Computational fluid dynamics for thermal ...

International Journal of Numerical Methods for Heat & Fluid Flow Computational fluid dynamics for thermal performance of a water-cooled minichannel heat sink with different chip arrangements Gongnan Xie Shian Li Bengt Sunden Weihong Zhang

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Article information: To cite this document: Gongnan Xie Shian Li Bengt Sunden Weihong Zhang , (2014),"Computational fluid dynamics for thermal performance of a water-cooled minichannel heat sink with different chip arrangements", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 Iss 4 pp. 797 - 810 Permanent link to this document: http://dx.doi.org/10.1108/HFF-01-2013-0013 Downloaded on: 27 February 2016, At: 22:47 (PT) References: this document contains references to 24 other documents. To copy this document: [email protected] The fulltext of this document has been downloaded 136 times since 2014*

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Computational fluid dynamics for thermal performance of a water-cooled minichannel heat sink with different chip arrangements Gongnan Xie and Shian Li

CFD for thermal performance

797 Received 14 January 2013 Revised 24 February 2013 Accepted 4 March 2013

Engineering Simulation and Aerospace Computing (ESAC), Northwestern Polytechnical University, Xi’an, Shaanxi, China

Bengt Sunden Division of Heat Transfer, Department of Energy Sciences, Lund University, Lund, Sweden, and

Weihong Zhang Engineering Simulation and Aerospace Computing (ESAC), Northwestern Polytechnical University, Xi’an, Shaanxi, China Abstract Purpose – With the development of electronic devices, including the desires of integration, miniaturization, high performance and the output power, cooling requirement of chips have been increased gradually. Water-cooled minichannel is an effective cooling technology for cooling of heat sinks. The minichannel flow geometry offers large surface area for heat transfer and a high convective heat transfer coefficient with only a moderate pressure loss. The purpose of this paper is to analyze a minichannel heat sink having the bottom size of 35 mm  35 mm numerically. Two kinds of chip arrangement are investigated: diagonal arrangement and parallel arrangement. Design/methodology/approach – Computational fluid dynamics (CFD) technique is used to investigate the flow and thermal fields in forced convection in a three-dimensional minichannels heat sink with different chip arrangements. The standard k-e turbulence model is applied for the turbulence simulations on the minichannel heat sink. Findings – The results show that the bottom surface of the heat sink with various chip arrangements will have different temperature distribution and thermal resistance. A suitable chip arrangement will achieve a good cooling performance for electronic devices. Research limitations/implications – The fluid is incompressible and the thermophysical properties are constant. Practical implications – New and additional data will be helpful as guidelines in the design of heat sinks to achieve a good thermal performance and a long lifetime in operation. Originality/value – In real engineering situations, chips are always placed in various manners according to design conditions and constraints. In this case the assumption of uniform heat flux is acceptable for the surfaces of the chips rather than for the entire bottom surface of the heat sink. Keywords Minichannel, Chip Arrangement, Heat Sink, Thermal Performance Paper type Research paper

This work was supported by NPU Foundation for Fundamental Research (NPU-FFRJC20130115) and NPU Foundation for Ao-xiang Star Program, and by Specialized Research Fund for the Doctoral Program of Higher Education of China (20116102120021).

International Journal of Numerical Methods for Heat & Fluid Flow Vol. 24 No. 4, 2014 pp. 797-810 r Emerald Group Publishing Limited 0961-5539 DOI 10.1108/HFF-01-2013-0013

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Nomenclature Dh H k L Pr Q R Re T u W

hydraulic diameter (m) height (m) turbulent kinetic energy Length(m) Prandtl number power generated by the chip (W) thermal resistance (K/W) Reynolds number, Re ¼ rumDh/m Temperature (K) flow velocity (m/s) width (m)

Greek symbols e

Dp l m r

pressure drop (Pa) thermal conductivity (W/m.K) dynamic viscosity (Pa.s) fluid density (kg/m3)

