Numerical study of laminar heat transfer and pressure drop characteristics in a water-cooled minichannel heat sink

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Abstract

With the rapid development of the information technology (IT) industry, the heat flux in integrated circuit (IC) chips cooled by air has almost reached its limit about 100 W/cm2. Some applications in high technologies require heat fluxes well beyond such a limitation. Therefore the search of a more efficient cooling technology becomes one of the bottleneck problems of the further development of IT industry. The microchannel flow geometry offers large surface area of heat transfer and a high convective heat transfer coefficient. However, it has been hard to implement because of its very high pressure head required to pump the coolant fluid though the channels. A normal channel could not give high heat flux although the pressure drop is very small. A minichannel can be used in heat sink with a quite high heat flux and a mild pressure loss. A minichannel heat sink with bottom size of 20 mm × 20 mm is analyzed numerically for the single-phase laminar flow of water as coolant through small hydraulic diameters and a constant heat flux boundary condition is assumed. The effects of channel dimensions, channel wall thickness, bottom thickness and inlet velocity on the pressure drop, thermal resistance and the maximum allowable heat flux are presented. The results indicate that a narrow and deep channel with thin bottom thickness and relatively thin channel wall thickness results in improved heat transfer performance with a relatively high but acceptable pressure drop. A nearly-optimized configuration of heat sink is found which can cool a chip with heat flux of 256 W/cm2 at the pumping power of 0.205 W. The nearly-optimized configuration is verified by an orthogonal design. The simulated thermal resistance agrees quite well with the result of conventional correlations method with the maximum difference of 12%.

Introduction

With the rapid development of the IT industry, the heat flux in IC chips cooled by air has almost reached its limit about 100 W/cm2. Some applications in high technologies require heat fluxes well beyond such a limitation. Therefore, the search for a more efficient cooling technology becomes one of the bottleneck problems of the further development of the IT industry. Microchannel liquid cooling is one of the candidates for this purpose. Microchannel cooling technology was first put forward in 1981 by Tuckerman and Pease [1], who employed the direct water circulation in microchannels fabricated in silicon chips. They were able to reach the highest heat flux of 7.9 MW/m2 with the maximum temperature difference between substrate and inlet water of 71 °C. However, the penalty in pressure drop was also very high, i.e., 200 kPa with plain microchannels and 380 kPa with pin fin enhanced microchannels. Later, Philips [2] analyzed the heat transfer and fluid flow characteristics in microchannels in more details and provided formulations for designing microchannel geometries. Recently, Kandlikar et al. made a series studies on the direct liquid cooling technology by microchannels [3], [4], [5].

The microchannel flow geometry offers a large surface area of heat transfer and a high convective heat transfer coefficient. However, it has been hard to implement in the compact/slim design of computers or consumer electronic devices. The major difficulty is driving water with high pressure head, which is required to pump the coolant fluid though the channels. A normal channel could not give such high heat flux although the pressure drop is very low. Thus, an idea comes into being that water-cooled minichannel can be used in heat sink with a high heat flux and a mild pressure loss. Here, by minichannels, we refer to the channels with their characteristic lengths within 0.2–3 mm [6]. In the following, a brief review on fluid flow and heat transfer of liquids in minichannels is presented.

