Experimental investigation of liquid metal alloy based mini-channel heat exchanger for high power electronic devices

Abstract

There is currently a growing demand for developing efficient techniques for cooling integrated electronic devices with ever increasing heat generation power. To better tackle the high-density heat dissipation difficulty within the limited space, this paper is dedicated to clarify the heat transfer behaviors of the liquid metal flowing in mini-channel exchangers with different geometric configurations. A series of comparative experiments using liquid metal alloy Ga68%In20%Sn12% as coolant were conducted under prescribed mass flow rates in three kinds of heat exchangers with varied geometric sizes. Meanwhile, numerical simulations for the heat exchangers under the same working conditions were also performed which well interpreted the experimental measurements. The simulated heat sources were all cooled down by these three heat dissipation apparatuses and the exchanger with the smallest channel width was found to have the largest mean heat transfer coefficient at all conditions due to its much larger heat transfer area. Further, the present work has also developed a correlation equation for characterizing the Nusselt number depending on Peclet number, which is applicable to the low Peclet number case with constant heat flux in the hydrodynamically developed and thermally developing region in the rectangular channel. This study is expected to provide valuable reference for designing future liquid metal based mini-channel heat exchanger.

Keywords

heat exchanger / liquid metal / mini-channel / heat dissipation / heat transfer coefficient

Introduction

In the last few decades, with the prodigious advancements of the industry, modern electronics yielded ever increasing complexity, precision and miniaturization. Although the size of semiconductor chip kept decreasing, the heat load increased. As a result, a large amount of waste heat was dissipated within the limited space, which resulted in detrimental hot-spots and even caused damages to the electronics. To accommodate to such growing heat flux, many innovative cooling methods were tremendously investigated, such as improved forced convective liquid cooling, heat pipe cooling, and thermoelectric cooling, etc. [1].

Apart from the ways as outlined above, the mini-channel cooling technique was especially found as an effective way of heat removal for a long time. Compared with the conventional cooling methods, it owns many evident merits such as smaller size, less coolant charge, and higher heat transfer coefficient [2]. In recent years, a series of newly emerging works were made to interpret the cooling mechanisms and then develop enhanced techniques. Most of such works could be roughly classified into the following categories: theoretical analyses [3,4], numerical simulations [5,6], structure optimizations [7-10], working medium [11], and practical applications [12,13]. A majority of these efforts was contributed significantly to improving the cooling performance through structure optimizations, while only relatively a few works were made to find new working medium including gas, water in mini-channel heat exchangers. In addition, the two-phase working medium was also studied [14-16]. Meanwhile, in order to evidently improve the thermal conductivity of the working medium, metal nanoparticles with high thermal conductivity were loaded into the base fluids to make ever conductive coolant. However, new troubles were also brought about by metal nanoparticle mediated fluids such as sediment and quality deterioration [17].

Overall, the enhancement of heat transfer coefficient by optimizing only the device structure or the mixing coolants is still unsatisfactory. Recently, the liquid metal whose low melting point is around room temperature and thermal conductivity much higher than that of common liquids is identified as a very promising working fluid in mini-channel heat exchanger. Liu et al. [18] first proposed to use liquid metal as an ideal coolant for thermal management of electronics. It was proven that the cooling technique was powerful owing to its high efficiency, low energy consumption, high reliability and easy production [19]. In addition, the liquid metal possesses excellent electric-physical property that can be easily driven by a non-moving pump [20]. Miner and Ghoshal [21] compared the heat transfer coefficients of gallium alloys with water in a pipe under constant wall heat flux and varied Reynolds numbers. Ma et al. [22] investigated the thawing behavior of liquid metals, which solved the solidification problem in the heat transfer process. Other studies involving the thermal management of computer chip and LED with liquid metal were also separately performed [23-25].

Although there were increasing investigations associated with liquid metal, studies of liquid metals in mini-channel exchangers were rarely reported. Recently, Deng et al. [20] and Twak et al. [26] respectively researched the heat transfer of liquid metal in mini-channels for electronic devices, and proved its superiority. Wilcoxo et al. [27] constructed a substrate of 1mm in thickness with integrated flow channels to circulate liquid metal, and found that the substrate had a thermal conductivity of more than 6000 W/(m·°C). As a significant extension of the former liquid metal based mini-channel cooling method, the present paper is dedicated to carrying out a comprehensive experimental study of a series of heat exchangers with particularly varied channel geometries, using liquid metal as coolant. This is expected to clarify the critical factors to dominate the working performance of the device. Besides, numerical simulations under the same conditions were also performed and compared with the experiments which helped interpret the phenomena observed. In addition, the correlation of dimensionless heat transfer coefficient depending on Peclet number was obtained. The results are expected to be significant for future design of liquid metal based mini-channel heat exchanger.

