. The cooling water could dissipate heat flux about 790 W/cm2 by forcing a coolant through the microchannel etched onto a silicon wafer. With the recent development of very large-scale integration technology and Micro-Electro Me-chanical Systems, the adoption of the microchannel heat sink has become an important cooling approach because it has the advantages of high heat dissipation, low cost, small space, etc. By matching with the semi-conductor manufacturing process, the microchannel heat sink has become one of the focal points of current micro cooling technology. Qu and Mudawar [2, 3] presented thermal performance of the microchannel heat sink. The temperature at the heated base surface of the heat sink reduced with the increase in the thermal conductivity of the solid substrate, especially near the channel outlet. The effects of geometrical and flow parameters affecting the absolute thermal resistance of microchannel heat sink were analyzed by Saidi et al. [4]. The accuracy of analytical method in predict-

ing heat transfer and fluid flow regimes in micro channel is checked in comparison with numerical method, it was investi-gated that there will be a 20 percent difference in the evalua-tion of the absolute thermal resistance in these two methods if the effects of entrance length could be taken into account in the numerical method and ignored in the analytical method. Wang and Ding [5] presented the effects of flow rate and heat flux levels on heat transfer characteristics. A uniform tempera-ture distribution is obtained through the heating area to inves-tigate the heat transfer performance for a novel microchannel heat sink.

Recently, structure correlations research publications on the microchannel heat sink have arised. Cheng [6] designed a fractal tree-like microchannel net for cooling of electronic chips. The design was inspired by the fractal pattern of mam-malian circulatory and respiratory systems. The new fractal branching channel net has a stronger heat transfer capability and required a lower pumping power compared with the tradi-tional parallel net. Senn and Poulikakos [7] investigated the laminar convective heat transfer and pressure drop characteris-tics in tree-like microchannel nets. The intrinsic advantage of tree-like nets with respect to both heat transfer and pressure drop is demonstrated, in comparison with the corresponding characteristics in traditional serpentine flow patterns by solv-ing the Navier-Stokes and energy equation for an incom-pressible fluid with constant properties in three dimensions. A novel comby fractal microchannel network was designed by Dong et al. [8], whth heat removal capacity over 5 times as

*Corresponding author. Tel.: + 86 02861830242, Fax.: + 86 02861830217 E-mail address: [email protected]

† Recommended by Associate Editor Man-Yeong Ha © KSME & Springer 2012

1258 S. Xu et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1257~1263

that of traditional parallel microchannels. The heat transfer and pressure drop correlations of microchannel heat exchang-ers (MCHE) with S-shaped and zigzag fins was investigated by Ngo et al. [9] using the three-dimensional computational fluid dynamics FLUENT code. Results showed that the MCHE with s-shaped fins provided 6-7 times lower pressure drop while maintaining heat-transfer performance that was almost equivalent to that of a conventional MCHE with zigzag fins. Dang et al. [10] conducted a number of studies to seek appropriate designs for microchannel heat sinks. A straight channel and two cross-linked channel models were simulated by using the three-dimensional mixture model from the com-putational fluid dynamics software FLUENT. The cross-links were located at 1/3 and 2/3 of the channel length, their width varied by one and two times the channel width. All test mod-els had 45 parallel rectangular channels, with a hydraulic di-ameter of 1.59 mm. The results showed that the trend of flow distribution agrees with experimental results. A new design, with cross-links incorporated, was proposed and the results showed a significant improvement, up to 55%, on flow distri-bution, compared to the standard straight channel configura-tion without a penalty in the pressure drop. The maximum heat transfer and the optimum geometry for a given pressure loss have been calculated by Asgari and Saidi [11] for forced convective heat transfer in microchannels of various cross-section having finite volume for laminar flow conditions. And the model with a function of Prandtl number and geometrical parameters of the cross-section is performed.

The previous studies investigate the heat transfer and flow characteristics of the microchannel heat sink for electronic chips cooling. The research objectives are fastened on chan-nel’s geometrical parameters or one structure’s flow and heat exchange characteristics. But the effect of microchannel net-works on the heat dissipation is not presented. This study de-signs four microchannel heat sinks in order to clarify the in-fluence of the heat dissipation and fluid flow by the micro-channel networks. The electronic chip’s temperature, heat flux and flow rate distributions are studied to predict the heat trans-fer properties of four microchannel heat sinks. Furthermore, the percentages of the electronic chip’s temperature distribu-tion on four microchannel heat sinks are analyzed. Then the relationship between electronic chip’s average temperature and coolant’s average flow velocity and correspondence be-tween pressure drop in the microchannels and chip’s tempera-ture is obtained, which is useful to develop a heat dissipation system with specific certain heat performence for electronic chips cooling.