Subscripts c s t tc w in max

channel substrate turbulent top cover wall inlet maximum

rate of energy dissipation

1. Introduction With the shrinking volume of electronic components and continuous improvement in performance and speed, energy consumption and calorific value of the chip is also growing. The conventional cooling methods are using fans or metal fins to meet the cooling demands of electronic devices. Too high temperature would make the components exposed to excessive thermal stress which would lead to structural damage and failure. In this case, the conventional cooling methods cannot meet this requirement. Accordingly minichannel and microchannel cooling technologies have started to appear. Tuckerman and Pease (1981) first introduced a kind of water-cooled heat sink made of silicon, used in very-large-scale integrated circuits. The microchannels were fabricated with a 50 mm width and a 300 mm height so that heat fluxes as high as 790 W/cm2 could be removed with the maximum temperature difference between substrate and inlet water of 71 K and a pressure drop across the microchannels of 31 Pa. The thermal performance is much better than for conventional thermal dissipation technologies. After that, many researchers focussed on such new kind of chip cooling technology. Kandlikar and Grande (2004) did a series studies and reviews on the minichannels and microchannels liquid cooling technology. Xie et al. (2007, 2009) performed numerical studies on the laminar/turbulent flow and heat transfer characteristics of a water-cooled straight microchannel heat sink. The results showed that heat flux could be removed from 256 W/cm2 to 350 W/cm2 for a nearly optimized microchannel, and the pumping power increased from 0.205 W to 5.365 W as well. Farnam et al. (2009) analyzed the thermal performance of a microchannel heat sink to cool a chip with output power of 100 W. An experimental system was fabricated by Kumaraguruparan and Sornakumar (2010) to conduct tests on the heat transfer coefficient, pressure drop, friction factor and thermal resistance of a microchannel heat sink. Steinke et al. (2006) also developed an experimental facility for investigation of single-phase liquid flow in microchannels. The thermohydraulic performance of microchannels was studied as a function of channel geometry, heat flux and liquid flow rate. Qu and Mudawar (2002) analyzed heat transfer characteristics in a rectangular microchannel heat sink using water as the cooling fluid. Chen (2007) presented an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. The velocity profiles,

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temperature distributions of the solid and fluid phases, and the overall Nusselt number were obtained and analyzed. Cho et al. (2010) simulated the flow distribution in microchannel heat sinks with non-uniform heat flux conditions. In order to investigate the effect of non-uniform heat flux, three different conditions over the channel area were evaluated and compared. The computational fluid dynamics (CFD) technique has been widely used in the electronic industry. The finite volume method (FVM) is a technique used for solving a set of partial differential equations in a domain, using control volume-based discretization. Kandasamy and Subramanyam (2005) used CFD simulation tools to study the thermal performance of electronic packages. Their study showed that applying CFD techniques can provide accurate results on estimating thermal characterization of an electronic package. A finite element method (FEM) was applied to evaluate the performance of microchannel heat exchangers (Quadir et al., 2000). Over the past few decades, many studies have focussed on the behavior of fluid flow and heat transfer in various types of microchannel heat sinks. Levac et al. (2011) numerically analyzed the thermal performance of a double-layer microchannel under laminar flow condition, and compared the thermal performance for parallel-flow and counter-flow layouts at different Reynolds numbers. Manglik et al. (2005) considered steady forced convection in wavy-plate fin channels at periodically developed low Reynolds number. The numerical results showed that counter-rotating vortices occurring in the wall-trough regions of the flow cross-section enhanced fluid mixing and gave improved heat transfer performance, but for lower wavy-fin density and Reynolds number, viscous forces may dominate and suppress or diminish the extent of swirl. Lan et al. (2012) studied the flow characteristics and heat transfer performance in a rectangular microchannel (AR ¼ 4) with dimple/protrusions. The results showed that these microchannels have the potential to provide heat transfer enhancement with low-pressure penalty. Recently, Xie et al. (2013a, b, c, d) have performed several computational studies about laminar heat transfer and pressure loss of single-layer and double-layer straight or wavy microchannels. The shape and size of microchannels cooling heat sink affected the heat transfer performance. Khan et al. (2009) applied an entropy generation minimization procedure to optimize the overall performance of microchannel heat sinks. Shao et al. used a thermal resistance network model (2009) and an adaptive genetic algorithm (2011) to optimize a microchannel cooling heat sink. In these studies, the thermal resistance and the pressure drop were the goal function. Although there exist many studies on minichannels heat transfer characteristics, only one-branch minichannel channels have been investigated. Symmetric or periodic geometries were studied, and a simplified constant heat flux condition was assumed for the overall bottom surface where the heating chips were bonded at some covering regions. Only a few researchers have focussed on partially heated microchannel heat sinks. Lelea (2009) analyzed numerically the influence of the heating position (i.e. upstream heating, central heating and downstream heating) on the hydrodynamic and thermal parameters of the micro-heat sink. In real engineering situations, chips are always placed in various manners according to design conditions and constraints. In this case the assumption of a uniform heat flux is acceptable for the surfaces of the chips rather than for the entire bottom surface of the heat sink. Therefore, it is necessary to perform overall simulations of the entire minichannel with fluid and solid portions, and to observe the effects of chip placement on liquid cooling performance.