Experimental setup and numerical simulation methods

Experimental materials

Generally speaking, low melting-point metals and alloys including gallium, indium, and Na-K and their alloys can be adopted as working fluids in the cooling system. Considering the availability and safety, gallium and its alloys are the most appropriate candidates in the present study because of their low melting point, high thermal conductivity, stable, non-flammable and non-toxic activity, low vapor pressure, and high boiling point, etc. [24]. However, gallium and its alloys have certain defects such as oxidation and corrosion problems. Though the surface of gallium alloys are easily oxidized when exposed to the air, the formed oxide film would protect the liquid metal from being further oxidized. Meanwhile, gallium alloys may react more or less with some metal materials such as copper and aluminum. In this regard, Deng and Liu [28] performed a detailed study of the corrosion problems between gallium alloys and four typical metal substrates, which preliminarily clarified the issue. They found that metal substrates which were pretreated by film oxidation showed excellent corrosion resistance and compatibility with gallium alloys.

In this paper, the gallium alloy Ga68%In20%Sn12%, whose properties are listed in Table 1 with water for comparison, was selected as working fluid, and sealed in the channel throughout the experiments. The T2 copper-alloy, which was pretreated by film oxidation, was used as the substrate material of mini-channel heat exchanger. The mini-channel heat exchangers were fabricated by wire-electrode cutting and assembled by electron-beam welding, as shown in Fig. 1. Three kinds of heat exchangers, whose dimensional parameters are listed in Table 2, were constructed with a size of 40 mm × 20 mm × 10 mm, and named 1#, 2#, 3# heat exchanger, respectively. The thickness of the plate between the heat source and the channels is 2 mm.

Experimental platform

Figure 2 depicts the flow chart of the system. The experimental platform is composed of a gallium alloy heat transfer module and a data acquisition module. The gallium alloy heat transfer module is made up of a heat exchanger, a peristaltic pump, a distal radiator, a fan, connected pipes and a filter. The computer chip was simulated by a heating plate with a size of 40 mm × 10 mm × 10 mm, placed on the top of the mini-channel. The power applied on the heating plate was produced by DH1720A-1 regulated DC power supply. Hence, in a circulation loop, the gallium alloy driven by a peristaltic pump first took heat from the heat exchanger to the distal finned radiator made of aluminum, dissipated heat to the surrounding air, and then flowed back to heat exchanger after being cooled down. Among these, the connected pipes adopted silicon tubes, and the filter was used to purify liquid metal. The whole heat exchanger was packed with insulation foam to prevent the heat leakage.

The data acquisition module consists of an Agilent 34972A Data Acquisition Unit (USA), a computer and seven thermocouples. The Agilent Unit was connected to computer to record the readings on the thermocouples. The T-typed thermocouples with a tip diameter of 0.5 mm were adopted as temperature sensors. The thermocouples were fixed in the slots drilled on the surface of the simulated heat source in line with an interval of 4 mm. The inlet and outlet temperatures of the heat exchanger were measured with pinpoint-shaped thermocouples inserted into the two ends. Thus, there are all together seven positions for temperature measurement as illustrated in Fig. 2. Besides, the calculation of mass flow rate adopted mass weighting method by using a stopwatch and electronic scale.

Numerical simulation methods

To better understand the flow and heat transfer behavior of the liquid metal in the mini-channel, the commercially available CFD software ANASYS 14.0 was adopted for the numerical simulation. A three-dimensional cubic model was established to characterize the flow of the liquid metal in the mini-channel and a gird generation was performed using the hexahedral meshing method. The solver adopted the Pressure-based type with steady-state. The solution was obtained using the SIMPLE arithmetic, and the spatial discretization was based on the second order upwind scheme.

The whole model consists of four kinds of boundary conditions: inlet, outlet, heating and adiabatic faces. The inlet face adopted velocity-inlet while the initial velocity was set to zero. The outlet face was defined as outflow. The heating face adopted constant heat flux condition while the rest were treated as adiabatic. The initial temperature was set to 300 K. The working medium employed Ga68%In20%Sn12% whose physical properties were the same as those used in the experiments and listed in Table 1.