2. Microchannel heat sinks design

The microchannel heat sink comprising of an adiabatic cover plate and a silicon substrate with many microchannels fabricated on the other side. In order to investigate the influ-ence of microchannel structure on heat dissipation, four mi-crochannel heat sinks with different structures are designed

here and are shown in Fig. 1. The coolant flows though these microchannels and takes away the heat generated by elec-tronic chips.

As show in the Fig. 1, TPA is the ordinary parallel structure heat sink; TPB is the reticular structure heat sink with vertical and connective microchannel; TPC is the toroidal heat sink includes rounding microchannel; TPD is the tree-like heat sink enlightened from the fractal pattern of foliage’s venation with the 45 degree’s angle between offshoot and trunk. In this study, to make sure the comparability of these four micro-channel heat sinks, the same conditions such as the same di-mensions of the substrate, the same cross-section, the same aspect ratio and the same heat exchange area of microchannels are considered. The dimensions of four microchannel’s sub-strates fixed with12mm×12mm×1mm, the rectangular cross-section with aspect ratio of 1:1 is used to all the microchannels which are fabricated on substrates. In order to make the four microchannels nearly have the same heat exchange area, the parameters of various microchannels are designed and was shown in Table 1.

3. Computational models

3.1 Governing equations

In order to simplify the computational model, some as-sumptions are considered as:

Table 1. Parameters of microchannels in four heat sinks.

Types of structures

Cross-sectionform

Height (mm)

Width (mm)

Aspect ratio

Heat exchange area (mm2)

TPA Rectangle 0.4 0.4 1:1 147.8

TPB Rectangle 0.4 0.4 1:1 149.6

TPC Rectangle 0.4 0.4 1:1 148.6

TPD Rectangle 0.4 0.4 1:1 148.0

(a) Parallel structure (b) Reticular structure

(c) Toroidal structure (d) Tree-like structure structure Fig. 1. Schematic drawing of four structures in heat sinks.

S. Xu et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1257~1263 1259

(1) Constant solid and fluid properties; (2) Steady and laminar flow; (3) Incompressible fluid; (4) Gravitational ambient and buoyancy force is neglected; (5) Radiative heat transfer is neglected. The governing equations used to describe the fluid flow and

heat transfer process in the unit cells are established. Then, the transport equations can be rewritten as follows [12]:

3.1.1 Continuity equation

From the law of conservation of mass law comes the conti-nuity equation:

( ) 0u v wdiv Ux y z∂ ∂ ∂

= + + =∂ ∂ ∂

(1)

where ,u v and w = components of the velocity vector U in the x, y and z directions, respectively, m/s; ρ=density, kg/m3.

3.1.2 Momentum equation

For the steady, incompressible and fully developed flows, the momentum equations are given as follows:

1div( ) div( grad )u puU u

t xν

ρ∂ ∂

+ = −∂ ∂

(2a)

1div( ) div( grad )v pvU vt y

νρ

∂ ∂+ = −

∂ ∂ (2b)

1div( ) div( grad )w pwU wt z

νρ

∂ ∂+ = −

∂ ∂ (2c)

where ν = kinematic viscosity, kg/ms; ρ = density, kg/m3; p = pressure, N/m2.

3.1.3 Energy equation

The energy equation for the incompressible case takes the form of a thermal transport equation for the static temperature:

div( ) div( grad ) T

p

T SUT Tt c

λρ ρ

∂+ = +

∂ (3)

where T = temperature, °C; λ = Coolant’s thermal conductiv-ity, W/m°C; pc = specific heat, J/kg°C; TS = volumetric heat source, J.

Eqs. (1)-(3) are the governing equations to solve the heat-flow coupling fields for mircochannels in electronic chips cooling.

3.2 Boundary conditions and FEM model

The solid region of the heat sink is made of silicon with thermal conductivity of ks = 82 W/m°C. Uniform heat flux of q is applied to the bottom surface of the heat sink. It is 1000 W/cm2. The inlet flow speed of microchannel is fixed with vl = 1m/s. The inlet temperature is 20°C. The outlet pressure is

assumed as 0 Pa. The coolant used is water, where ρl = 1000 kg/m3, μl = 8.55×10-4 kg/ms, Cpl = 4179 J/kg℃ and kl = 0.613 W/m℃. The Renault number, Re = ρlvlDl /μl, is approximately 468. The analysis type was steady and laminar flow (Dl is hydrodynamic diameter).

Since the microchannel structures are complex, the CAD commercial software PRO/E is used to build heat sinks’ geo-metrical models, and commercial software ANSYS is used throughout this study to solve these heat-flow coupling proc-ess. Flotran CFD model and direct-coupling method are used to simulate the three-dimension flow and temperature fields. The TDMA and PGMR solver are adopted to solve the veloc-ity and temperature. The 3-D fluid-thermal element is used. It is a eight-node element. The model was meshed by an adap-tive gridding meshing method (Fig. 2). The flow channel space was broken into a large number of elements. Each ele-ment comprised of a set of nodes. Then, the problems are solved with the minimum reduction in normalized residuals for each variable at less than 1.0 ×10-3.