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2. Description of physical models A schematic diagram of the geometric models (A, B, C) and the chip arrangements (a, b, c, d) considered in this study are provided in Figures 1 and 2 There are 20 minichannels in this heat sink with the bottom surface (heated by two chips) size of 35 mm  35 mm, and two different kinds of chip arrangements are designed. The size of a chip is 15 mm  15 mm. A simple notation is introduced as: Case I-A þ a, Case II-A þ b, Case III-B þ c, Case IV-B þ d, Case V-C þ c, and Case VI-C þ d. For models B and C, the length of the inlet and outlet ducts is 5 mm and the inner diameter is 2 mm. The geometry parameters of a single minichannel as shown in Figure 3 are given as follows: the wall thickness Ww ¼ 0.75 mm; the channel length Lc ¼ 35 mm (Lc ¼ 30 mm for models B and C); the channel width Wc ¼ 1 mm; the channel height Hc ¼ 4 mm; the cover plate thickness Htc ¼ 0.5 mm; the substrate thickness Hs ¼ 0.5 mm. (a)

(b)

(c)

Figure 1. The heat sink configuration

(a)

(b)

Coolant Chip1

Chip1

Chip 2

(c)

(d)

Chip1

Chip1

Chip 2

Figure 2. The different chip arrangements

Chip 2

x z

Chip 2

CFD for thermal performance

Lc

Htc

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Hc

Figure 3. Geometry parameters of a minichannel

Hs Ww /2 Wc

3. Computational method and procedure Nowadays, the integrated circuit chips are commonly made of silicon, and the thermal expansion coefficients of various materials are different, resulting in thermal stress at different temperature. In order to reduce the thermal stress between the heat sink and chip, silicon with a thermal conductivity of 148 W/m K, is chosen as the material of the heat sink. It is helpful for improving the reliability of chips. In addition, water is used as the coolant to remove the heat load from the chips because it has high heat-transfer capability. 3.1 Selection of turbulence model In general, there are many turbulence models available nowadays, e.g., the large eddy simulation model, Reynolds Stress Models and the direct numerical simulation (DNS). However, these models require more computational time and a lot of computer resources. Naphon et al. (2009) used the standard k–e turbulence model to predict heat transfer and flow in a heat sink. They found a reasonable agreement between the numerical results and experimental data. In the present study, therefore, the standard k–e turbulence model is employed to simulate the problem. 3.2 Governing equations The governing equations of fluid flow and heat transfer for different variables can be expressed as follows (see, e.g. Naphon et al., 2009). Continuity equation: qrui ¼0 qxi

ð1Þ

Momentum equation: qui qp q ¼ þ ruj qxj qxi qxj



m1 m þ t Pr1 Prt

  qui quj þ qxj qxi

ð2Þ

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Energy equation for fluid: ruj

802

qT q ¼ qxj qxj



  m1 m qT þ t Pr1 Prt qxj

Energy equation for solid: q qT ðl Þ ¼ 0 qxi qxi

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ð3Þ

ð4Þ

Turbulent kinetic energy k equation:     qk q mt qk qmi qmj qmi þ mt ¼ þ e ruj qxj qxi qxj qxj qxj sk qxj

