Numerical investigation of laminar flow and heat transfer in a liquid metal cooled mini-channel heat sink

https://doi.org/10.1016/j.ijheatmasstransfer.2019.119265Get rights and content

Highlights

  • A detailed numerical analysis of a liquid metal cooled mini-channel is presented.

  • Geometric and flow parameters of the mini-channel heat sink are optimized.

  • Hydraulic and thermal performance of the liquid metal is critically analyzed.

  • Performance of liquid metal is compared with other coolants like water and nanofluids.

  • Numerical results of this study are compared with analytical correlations.

Abstract

With the recent trend of miniaturization and high-power output, effective heat dissipation has become the top priority in several industrial applications. This work contributes to the novel and efficient cooling technique that utilizes the liquid metal as working fluid. A numerical analysis of laminar flow and forced convective heat transfer of Galinstan through a mini-channel heat sink exposed to a constant heat flux has been presented. A detailed parametric analysis of the influence of heat sink's geometry, and the inlet velocity on the pressure drop, pumping power and the maximum heat flux has been carried out. Optimized heat sink's dimensions and inlet velocity are obtained. Furthermore, the numerical results are compared with the analytical correlations and discussion concerning the agreement and discrepancy is made. In addition, the flow and heat transfer performance of mini-channel heat sink cooling using liquid metal, nanofluid and water are compared, which intuitively shows the advantage of using liquid metal as coolant.

Introduction

Recent advancements in technology have led to the trend of miniaturization and high power output, and high-density heat flux dissipation has become the main requirement in various industrial applications. Examples include electronic chip cooling, power electronics, opto-electronic devices, laser diodes, cooling of high-power light-emitting diodes (LEDs), phased array radars, vehicle batteries, concentrating photovoltaic cells, high-power microwave devices and Insulated Gate Bipolar Transistor (IGBT) modules [1], [2], [3], [4]. Various passive and active cooling technologies have been reported in the literatures [5,6]. Among these methods, the micro/mini-channel cooling has gained a particular attention for its promising capability to remove very high density fluxes (up to 102–103 W cm−2) [7], [8], [9], [10], [11], [12]. Furthermore, the micro/mini-channel cooling technique possesses some advantages, such as high convective coefficient, less coolant volume and comparatively smaller cooling system size among others. In spite of numerous attempts to improve heat transfer, the maximum heat flux that can be removed is limited by the inherent thermophysical properties of coolants [12]. In recent years, liquid metals with low melting point (such as Gallium alloys) have become popular coolants due to their superior thermal conductivity, low viscosity, low toxicity, non-flammablility, high boiling point and low thermal resistance [13,14].

Many studies have been conducted to explore the applications of employing liquid metals as coolants for removing high-density heat flux [15], [16], [17], [18], [19], [20]. Deng et al. [21] carried out experiments to compare the heat and flow performance of Gallium alloy and water in mini- and micro-channels. Their results show that, when working fluids are operated at high velocity, the liquid metal based micro-channel produces higher heat transfer coefficient than that of water. Tawk et al. [22] numerically and experimentally investigated the liquid metal cooled mini-channel heat sink of power electronic devices. They showed that the maximum discrepancy of temperature between numerical and experimental results was less than 7%. Luo and Liu [23] experimentally investigated the thermal performance of liquid metal based mini-channel heat sinks with different channel widths. Their results show that the heat transfer coefficient increases with the raise in the coolant's mass flow rate and the heat sink with smaller width shows better thermal performance. Zhang et al. [24] experimentally found that thermal resistance 0.077 K W−1 with the maximum heat flux of 1504 W cm−2 can be achieved using Galinstan-based mini-channel. Yang et al. [25] presented results for both water and liquid metal cooling in the micro/mini-channel heat sinks and observed that the liquid metal displays a much better thermal and flow performance in mini-channel scale. Their numerical results were also compared with different correlations, and it is noted that there is significant deviation between the thermal resistances computed using 1-D model and the direct numerical technique for liquid metal. Zhang et al. [26] experimentally studied the Galinstan based mini-channel by varying pumping power and heating loads. They demonstrated that the system can dissipate heat power 1500 W with heat flux 300 W cm−2. Moreover, it has also been proved that the loss in pressure for the mini-channel cooling with Galinstan is much lower than micro channel with water.

Although the flow of Ga alloys passing through the mini-channels has been investigated by different approaches, the influence of heat sink's geometry and the inlet velocity has not been fully investigated. In addition, study of the maximum heat flux capacity of Ga alloys in mini-channel has less been discussed. Typically, the maximum temperature of the silicon chip should be kept well below 398 K for its efficient working and reliability. Furthermore, normally the operating temperature for the electronic devices is under 343 K, since the system's reliability declines sharply along with the increase in temperature [26], [27], [28]. Considering this temperature constraint and to keep the temperature within an appropriate range, we also aim to quantitatively investigate the maximum heat flux dissipation capacity of Galinstan based mini-channel by setting the temperature's upper limit for the electronic devices as 343 K. In addition, the superior performance of liquid metal in mini-channel heat sink is intuitively demonstrated by comparing with water and nanofluid.

Section snippets

Problem statement and mathematical formulation

We consider a 3-D mini-channel with height H, width Wc, base thickness tb and wall thickness Ww. The overall dimensions for the heat sink (L = 2 cm, W = 2 cm) are selected after considering the typical chip sizes as shown in Fig. 1.

A laminar, forced convective flow of Galinstan (21.5 wt% In, 10.0 wt% Sn and 68.5 wt% Ga) towards positive z-direction with a uniform inlet velocity Ui and at inlet temperature Tin (300 K) is considered. This kind of material is one of the most popular liquid metals

Flow and thermal model

The pumping power (Wpp) consumed in driving the flow of coolant through the heat sink and the pressure drop ΔP can be calculated asWpp=nΔPUiWcHΔP=fLDhρUi22where n is the number of channel and Dh is the hydraulic diameter, Dh=2WcHWc+H, f is the friction factor. The following theoretical correlations [25] are used for calculating f and are termed as correlation A1 in the present discussion.fappRe=21.04(xhyd)0.434α0.010.001<xhyd<0.02fappRe=45.2(xhyd)0.202α0.0940.02xhyd<0.1where α is the

Numerical method and validation

The software FLUENT 19.0 is employed for all simulations. The whole computational domain (including both the solid and fluid regions) is discretized using hexahedral cells generated with ICEM CFD 19.0. The momentum, mass and energy equations have been numerically solved using the Pressure-based type solver with steady-state. The 2nd order upwind and central differencing schemes are used for the convective and diffusive fluxes, respectively. The SIMPLE algorithm is adopted for the

Results and discussion

In this section, first of all, the effects of geometric parameters (channel height, channel width, channel wall thickness and base thickness) on the pumping power Wpp, pressure drop ∆P, the maximum heat flux qmax, and the total thermal resistance Rtot were examined, and optimized heat sink's dimensions and appropriate coolant velocity are obtained. In order to compute the ∆P and Rtot, uniform heat flux qb is fixed to 100 W cm−2, while for qmax the temperature constraint of 343 K (as noted from

Concluding remarks

In this paper, numerical results are presented for the thermal and flow performance of a mini-channel heat sink using Galinstan as coolant for high heat flux devices. Two analytical correlations are adopted to help evaluate the results. The performance of Galinstan has been also compared with nanofluid and water. The main findings can be summarized as follows.

  • (1)

    The flow resistance depends on the channel height, channel width and the velocity of coolant for a given channel length. The influence of

Declaration of Competing Interest

None.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No.11802079). The authors are very grateful to Dr. Alfredo Iranzo for various useful discussions.

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