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Proceedings of the Seventh International ASME Conference on Nanochannels, Microchannels and Minichannels ICNMM2009

June 22-24, 2009, Pohang, South Korea

ICNMM2009-82046

LIQUID METAL BASED MINI/MICRO CHANNEL COOLING DEVICE

Yue-Guang Deng Technical Institute of Physics

and Chemistry, Key Laboratory of Cryogenics, Chinese Academy of Sciences, Beijing 100190, China

Jing Liu Technical Institute of Physics

and Chemistry, Key Laboratory of Cryogenics, Chinese Academy of Sciences, Beijing 100190, China,

E-mail: [email protected]

Yi-Xin Zhou Technical Institute of Physics

and Chemistry, Key Laboratory of Cryogenics, Chinese Academy of Sciences, Beijing 100190, China

ABSTRACT

Effective heat dissipation is of great importance in many engineering fields. In this paper, we investigated a newly emerging method to significantly improve the cooling capability of micro channel devices, through implementing liquid metal with low melting point as the powerful coolant. A series of experiments with different working fluids and volume flow were performed, and the different cooling effects between liquid metal and water were compared. In order to better evaluate the cooling capability of liquid metal based micro channel cooling device, the hydrodynamic and heat transfer theory involved was discussed. The results indicated that, when the system operated in a relatively high velocity, micro channel cooling devices with liquid metal as coolant could produce higher convective heat transfer coefficient compared to those with traditional cooling fluids. And under the same pump power, not only the thermal resistance of liquid metal based micro channel could be much smaller, but also the coolant volume flow could be decreased. What is more, the liquid metal can be driven by a highly efficient electromagnetic pump without any noise. Therefore, more compact and energy-saving micro channel cooling devices with better cooling capability may come into reality. This new method is rather practical, and is expected to be important for realizing an extremely high heat dissipation rate.

INTRODUCTION

Mini/micro channel cooling has long been identified as an effective way for heat dissipation of many cutting-edge electronic devices with high heat flux. That is mainly because it has many evident merits, such as smaller size, less coolant inventory, higher convection coefficient, and larger heat transfer area when compared to traditional convection [1].

In recent years, lots of researches have been performed to better understand the cooling mechanism and improve the cooling capability of mini/micro channel, which are mainly classified as theoretical analysis [2], numerical simulation [3,

4], structure optimization [5], fabrication technology [6, 7], practical application [8], and two-phase flow [9]. However, most of the works try to raise the cooling capability of mini/micro channel from the view point of structure optimization. Researches on better and superior coolant for mini/micro channel were rarely reported. A majority of the mini/micro channels used traditional coolant, such as air, water [10], Freon [11], and ethanol solution [12]. Except that, two-phase coolant, such as water-vapor [13], nitrogen-water [14], and ethanol-CO2 [15] were also widely studied. However, all of these coolants would lack the ability to coupe with even higher heat dissipation requirements due to the limitation of their thermal-physical properties. Some novel coolants, such as nanofluids was proposed for mini/micro channel cooling [16, 17], but its improvement of cooling capability was also limited and might involve deposition problems[18]. Therefore, searching for better coolant with superior thermal-physical property is very important to greatly improve the cooling capability of mini/micro channel devices.

Recently, the liquid metal cooling was identified as a powerful thermal management method for many high heat flux density devices [19-21]. But no theoretical or experimental results on liquid metal based mini/micro channel are reported in literatures until now. This paper is dedicated to evaluate the cooling performance and flow resistance characteristic of a liquid metal based micro channel. So far, the best candidates of liquid metals are gallium and its alloys, because they own excellent properties such as low melting point, high thermal conductivity, non-flammable and non-toxic activity, low vapor pressure, and high boiling point etc [20]. What is more, the flowing liquid metal can be driven by a silent, nonmoving electromagnetic pump efficiently. In this paper, a liquid metal based micro channel was fabricated. The experiments and theoretical analysis indicated that micro channel with liquid metal as the coolant is a powerful way for heat dissipation of high heat flux density electronic devices.