ð5Þ

Rate of energy dissipation e equation: ruj

    qe q mt qe e qmi qmj qui e2 þ C1 mt ¼ þ  C2 r k qxj qxj sk qxj k qxj qxi qxj

ð6Þ

Cm ¼ 0.09, C1 ¼ 1.47, C2 ¼ 1.92, sk ¼ 1.00, se ¼ 1.30 Reynolds number is defined as: Re ¼

rum Dh m

ð7Þ

where r is the fluid density, um is the average velocity of fluid in the channel, which is equal to the inlet velocity, Dh is the hydraulic diameter and m is the dynamic viscosity. To evaluate and compare the overall thermal performance of the heat sink, a thermal resistance is defined as: R¼

Tmax  Tin Q

ð8Þ

where Tmax is the maximum temperature on the chip, Tin is the inlet fluid temperature and the value is 293.15 K. Q is the power generated by the chip and its value is 150 W. The commercial software Fluent is applied to solve the governing equations with appropriate boundary conditions. The coupling of pressure and velocity fields is handled by the Semi-Implicit Method for Pressure Linked Equations algorithm. 3.3 Boundary conditions Due to the relatively high thermal conductivity of silicon, a uniform heat flux is applied on the bottom surfaces of the heat-generating chips. No-slip boundary conditions are applied to all channel walls. In this study, because of the complicated computational model due to the entire heat sink, the standard wall functions of the standard k-e model are applied on the walls for the near wall treatment. Turbulence intensity levels of

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5 percent and Dh are used to compute the turbulence at the inlet. Due to the conjugation of fluid and solid heat transfer, the boundary conditions for the interfaces (wall surfaces facing the fluid) are automatically coupled. The initial temperature of coolant was assumed as 293.15 K. Pressure outlet is selected at the outlet. The enhanced wall functions of the standard k–e model are applied on the walls for the near wall treatment, and most y þ values lie between 1 and 5. The computations are considered to have converged when the residuals for all governing equations were o105.

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3.4 Grid independence In general, a hexahedral mesh provides a more accurate solution than a tetrahedral mesh for the same conditions. Three different mesh number systems have been tested for the same condition, namely 1.5 M, 2.3 M and 3.0 M for Case I. From the tested results as listed in Table I, it was found that the differences in pressure loss and thermal resistance for Mesh II were smaller than those of Mesh I. For the pressure loss, the deviations of Mesh I and Mesh II are 3.261 and 1.865 percent, respectively. The mesh density has influence on the thermal characteristics, e.g., the maximum deviation of the thermal resistance is 0.929 percent for Mesh II, while it is 2.476 percent for Mesh I. Thus, to keep a balance between computational economy and prediction accuracy, the Mesh II system is chosen. 4. Results and discussion The two chips have different maximum temperatures and temperature distributions due to the different chip locations on the heat sink bottom surface in the same geometrical model. Figure 4 shows the streamtraces at the middle plane of six cases. Case I and Case II have the same flow trend because the flow is laminar. Case III and Case IV have a complex flow condition inside the heat sink. The coolant close to the up-side turns right, flow through the chip 1, and is then divided into two parts. One part turns left toward the outlet, the other turns to the right, then flows through the chip 2 and finally merges together with the inlet coolant. Case V and Case VI have a complex and symmetric flow. After flowing into the heat sink, the coolant is also divided into two parts and then flows to the outlet of the heat sink due to the special locations of the inlet and outlet. The flow nearby becomes very complex and violent. Figure 5 shows the temperature contours on the bottom surfaces of the six cases. It can be seen that the high temperature areas are on the chips because the energy is generated by the chips. Further away from the chip, lower temperatures will appear. For Case I and Case II, the maximum temperature spot is located on the rear side of the chips. Because the coolant is heated by the chips, the cooling performance is reduced when the coolant flows through the rear side of the chips. The two chips of Case I have different temperature distributions but chip 2 has higher temperature. The two chips of

Dp R (chip 1) R (chip 2) Difference (%)

Mesh I (1.5 M)

Mesh II (2.3 M)

Mesh III (3 M)