Calculation model

Mean heat transfer coefficient

The mean heat transfer coefficient is often used to evaluate the performance of heat exchangers. The heat transfer equation can be written as

(1)Q=hA\mathrm{\Delta }{t}_m.

with

(2)Q=\dot{m}{c}_p(t_{\mathrm{out}}-t_{\mathrm{in}}),

where Q is the amount of total heat transfer, h is the coefficient of mean heat transfer, A is heat transfer area, \dot{m} is the mass flow rate, c_p is the heat capacity of coolant, t_{\mathrm{in}} and t_{\mathrm{out}} are the inlet and outlet temperatures of the exchanger, and \mathrm{\Delta }{t}_m is the logarithmic mean temperature difference, which can be estimated with [29].

(3)\mathrm{\Delta }{t}_m={\displaystyle \frac{\mathrm{\Delta }{t}_{\max }-\mathrm{\Delta }{t}_{\min }}{\ln (\mathrm{\Delta }{t}_{\max }/\mathrm{\Delta }{t}_{\min })}}.

So

(4)h={\displaystyle \frac{\dot{m}{c}_p(t_{\mathrm{out}}-t_{\mathrm{in}})\ln (\mathrm{\Delta }{t}_{\max }/\mathrm{\Delta }{t}_{\min })}{A(\mathrm{\Delta }{t}_{\max }-\mathrm{\Delta }{t}_{\min })}},

where \mathrm{\Delta }{t}_{\max } and \mathrm{\Delta }{t}_{\min } are respectively the maximum and minimum value of the temperature difference between simulated heat source and coolant.

Thermal resistance

The thermal resistance model is a good tool to analyze the performance of the heat exchanger. The total thermal resistance (TR) usually consists of the conductive TR, the convective TR, and the capacitive TR in heat exchangers, respectively, and can be calculated by

(5)R_t={\displaystyle \frac{\mathrm{1}}{hA}}

with

(6)R_t=R_{\mathrm{con}}+R_{\mathrm{cap}}+R_{\mathrm{conv}},

where R_t is the total TR, R_{\mathrm{con}} is the conductive TR depending on substrate material, R_{\mathrm{cap}} is the capacitive TR depending on the properties of coolant, and R_{\mathrm{conv}} is the convective TR depending on the fluid and the heat exchanger.

Results and discussion

Mean heat transfer coefficient of experiments and numerical simulation

The experiments were first constructed through performing liquid metal flow tests in various rectangular mini-channels. A series of experiments and numerical simulation were conducted to obtain the surface temperature of the simulated heat source along the flow direction and the mean heat transfer coefficient of liquid metal flowing in one-side heated rectangular mini-channel with constant heat flux. For all the experiments, flow conditions were hydrodynamically developed and thermally developing at a laminar state with Re≥115. All the cases, therefore, fell into Graetz type with entrance heat transfer investigation. The experiments and numerical simulation were both performed with eight groups of mass flow rates as listed in Table 3 and heating power was 80 W.

Figure 3 shows the surface temperature distribution of the simulated heat source along the flow direction under three kinds of heat exchangers with a heating power of 80 W and a rotation speed of 100 r/min. The values from the experiments are compared with the results obtained by the numerical simulation. From Fig. 3 it can be seen that the temperatures of simulated heat source increase along the flow direction for all the exchangers. Secondly, the heat source cooled by 3# heat exchanger retains the lowest surface temperature at all positions. There is a small difference between simulated and experimental values, which is caused by the heat leakage and instrumental error in experiments.

Figure 4 illustrates the mean heat transfer coefficient calculated from the experimental and simulated results at different mass flow rates with the heating power of 80 W. From Fig. 4 it can be seen that the mean heat transfer coefficients of the three heat exchangers increase with the increases of mass flow rate. Under the same flow rate, the largest mean heat transfer coefficient is obtained in 3# heat exchanger with the smallest channel width. The results have confirmed that the heat transfer performance of 3# heat exchanger is superior to that of other two cooling devices, which is mainly due to the following two reasons. First, the heat exchanger with a smaller channel width has a larger heat transfer area, which can decrease the thermal resistance, and improve the amount of heat transfer. Figure 5 describes the total thermal resistance of the three kinds of heat exchangers at different mass flow rates. It can be found that the thermal resistance of 3# heat exchanger accounts for the smallest area of bar block under all flow rates. And it is apparent that the thermal resistance can be reduced by enlarging the flow rate of coolant. Next, in the mini-channel, the laminar flow state is easy to be disturbed and transformed into a turbulent state. The heat transfer performance of the turbulent flow is better than that in the laminar state. Besides, the experimental values deviate somewhat from the simulated results, although generally they accord well with each other. The main reason lies in the fact that the numerical simulations are performed at such an ideal condition that many real factors have to be neglected, while the real experiments contain uncertainties caused by the measurement approach itself and the testing errors. Taking these reasons into consideration, it can be found that there is a good agreement between the experimental measurements and the simulation results.