Proceedings of the ASME 2009 7th International Conference on Nanochannels, Microchannels and Minichannels ICNMM2009

June 22-24, 2009, Pohang, South Korea

ICNMM2009-82046

Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 05/04/2014 Terms of Use: http://asme.org/terms


NOMENCLATURE p Pressure, Pa ρ Density, Kg/m3 H Height, m f On-way resistant coefficient, 1 ζ Local resistance coefficient, 1 l Length, m d Diameter, m v Velocity, m/s h Convection coefficient, W/(m2•K) Q Heat quantity, W A Area, m2 T Absolute temperature, K m Mass flow, kg/s

pc Heat capacity, J/(kg·K)

R Thermal resistance, ºC/W P Pump power, W G Volume flow, m3/s Re Reynolds number, 1 ν Kinematic viscosity coefficient, m2/s

cA Cross-sectional area, m2

U Circumference, m γ Aspect ratio, 1 λ Thermal conductivity, W/(m•K) Pr Prandtl number, 1 Nu Nusselt number, 1

EXPERIMENTAL SETUP At present, the liquid metal with low melting point suitable

for room temperature cooling system mainly are mercury, NaK alloy, Wood' s metal, gallium and its alloys. Compared to other liquid metals, gallium and its alloys are the best candidates used in liquid metal cooling system, for their evident merits of non-toxic activity, no reaction with air or water, excellent stability as well as low melting point. In our experiment, GaIn20 (Ga 80%, In 20%), which was confected by pure gallium and indium, was used as the coolant for the micro channel cooling system. Its melting point, density, thermal conductivity (Mathis TCi, SETARAM, France) and heat capacity (DSC 200F3, NETZSCH, Germany) were measured in the experiment. And the measured data of GaIn20 and literature values of gallium and water are shown and compared in Table 1:

Gad GaIn20

e Waterf

Melting point (ºC) 29.8 16 0 Density (Kg/m3) 6093a 6335c 998.2c

Thermal conductivity (W/(m·K))29.28b 26.58c 0.599c

Heat capacity (J/(Kg·K)) 409.9b 403.5c 4183c

a32.4ºC b29.8ºC c20ºC dFrom Ref [22] eExperimental measurement fFrom Ref [23]

Table 1. Thermophysical properties of liquid metal and water

The micro channel module which used T2 copper as substrate material was fabricated by milling machine, and the channel size was 0.5 mm× 0.8 mm × 35 mm with the number of 10 and spacing of 1 mm. Inlet and outlet were set at both ends of module to enable fluid flow in and out the micro channel. The heating plate was placed in a milled rectangular slot at the bottom of the micro channel. And the top of micro channel was covered with a piece of organic glass so as to observe the flow condition conveniently. The whole heating region was 30 mm × 14 mm, and heat flux can achieve 40W/cm2 with a 168W heating power. The scheme of micro channel in the experiment is shown in Fig. 1.

Figure 1. The scheme of micro channel

The experimental platform consisted of micro channel,

peristaltic pump, radiator, weighing-measuring module, manometer, filter, and data acquisition system. Driven by the peristaltic pump, the fluid first went through the filter, test section of micro channel, and radiator successively, then passed through the weighing-measuring system for flow measurement, and finally entered the liquid collection for the next round of circulation. In the experiment, four temperature holes were drilled in the micro channel test section evenly along the flow direction, and T-typed thermocouples and Agilent 34970A Data Acquisition Unit was adopt for real-time temperature data acquisition of micro channel as well as inlet and outlet fluid. Weighing-measuring module used electronic balance and stopwatch to measure the mean mass flow. The precision of balance and stopwatch were 0.1g and 1s respectively. The static pressure of inlet and outlet in micro channel was measured by manometers, so the pressure difference between inlet and outlet of micro channel is the function of manometer height difference. The scheme of experimental platform is shown in Fig. 2.

Figure 2. The scheme of experimental platform



EXPERIMENTAL RESULTS The objective of this experiment is to evaluate the different

flow and heat transfer characteristics in micro channel when taking liquid metal as flowing medium instead of water. It is clear from Table 1 that liquid metal has much higher thermal conductivity than water, so micro channel with liquid metal as the coolant could show superior heat dissipation capacity than that based on water. However, the density of liquid metal is nearly six times of water, so under the same flowing condition, the flow resistance of liquid metal in micro channel is greater and would consume more pump power. Therefore, the flowing characteristic and cooling capability of liquid metal based micro channel could be evaluated from the following three aspects: (1) the flow resistance (pressure difference between inlet and outlet) under different coolant volume flow; (2) convective heat transfer coefficient under different coolant volume flow; (3) convection thermal resistance under different pump power.

Pressure difference under different coolant volume flow The pressure difference between inlet and outlet of micro

channel can be calculated as: p g HρΔ = Δ （1）

where, pΔ is the pressure difference, ρ is the fluid density, g is taken 10N/Kg， and HΔ is the manometer height difference between the inlet and outlet of the micro channel.