72.10 0.315 0.337 3.261% 2.476% 2.035%

73.14 0.326 0.343 1.865% 0.929% 0.291%

74.53 0.323 0.344 Baseline

Table I. Grid independence study for case I

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Case I

Case III

Figure 4. The middle plane velocity streamtraces

Case II

Case IV

x Case V

Case VI

z

Case II have the same temperature distribution because of the symmetric chip arrangement. For Case III and Case IV, the maximum temperatures are both on the chip 2 area, and they are also close to the center of the bottom surface of the heat sink. For Case V and Case VI, the chips have relatively close temperature distributions. The sliced temperature distributions of six cases are shown in Figure 6. It can be seen that the chip arrangement and the configuration obviously affect the three-dimensional temperature distribution. From the above results, it is suggested that with a reasonable arrangement of the chips, one can obtain a good cooling performance when the minichannel heat sink has been designed in advance. The relationship between thermal resistance and Reynolds number is presented in Figures 7 and 8. The larger flow rate of the coolant through the cooling minichannels, the more thermal load generated by chips can be taken away. It can be seen from the Figures that the thermal resistance decreases with increasing Reynolds

T, K 343 340 337 334 331 328 325 322 319 316 313 310 307 304 301 298 295

310 30

3 31

7

33

31

340

325

295

0

334

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337 343

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313 319 310

348 345 342 339 336 333 330 327 324 321 318 315 312 309 306 303 300

31

5 31

300 321

303

318 321

300

30 6

327

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312

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4 32

333 339

15

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6

309 330 315

327

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321

348

3

348

324 312

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339 318 309

333 330 324

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Case III

T, K

Case IV

332 329

314 320

317 323

323 326 329

29 9

326

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320 317

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302 326 323 320 317

326 323

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311 323 317 311

302 299 296

x Case V

805

T, K

Case II

2

Case I

CFD for thermal performance

Case VI

z

number. It is also observed obviously that for Case I, chip 1 presents the smallest thermal resistance at all Reynolds numbers and thereby has the best cooling effectiveness, while chip 2 has a little higher thermal resistance. This is reasonable because the coolant on the up-side first flows through the minichannels above chip 1

Figure 5. Temperature distributions on bottom surface, Re ¼ 210

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Y

Z

295 300 305 310 315 320 325 330 335 340

X

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806

Case I

Case II

295 300 305 310 315 320 325 330 335 340 345 350

Case III

Case IV

295 300 305 310 315 320 325 330 335

Figure 6. Slice temperature distributions, Re ¼ 210 Case V

Case VI

and thus the cooling potential of the coolant is fully utilized, whereas the down-side coolant flows through the regions without chip and later through the minichannels above chip 2. Besides, the temperature in the down-side is slightly increased along the flow direction from the inlet due to the streamwise heat conduction from the heat generated by the chip 1. For Case II, the two chips have almost the same

0.42 Case I chip 1 Case I chip 2 Case II chip 1 Case II chip 2

0.40

R,K/W

0.38

CFD for thermal performance

807

0.36

0.32 0.30 0.28

0.60 0.56 0.52 0.48 R,K/W

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0.34

0.44

100

150

200 Re

250

300

Figure 7. Thermal resistance vs Reynolds number

Case III chip 1 Case III chip 2 Case IV chip 1 Case IV chip 2 Case V chip 1 Case V chip 2 Case VI chip 1 Case VI chip 2

0.40 0.36 0.32 0.28 0.24 0.20

3x103 4x103 5x103 6x103 7x103 8x103 9x103 1x104 Re

thermal resistance, but it is slightly larger than that of Case I-chip1. This is because only the coolant inside the central minichannels is used to cool the two chips. For Case III, the two chips have the lowest and highest thermal resistance. Case IV shows similar results. These conditions are caused by the complex fluid flow in the minichannels. Besides, the configuration also affects the coolant distribution and thus the cooling performance. For Case V, chip 1 has lower thermal resistance than chip 2. For Case VI, the two chips have the same value. Figure 9 shows the relationship between thermal resistance and volumetric flow rate. It is also indicated that a proper chip arrangement can achieve a good cooling performance at low fluid flow rates. In Figure 10 it can be seen that the pressure drop is increasing as the volumetric flow rate is increasing. Case I and Case II have almost the same pressure drop values at a fixed volumetric flow rate. Case III, Case IV, Case V and Case VI also present identical pressure drops but with a higher growth rate due to the specific configurations.