4. Results and discussion

Fig. 3 shows the temperature distributions of the electronic chip respectively cooled by four heat sinks. It can be observed that microchannel heat sinks with different structures have the different heat dissipation although they have the same heat exchange area. The maximal temperature of the electronic chip cooled by microchannel heat sink with parallel structure is near 80°C, while the maximal temperature of the electronic chip cooled by microchannel heat sink with reticular and tor-oidal structure is above 90°C and 100°C，respectively, but the maximal temperature of the electronic chip cooled by heat sink with tree-like structure microchannel is below 70°C. Fur-thermore, in order to investigate the electronic chip’s tempera-ture distribution state, nodes’ temperature intervals distribu-tion of electronic chip separately cooled by heat sinks is statis-tically analyzed and is given in Table 2.

It can be observed from Table 2 that the proportionment of temperature between 20°C and 60°C on electronic chip separately cooled by TPA, TPB, TPC and TPD is 81.45%, 61.78%, 61.02% and 94.01%, respectively. In addition, the

Fig. 2. The mesh model of a microchannel network.


proportionment of temperature above 70°C is different, which respectively is 4.57%, 23.79%, 25.04% and 0.

The heat flux distribution in the four microchannel heat sinks is also obtained. While heat flux is the independent variable in the study, the same initial heat flux through four chips with different microchannels can lead to different elevated temperatures within the microchannels and differ-ent heat flux distribution on the chips. The maximal heat flux of the electronic chip cooled by microchannel heat sink with parallel, reticular, toroidal and tree-like structure is 420 W/cm2, 392 W/cm2, 435 W/cm2 and 211 W/cm2, respec-tively. The corresponding fluid temperature difference be-tween inlet and outlet of the four microchannel networks is 23°C, 25°C, 22°C, 29°C, respectively. The radial heat flux distibution on microchannel outlet section is shown in the Fig. 4. D is the diameter of the channel. x/D is the location along radial direction from one side to other side of channel wall. The minimum heat flux of the fluid is at the center of channel. The heat flux of the fluid linealy increases with the location varies from the channel center to channel wall, which is more than 500%.

Thus it can be seen that the influence of the electronic

(a) Parallel structure

(b) Reticular structure

(c) Toroidal structure

(d) Tree-like structure

Fig. 3. Temperature distribution of electronic chip respectively cooled by four different structures (°C).

Table 2. Nodes’ Temperature intervals distribution of electronic chip separately cooled by four heat sinks.

Temperature intervals TPA TPB TPC TPD

20°C-30°C 4.95% 5.91% 11.99% 5.72%

20°C-40°C 36.06% 27.66% 35.01% 24.13%

20°C-50°C 58.11% 49.04% 48.99% 59.67%

20°C-60°C 81.45% 61.78% 61.02% 94.01%

20°C-70°C 95.43% 76.21% 74.96% 100.00%

20°C-80°C 100.00% 93.34% 85.46% -

20°C-90°C - 99.76% 94.01% -

20°C-100°C - 100.00% 99.09% -

20°C-110°C - - 100.00% -

Fig. 4. Radial heat flux distibution on microchannel outlet section. D is the diameter of the channel. x/D is the location along radial direction from one side to other side of channel wall.


chip’s cooling effects is different by using heat sink with dif-ferent microchannels which has the particular advantage in electronic cooling. The electronic chip cooled by tree-like mirochannel heat sink has uniform temperature distribution. The chip’s temperature is below 70°C. So the tree-like miro-channnel heat sink is preponderant for the high heat flux elec-tronic chips cooling. But the parallel mirochannnel heat sink has the advantage in the MEMS process technology when the electronic chip’s heat flux is not reached to 1000 W/cm2. The advantage of toroidal heat sink used in electronic chip cooling in the case of heat flux is fasten on the center of chip, on ac-count of the temperature in nearly 1/4 of the center of chip is below 40°C.

The distributions of flow velocity in microchannels are given in Fig. 5 in order to investigate the effects of flow veloc-ity on temperature. It shows that the maximum flow speed occurs in TPA, but the lowest temperature of electronic chip is cooled by TPD. Compare with the electronic chip’s tempera-ture distribution, respectively, it can be found that chip’s tem-perature is low where close-by microchannel has a high flow speed. In addition, the flow distance in every microchannel is divided respectively into five equal parts, and Fig. 6 shows the average temperature of each part for coolant flows in four microchannels. The fluid temperature is raised gradually along the direction of fluid flow. The fluid temperature of the part near the channel inlet in toroidal microchannel is the mini-mum. It gradually exceeds the fluid temperature in tree-like and parallel microchannel. This is consistent with the tempera-ture of chip cooled by toroidal heat sink is quite low near the channel inlet.