Figure 3 shows the pressure difference under different coolant volume flow when liquid metal and water flow through the micro channel respectively.

Figure 3. Pressure difference under different volume flow

It can be seen from Fig. 3 that both curves have almost linear increasing trend as volume flow increases, and in the higher velocity region, the curve slope gets slightly larger. Under the same volume flow, liquid metal has larger pressure difference between inlet and outlet than water when flowing through the micro channel. The mean pressure difference radio between liquid metal and water in Fig. 3 is about 2.5.

According to the definition of flow resistance: 2 2

2 2l v vp fdρ ρζΔ = + （2）

where, the first item on the right is the on-way resistance while the second is the local resistance, and f , ζ , l , d , ρ , v are the on-way resistance coefficient, local resistance coefficient, flow distance, equivalent diameter, fluid density, mean velocity respectively. Easy to know that under the same velocity and flowing geometry conditions, the flow resistance is closely related to the coolant density, on-way resistance coefficient as well as the local resistance coefficient. The density of GaIn20 is about six times as large as water’s, but its viscosity is relatively lower than that of water, which is about one-third of water’s. That means in the low-velocity laminar flowing region, when fluid viscosity affects flow resistance a lot, the on-way resistance coefficient and local resistance coefficient of liquid metal would be lower than that of water.

Therefore, under the comprehensive effects of density and viscosity, it can be found in the low-velocity region of Fig. 3, the pressure difference between inlet and outlet of liquid metal is about two times larger than that of water. And with the increase of velocity, the turbulent fluctuation impact would increase and viscosity effect would get smaller, so the difference of flow resistance between liquid metal and water when flowing through the micro channel will get larger in the relatively higher velocity region of Fig. 3.

Convection coefficient under different coolant volume flow The mean convective heat transfer coefficient of coolant

flowing through micro channel can be calculated as:

( )w f

QhA T T

=−

（3）

with ( )p out inQ mc T T= − （4）

1 2 3 4( ) / 4wT T T T T= + + + （5）

( ) / 2f out inT T T= + （6）

where, h is the convective heat transfer coefficient, Q the total heat carried away by coolant, A the heat transfer area,

wT the wall temperature, fT the coolant mean temperature in

micro channel, m the mass flow, pc the coolant heat

capacity， inT , outT the inlet and outlet temperatures of

micro-channel respectively, and 1T ， 2T ， 3T ， 4T are the temperatures of four evenly distributed temperature-measured holes at the bottom of micro channel.

Figure 4 shows the convective heat transfer coefficient under different volume flow when liquid metal and water flow through the micro channel respectively.



Figure 4. Convection coefficient under different volume flow

From Fig. 4 it can be seen that in the low-velocity region,

the convective heat transfer coefficient of liquid metal is lower than water when flowing through micro channel. However, in the relatively higher velocity region, the convective heat transfer coefficient of liquid metal is obviously much higher than that of water. That is mainly due to: (1) liquid metal has much higher thermal conductivity than water, but its thermal capacity is relatively smaller (Table 1). In the low-velocity region, both liquid metal and water are easy to be heated in micro channel. So the cooling capability mainly depends on the coolant’s heat capacity, and the liquid metal’s advantage of high thermal conductivity would have little effect at that time. However, in the high-velocity region, the coolant flows through the channel in a short time and the temperature rise is not very significant, in that case heat capacity has little effect and the cooling capability mainly depends on the thermal conductivity of the coolant. Therefore, liquid metal shows higher convective heat transfer coefficient at that time. (2) Liquid metal has larger surface tension and is not easy to pass through small holes. Moreover, for some design and fabrication reasons, each micro channel’s flow resistance characteristics are not the same. Therefore, in the low-velocity region, liquid metal would only flow through parts of the micro channels with smaller flow resistance. So the reduction in actual convective heat transfer area may also lead to the smaller calculated convective heat transfer coefficient in Eq. (3).

Thermal resistance under different pump power Liquid metal has a much higher thermal conductivity than

water, therefore could effectively improve the cooling capability of micro channel. However, its density is also much higher, thus being used in micro channel would also increase the required pump power. Therefore, a comprehensive evaluation of the thermal resistance and pump power of liquid metal based micro channel is needed. The convection thermal resistance of micro-channel can be calculated as:

w fT TR

Q−

= （7）

where, the definition of Q， wT ， fT are the same as Eq. (3). The required pump power for fluid flowing through micro channel can be calculated as:

P pG= Δ （8）

Of which, P is the pump power, pΔ is the pressure difference between inlet and outlet of micro channel, and G is the volume flow of coolant.