Figure 8. Thermal resistance vs Reynolds number

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0.60

Case I chip 1 Case II chip 1 Case III chip 1 Case IV chip 1 Case V chip 1 Case VI chip 1

0.55 0.50

Case I chip 2 Case II chip 2 Case III chip 2 Case IV chip 2 Case V chip 2 Case VI chip 2

808

R,K/W

0.45 0.40 0.35

0.25

Figure 9. Thermal resistance vs volumetric flow rate

0.20 0.3

0.4

0.5 0.6 0.7 0.8 Volumetric flow (L/min)

0.9

1.0

0.9

1.0

2.5x104 Case I Case II Case III Case IV Case V Case VI

2.0x104 1.5x104 ΔP,(pa)

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0.30

1.0x104 5.0x103

8.0x101

Figure 10. Pressure drop vs volumetric flow rate

4.0x101 0.0

0.3

0.4

0.5 0.6 0.7 0.8 Volumetric flow (L/min)

5. Conclusions The minichannel heat sink is an effective way to cool electronic chips. In this study, the laminar and turbulent heat transfer in a water-cooled minichannels heat sink with two kinds of chip arrangements was investigated numerically by CFD simulations. The arrangement of chips would affect the chip surface temperature and thus the cooling performance. There are hot spots on the chip surface, and the temperature distribution on the chip wall is non-uniform. When the coolant flow is well-distributed at the inlet of minichannels, the diagonal arrangement of the chips has the highest and the lowest thermal resistance, and the parallel arrangement of the chips results in almost the same thermal resistance. It is suggested that a reasonable arrangement of the chips can remove larger heat loads and thus achieve a good cooling performance when the geometric model is fixed.