Furthermore, Table 3 gives the average flow velocity, chip’s temperature and flow’s temperature by calculating the nodes’ temperature of chip and nodes’ flow speed of fluid. It

can be observed that the average temperature of the total heat sink is above the average temperature of flow and below the average temperature of chip. The average temperature of chip cooled by tree-like heat sink is the minimum while the aver-age temperature of chip cooled by reticular heat sink is the maximum. Fig. 7 shows the effect of flow velocity on average temperature of chip. The temperature of the chip cooled by four heat sinks, respectively, is different. Besides structure, the average flow velocity in the microchannel is also the impor-tant factor to influence the heat sink’s heat dissipation. The chip’s average temperature is descending with the average flow rate raising.

(a) Parallel structure (b) Reticular structure

(c) Toroidal structure (d) Tree-like structure Fig. 5. Distributions of flow velocity in four microchannels (mm/s).

Table 3. Average temperature and flow velocity.

Microchannel Aveg. velocity（mm/s）

Aveg. temp. (chip) (°C)

Aveg. temp. (flow) (°C)

Aveg. temp.(total) (°C)

TPA 289.8 47.2 33.8 43.8

TPB 246.3 53.7 42.8 50.1

TPC 251.9 51.4 37.5 47.1

TPD 327.9 42.8 28.5 37.8

Fig. 6. Average temperature of each part along the direction of fluid flow for coolant flows in four microchannels.

Fig. 7. The correlations of average temperature of electronic chip and average flow velocity in the microchannel.


The correspondence between flow pressure drop in the four microchannels and chip temprature is also obtained from the results of computational results (Fig. 8). In general, increasing heat trasport leads to higher flow pressure drop. The pressure drop of toroidal microchannel structure is much higher than other three, which is approximately 220% of that of tree-like microchannel and over 10 times as that of parallel and reticu-lar microchannels. Corresponding to parallel structure, the temperature of chip cooled by tree-like heat sink is 14°C lower while the required pressure is 90kPa higher. It is also 10°C lower than the reticular structure while higher flow pres-sure, 97 kPa, is needed. Therefore, the topological structure of microchanels is a significant influence on the heat transfer and fluid flow performance for a microchannel heat sink.

5 Conclusions

In this study, four heat sinks with various microchannel structures are designed and heat-flow coupling is investigated in electronic chip cooling to search for the heat and flow pe-formence of microchannel structure. It is testified that the microchannel’s structure has a significant influence on elec-tronic chips cooling via the theoretic analysis and numerical computation of flow and heat exchange characteristics. The heat sink with tree-like microchannel can take away the most heat at the same inlet flow rate. The temperature of electronic chip cooled by it is the minimum and uniform. The minimum heat flux of the fluid is at the center of channel. The heat flux of the fluid linealy increases with the location varies from the channel center to channel wall, which is more than 500%. Comparison with other structures, the temperature of chip cooled by tree-like heat sink is lower. But it will lead to higher flow pressure drop than that of paralell and reticular structure, 90kPa and 97kPa, expectively.

Another factor of enhancing heat dissipation is to increase the average flow speed of microchannel heat sink in the condi-tion of the same pump power. Hence, we may refer to these conclusions in designing the structure of microchannel heat sink by using the objective function of the uniform and maxi-

mum flow rate or minimum flow pressure drop.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.50906009) and Research Fund for the Doctoral Program of Higher Education of China (New Teachers Fund, Project No. 200806141062).

References

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[11] T. L. Ngo, Y. Y. Kato, K. S. Nikitin and T. K. Ishizuka, Heat transfer and pressure drop correlations of microchannel heat exchangers with S-shaped and zigzag fins for carbon dioxide cycles, Experimental Thermal and Fluid Science, 32 (2007) 560-570.

[12] M. Dang, I. Hassan and S. I. Kim, Numerically investigat-ing the effects of cross links in scaled microchannel heat

Fig. 8. Correspondence between pressure drop in the microchannelsand chip’s temperature.


sinks, The 13th International Workshop on Thermal Investi-gation of ICs and Systems, Budapest (2007) 54-59.

[13] O. Asgari and M. H. Saidi, Asymptotic and exact analysis for constructal optimization of microchannel heat sink, in The ASME Micro/Nanoscale Heat Transfer International Conference, Taiwan (2008) 791-799.

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Shanglong Xu is an associate professor and PhD supervisor in University of Electronic Science and Technology of China. He received his Ph.D degree from Xi’an Jiaotong University, China, in 2007. His research interests include electronic cooling system and heat ex-changers.

a numerica1 study of fluid flow and heat transfer in different ......four different microchannel...

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