Deduction of Nusselt correlation

According to the conventional heat transfer theory, the dimensionless heat transfer coefficient (Nusselt number) can be expressed as the function of Peclet number, i.e.

(7)Nu=f(Pe)

with

(8)Pe=Re\cdot Pr.

Meanwhile, the heat transfer coefficient can be expressed with the function of Nusselt number as

(9)h={\displaystyle \frac{Nu\lambda }{d}},

where d is the characteristic length of the mini-channel, and \lambda the thermal conductivity of the coolant. So far, many authors have proposed new relations to predict the Nu number in mini-channel, but the results are not in agreement with each other, which results from several factors including experimental condition, structure design, fabrication precision and fluid characteristics, etc. Of the many efforts ever made, the form of Nusselt correlation depending on Pe number has received most attention.

The Nu numbers in the three kinds of heat exchangers, which are calculated from Fig. 4, are displayed with the Pe number in Fig. 6. With these data, the form of exponential function was selected to fit Nu number as

(10)Nu=a+bP{e}^m.

Through experimental data regression, an approximate correlation was derived:

(11)Nu=-\mathrm{0.20}+\mathrm{1.6213}P{e}^{\mathrm{0.3053}}.

The results obtained from the experiments and the fitting formula are demonstrated in Fig. 6, which indicates that all the experimental results accord with the fitting curve very well. This correlation is valid to the case with the low Pe number and the constant heat flux in hydrodynamically developed and thermally developing region in the rectangular duct channel.

To illustrate the validity of this correlation, comparisons are made between it and the other empirical correlations in Fig. 7. Here, the Nu__Twak proposed by Tawk is developed from the simulation data and validated in the case of forced heat transfer of liquid metal in the rectangular channel in fully thermal and semi hydraulically developed laminar and transition flow with a constant heat flux density on the wall. The correlation Nu__Ptukhov by Ptukhov is applicable to a fully developed transition flow in duct. The Nu__Bejan established by Bejan is suitable to a fully developed laminar flow in a rectangular channel [20].

From Fig. 7, it can be found that these correlations are generally in well agreement when the Pe number is close to 40. The differences are attributed to different applicable conditions including structure material, coolant, and channel shape as well as operational condition, etc.

Uncertainty analysis

The uncertainty in the present experiment was generally caused by systematic errors and random errors. The random errors are uncontrollable and can be reduced through multiple measurements. The systematic errors are caused by the experimental method itself, the environmental factors, and instrumental errors and so on, which can be detected and appropriately justified. This paper mainly dealt with instrumental errors in the calculation of the mass flow rate and heat transfer coefficient. The errors of the thermocouple, electronic scale, stopwatch, and vernier caliper are respectively±0.5°C,±0.1 g,±0.1 s, and±0.02 mm. The standard uncertainty of the flow rate and the mean heat transfer coefficient can be calculated by

(12)u\left(y\right)=\sqrt{{\displaystyle \sum _{i=1}^n{\left[{\displaystyle \frac{\partial y}{\partial x_i}}u\left(x_i\right)\right]}^2}},

where u refers to the instrumental error, y refers to the results calculated from measured variables, x_i refers to the measured variable, and n refers to the number of variables. According to formula (12), the uncertainties of the calculated parameters are listed and compared in Table 4 (in the case of a rotation speed of 100 r/min, and a heating power of 80 W for liquid metal).

Conclusions

Liquid metal is a promising candidate as a highly efficient working coolant owing to its superior thermal conductivity and low melting point around room temperature. If taking space and cost limit into consideration, heat exchangers with mini-channels are rather useful in cooling small electronic devices. This paper presents a comparative research on the working performance of mini-channel heat exchangers with different channel widths, using liquid metal as coolant. Based on the calculation models, it is known that the mean heat transfer coefficients for heat exchangers increase as the mass flow rate of coolant augments, and 3# exchanger with the smallest channel width is proven to have the best heat transfer performance of the three. The differences between numerical simulation and experimental measurements are acceptable due to uncertainties resulted from instrumental errors. Besides, an approximate correlation of Nusselt number depending on Peclet number has been developed, which applies well to small Peclet number case with constant heat flux in hydrodynamically developed and thermally developing region in rectangular channel.

Notations

References

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