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References Chen, C.H. (2007), “Forced convection heat transfer in microchannel heat sinks”, International Journal of Heat and Mass Transfer, Vol. 50 Nos 11-12, pp. 2182-2189. Cho, E.S., Choi, J.W., Yoon, J.S. and Kim, M.S. (2010), “Modeling and simulation on the mass flow distribution in microchannel heat sinks with non-uniform heat flux conditions”, International Journal of Heat and Mass Transfer, Vol. 53 Nos 7-8, pp. 1341-1348. Farnam, D., Sammakia, B., Ackler, H. and Ghose, K. (2009), “Comparative analysis of microchannel heat sink configurations subject to a pressure constraint”, Heat Transfer Engineering, Vol. 30 Nos 1-2, pp. 43-53. Kandasamy, R. and Subramanyam, S. (2005), “Application of computational fluid dynamics simulation tools for thermal characterization of electronic packages”, International Journal of Numerical Methods for Heat Fluid Flow, Vol. 15 No. 1, pp. 61-72. Kandlikar, S.G. and Grande, W.J. (2004), “Evaluation of single phase flow in microchannels for high flux chip cooling – thermohydraulic performance enhancement and fabrication technology”, Heat Transfer Engineering, Vol. 25 No. 8, pp. 5-16. Khan, W.A., Culham, J.R. and Yovanovich, M.M. (2009), “Optimization of microchannel heat sinks using entropy generation minimization method”, IEEE Transactions on Components and Packaging Technologies, Vol. 32 No. 2, pp. 243-251. Kumaraguruparan, G. and Sornakumar, T. (2010), “Development and testing of aluminum micro channel heat sink”, Journal of Thermal Science, Vol. 19 No. 3, pp. 245-252. Lan, J.B., Xie, Y.H. and Zhang, D. (2012), “Flow and heat transfer in microchannels with dimples and protrusions”, ASME Journal of Heat Transfer, Vol. 134 No. 2, pp. 021901-1-021901-9. Lelea, D. (2009), “The heat transfer and fluid flow of a partially heated microchannel heat sink”, International Communications in Heat and Mass Transfer, Vol. 36 No. 8, pp. 794-798. Levac, M.L., Soliman, H.M. and Ormiston, S.J. (2011), “Three-dimensional analysis of fluid flow and heat transfer in single- and two-layered micro-channel heat sinks”, Heat and Mass Transfer, Vol. 47 No. 11, pp. 1375-1383. Manglik, R.M., Zhang, J. and Muley, A. (2005), “Low Reynolds number forced convection in three-dimensional wavy-plate-fin compact channels: fin density effects”, International Journal of Heat and Mass Transfer, Vol. 48 No. 8, pp. 1439-1449. Naphon, P., Klangchart, S. and Wongwises, S. (2009), “Numerical investigation on the heat transfer and flow in the mini-fin heat sink for CPU”, International Communications in Heat and Mass Transfer, Vol. 36 No. 8, pp. 834-840. Qu, W. and Mudawar, I. (2002), “Analysis of three-dimensional heat transfer in microchannel heat sinks”, International Journal Heat and Mass Transfer, Vol. 45 No. 19, pp. 3973-3985. Quadir, G.A., Mydin, A. and Seetharamu, K.N. (2000), “Analysis of microchannel heat exchangers using FEM”, International Journal of Numerical Methods for Heat Fluid Flow, Vol. 11 No. 1, pp. 59-76. Shao, B.D., Wang, L.F., Li, J.Y. and Sun, Z.W. (2009), “Application of thermal resistance network model in optimization design of micro-channel cooling heat sink”, International Journal of Numerical Methods for Heat Fluid Flow, Vol. 19 No. 3, pp. 535-545. Shao, B.D., Wang, L.F., Li, J.Y. and Cheng, H.M. (2011), “Multi-objective optimization design of a micro-channel heat sink using adaptive genetic algorithm”, International Journal of Numerical Methods for Heat Fluid Flow, Vol. 21 No. 3, pp. 353-364. Steinke, M.E., Kandlikar, S.G., Magerlein, J.H., Colgan, E.G. and Raisanen, A.D. (2006), “Development of an experimental facility for investigating single-phase liquid flow in microchannels”, Heat Transfer Engineering, Vol. 27 No. 4, pp. 41-52. Tuckerman, D.B. and Pease, R.F.W. (1981), “High-performance heat sinking for VLSI”, IEEE Electron Device Letters, Vol. EDL-2 No. 5, pp. 126-129.

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Xie, G.N., Liu, Y.Q., Zhang, W.H. and Sunden, B. (2013a), “Computational study and optimization of laminar heat transfer and pressure loss of double-layer microchannels for chip liquid cooling”, ASME Journal of Thermal Science and Engineering Applications, Vol. 5 No. 1, Paper no. 011004. Xie, G.N., Liu, J., Zhang, W.H. and Sunden, B. (2013b), “Analysis of flow and thermal performance of a water-cooled transversal wavy microchannel heat sink for chip cooling”, ASME Journal of Electronic Packaging, Vol. 134. Xie, G.N., Chen, Z.Y., Sunden, B. and Zhang, W.H. (2013c), “Numerical predictions of flow and thermal performance of water-cooled single-layer and double-layer wavy microchannel heat sinks”, Numerical Heat Transfer-Part A, Vol. 63 No. 3, pp. 201-225. Xie, G.N., Chen, Z.Y., Zhang, W.H. and Sunden, B. (2013d), “Comparative study of flow and thermal performance of liquid-cooling parallel-flow and counter-flow double-layer wavy microchannel heat sinks”, Numerical Heat Transfer-Part A, Vol. 64 No. 1, pp. 30-55. Xie, X.L., Tao, W.Q. and He, Y.L. (2007), “Numerical study of turbulent heat transfer and pressure drop characteristics in a water-cooled minichannel heat sink”, ASME Journal of Electronic Packaging, Vol. 129 No. 3, pp. 247-255. Xie, X.L., Liu, Z.J., He, Y.L. and Tao, W.Q. (2009), “Numerical study of laminar heat transfer and pressure drop characteristics in a water-cooled minichannel heat sink”, Applied Thermal Engineering, Vol. 29 No. 1, pp. 64-74. Corresponding author Professor Gongnan Xie can be contacted at: [email protected]

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