Convective heat transfer and fluid flow in minichannel and their application in the cooling technology of electronic devices have attracted great attention of researchers in recent years. Gael et al. [7] indicated that the heat conduction in the walls of mini/microchannels makes the heat transfer multidimensional, and the axial heat conduction in the walls cannot be neglected. The surface roughness effects on pressure drop in single-phase flow in minichannels were investigated in Refs. [8], [9], [10], [11]. Gao et al. [12] made experimental investigations of scale effects on hydrodynamics and the associated heat transfer in two-dimensional mini and microchannels with channel height ranging from 0.1 to 1 mm. Their results showed that the conventional laws of hydrodynamics and heat transfer can be applied to channels with height larger than 0.4 mm. Wang et al. [13] experimentally examined the frictional characteristics inside minichannels (Dh = 0.198–2.01 mm) with water and lubricant oil as the working fluids, and the tests were performed in both round and rectangular configurations. The test results indicated a negligible influence of viscosity on the friction factor if the hydraulic diameter is greater than 1.0 mm, and the measured data can be well predicted by the conventional correlation in both laminar and turbulent flow conditions. Agostini et al. [14] presented an experimental study of friction factor and heat transfer coefficient for a vertical liquid up flow of R-134a in minichannels. Downing et al. [15], [16] experimentally investigated the single- and two-phase flow pressure drop and heat transfer characteristics in straight and miniature helical flow passages with R-134a as a working fluid. Debray et al. [17] performed the measurement of forced convection heat transfer coefficients in minichannels. Reynaud et al. [18] measured the friction and heat transfer coefficients in two-dimensional minichannels of 1.12–0.3 mm in thickness, and experimental results are in good agreement with classical correlations relative to channels of conventional size. From all the above-mentioned references, the following conclusions can be drawn: (1) In the liquid minichannels, the conventional physical and mathematical models for fluid flow and heat transfer with no-slip boundary conditions are still valid. (2) The friction factor and heat transfer correlations for conventional channels can also be used in minichannels as long as their relative surface roughness and relative channel wall thickness are not too high. The use of minichannels in the cooling technology of electronic devices can be found in the following references. Liu and Mui [19] proposed a microprocessor package with water-cooling in which a narrow water jacket was used to cool a thermal spread attached to the silicon die backside for an efficient cooling. Schmidt [20] described a microprocessor liquid cooled minichannel heat sink and presented its performance as applied to a microprocessor (IBM Power 4) chip. Yazawa and Ishizuka [21] gave an analytic model for laminar flow and conducted a numerical study to optimize the channel in cooling spreader on a smaller and transient heat source. It was concluded that when small pumping power was available, a deeper channel with a thicker base was the best profile for the miniature channel coolers, and the best cooling performance was found at 0.0586 K/W for 0.03 W pumping power.

The aim of this study is to numerically design a water-cooling jacket which has relatively high heat transfer performance while keeping the pressure drop in an acceptable range. In the present paper, a multi-minichannel device has been designed and three-dimensional numerical simulation for its heat transfer and friction characteristics have been performed. In the following, the outlines of such a jacket will first be introduced and followed by its physical and mathematical models. Next, three-dimensional numerical results will be presented along with performance comparisons. Finally, some conclusions will be drawn.

Section snippets

Description of the designed cooling model

Fig. 1 shows a pictorial view of the suggested model. The unvaried total area being cooled is W × L with individual minichannel flow passage dimensions of Wc × Hc. The wall separating the two channels is of thickness Ww and acts like a fin. The bottom plate thickness is Hb. The top cover is bonded, glued, or clamped to provide closed channels for liquid flow.

The channel dimensions Wc and Hc, the channel wall thickness Ww, the bottom plate thickness Hb, and the coolant flow velocity Uin are the

Mathematical formulation and numerical methods

To analyze the thermal and flow characteristics of this model, the following assumptions are made:

  • (1)

    The flow is three-dimensional, incompressible, laminar and in steady-state.

  • (2)

    The effect of body force is neglected.

  • (3)

    The fluid thermophysical properties are constant and viscous dissipation is neglected.

  • (4)

    All minichannels are supposed to be identical in heat transfer and fluid flow; hence, one channel can be picked out as the representation for computation as shown in Fig. 2, where the coordinates system

Results and discussion

Supplied pumping power Wpp to generate the flow is defined in equation:Wpp=n·V˙·Δpwhere n is the number of cooling channel, which is equal to the integer part of WWw+Wc, V˙ is the volumetric flow rate and Δp is the pressure drop through the heat sink.

The effects of channel width Wc, channel height Hc, bottom plate thickness Hb, channel wall thickness Ww and inlet velocity Uin are parametrically studied. The numerical results will first be presented about the influences of those parameters on

Conclusions

The heat transfer and pressure drop characteristics for single-phase laminar flow in minichannel heat sinks are analyzed in the present paper. The results are presented for a chip with an active cooling area of 20 mm × 20 mm. From the results and analysis, following conclusions can be obtained:

  • (1)

    Pressure drop, an important parameter for minichannel heat sink design is a strong function of the channel geometry. From heat transfer, a narrow and deep channel is better than that of a wide and shallow

Acknowledgement

This work has been supported by the National Natural Science Foundation of China (Grant Nos. 50636050, 50425620).

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