Figure 5 shows the relation between convection thermal resistance and the required pump power for fluid flowing through micro channel, with the coolant is liquid metal and water respectively.

Figure 5. Thermal resistance under different pump power

It can be seen from Fig. 5 that with the increase of pump power, coolant flow increases and the convection thermal resistance of micro channel gets smaller. When pump power is small, that is, in the case of small flow, thermal resistance of micro channel with liquid metal as coolant is larger than that based on water, which is mainly due to: (1) in the low-velocity region, the convective heat transfer coefficient of liquid metal is lower than that of water when flowing through micro channel (Fig. 4). (2) With the same pump power, the volume flow and the velocity of liquid metal would be smaller because of its high density. However, as the pump power increases, which means a larger coolant flow, the thermal resistance of micro channel with liquid metal as coolant would be smaller than that based on water. That means, even with the same pump power and a smaller volume flow, thermal resistance of micro-channel using liquid metal as coolant is still smaller than that based on water. In addition, the liquid metal can be driven by a silent, nonmoving electromagnetic pump, which has higher operating efficiency than mechanical pump. Therefore, when using liquid metal as the coolant, more compact and energy-saving micro channel cooling devices with better cooling capability may come into reality.

DISCUSSION At present, lots of conclusions and correlations on micro

channel are varied, which is mainly due to that different researches had different structure designs, fabrication precisions, fluid characteristics and so on. Some authors found their experimental results quite agreed with the conventional theory, but some others got the opposite conclusion for the same range of hydraulic diameter [24]. Besides, the data of physical properties, flow characteristics, and heat transfer characters of the liquid metal as studied in this paper were rare in literature. Therefore, in this paper, the analysis of micro



channel with liquid metal as coolant was performed based on the basic flow and heat transfer theories, and the conclusions from experiment were compared with the conventional theory. Further experimental correlations and theoretical model need to be studied in the next future.

Flow pattern discrimination According to the definition of Reynolds number:

cvdReν

= （9）

where, v is the mean flow velocity, ν is the kinematic viscosity coefficient, cd is the equivalent diameter and can be calculated as:

4 cc

AdU

= （10）

Here, cA is cross-sectional area of the channel and U is the wetted perimeter. Assuming that the kinematic viscosity coefficient of GaIn20 is 0.3×10-6m2/s [22], then the largest calculated Reynolds number of water and liquid metal in the pressure difference- flow curve are 437 and 666 respectively. In fact, there was a variety of critical Reynolds numbers for micro channel from the available experimental data. Different structure sizes and fabrication precisions led to different critical Reynolds numbers, and even similar micro channels could get varied critical Reynolds numbers [24]. Therefore, it is difficult to determine the flow pattern based on past literature data on critical Reynolds numbers. However, from Fig. 3 it can be seen that the majority of the pressure difference-flow curve is linear increasing, and in the relatively higher velocity region the curve slope gets slightly larger. From the viewpoint of conventional hydrodynamics theory, flowing pattern in most of the low-velocity region is still laminar flow, while in the higher velocity region it may have been gradually transformed to turbulence flow, but that may be also due to the effect of local resistance. More specific and real judgment need to be obtained through further experiments conducted in the high-velocity region.

Flow resistance comparison Liquid metal’s density is higher than water, but its

viscosity is smaller at the same temperature. Therefore, compared with water, the flow resistance of liquid metal flowing through micro channel must be evaluated under the consideration of both density and viscosity. According to Eq. (2), the flow resistance of micro channel can be expressed as:

2 2 2

2 2 2in outv l v vp f

dρ ρ ρζ ζΔ = + + （11）

where, inζ and outζ are local resistance coefficient for inlet and outlet of micro channel respectively, and the remaining parameters are the same as Eq. (2). According to the viewpoint of conventional hydrodynamics, in the low-velocity laminar flow region, the on-way resistance coefficient could be calculated as follows:

( )fRe C γ= （12） where, the constant ( )C γ depends on the aspect ratio of the rectangular micro channel. What is more, when the velocity is relatively low and the flow pattern remains laminar after local

interference, the local resistance loss would mainly depend on the viscous shearing stress between flow layers. At this point, the local resistance coefficient is inversely proportional to Reynolds number, and can be expressed as:

Re Bζ = （13） where, the constant B is determined by the shape of local obstruction. Substituting Eq. (12) (13) and (9) into (11), it can be concluded:

p νρΔ ∝ （14） Therefore, in the low-velocity condition, the resistance as fluid flow through the micro channel is proportional to the product of fluid viscosity and density. In the experiment under low-velocity condition, the measured pressure difference ratio of liquid metal and water was about 2, which was basically in accordance with the conclusion of Eq. (14). As the flow rate increases, some local obstruction areas start to have disturbances, so Eq. (13) no longer holds true. Subsequently, the main flow region begins to transit from laminar to turbulent flow, which means the disturbance effect is strengthening, the impact of viscosity on the flow resistance starts to diminish, and the flow resistance would mainly depend on the density difference. The measured pressure difference ratio in high-velocity region of Fig. 3 increases to about 3, which basically consists with the inference. In fact, if the flow becomes vigorous turbulent flow, the flow resistance will mainly depend on the fluid pulsating, and the viscosity impact will become very small. It can be further inferred that when the flow rate continually increases, the measured pressure difference ratio of liquid metal and water will gradually approach their density ratio, but this conclusion needs further experimental confirmation.

From the above analysis it can be concluded that the flow resistance conclusion shown in the experiment basically accords with the conventional theory. However, the Eq. (12) did not consider of the developing flow in the entrance region of micro channel, mainly due to that in the previous analysis, Eq. (12) could exist only in the low-velocity condition, where the entrance region was relatively short and the impact could be negligible. In the high-velocity region, Eq. (12) and (13) would no longer hold, for the reason of laminar-to-turbulent flow transition on the one hand and on the other hand was the intensifying impact of the entrance region.

Convective heat transfer coefficient comparison According to conventional convective heat transfer theory,

the dimensionless convective heat transfer coefficient (Nusselt number) can be expressed as the function of Reynolds number and Prandtl number

( , )Nu f Re Pr= （15） In the thermal management field, the convective heat transfer coefficient is often used to evaluate the cooling capability of convection, and its relationship with Nusselt number is:

Nuhd

λ= （16）

So far, a lot of authors proposed new correlations in order to predict the Nusselt number in micro channel, but the results varied a lot, which was due to that different researches had different structural designs, fabrication precisions and fluid



characteristics and so on. However, the convective heat transfer coefficient of micro channel can generally be expressed as:

( , , , , , )ph f K u cν λ ρ= （17）

Of which, K is related to the structure parameters of micro channel. In general, the convective heat transfer coefficient is the increasing function of coolant’s thermal conductivity, density as well as the heat capacity. Therefore, in the same flowing geometry condition and same velocity, liquid metal’s high thermal conductivity is the main reason for its excellent heat dissipation capability. But with low heat capacity, the product of its density and heat capacity is still lower than water, so being easy to get temperature rise is one of the main disadvantages for liquid metal to be the suitable coolant of micro channel.

All in all, using liquid metal as the coolant of micro channel can achieve very good cooling performance only when thermal conductivity acts as a dominant factor in the heat dissipation condition. Therefore, as can be seen in Fig. 4, when the velocity is very low, the dominant factor is the heat capacity, so the convection coefficient of liquid metal may be smaller than that of water for it has lower heat capacity and is easier to get a temperature rise. However, when the velocity is relatively higher, liquid metal’s high thermal conductivity will have obvious advantage in the convective heat transfer, just as Fig. 4 shows in the high-velocity region. In that case, liquid metal based micro channel could have better cooling capability even with same pump power and smaller volume flow than that based of water. If taking into further consideration that liquid metal can be driven by a silent and nonmoving electromagnetic pump which has relatively higher operating efficiency, it can be imaged that more compact, less power consumed micro channel cooling devices with better cooling capacity may come into reality. In fact, it can be further inferred that when the flow rate continually increases, the heat transfer process would gradually depend on the fluid pulsation and the effect of thermal conductivity would get smaller. Therefore, in the condition of very high velocity, liquid metal’s relative advantage of high cooling capability compared with water would be reduced, but this conclusion needs further experimental confirmation.

What is more, in the case of liquid metal based micro channel has the same pressure drop curve with that based on water, which can be achieved by enlarging the cross section of liquid metal based micro channel, it is easy to know that the velocity of liquid metal would be smaller than that of water, while the volume flow and pressure drop are the same. That case is similar to that under the condition of same pump power shown in Fig. 5. Therefore, it can be inferred that the thermal resistance of liquid metal based micro channel might also be smaller than that based on water in the relatively higher velocity region for liquid metal has high thermal conductivity, but this conclusion needs further experimental confirmation.

Other flowing issues Liquid metal’s surface tension is relatively large, but in the

experiment it was found not difficult to enter the micro channel. The obvious advantage for liquid metal’s large surface tension lies in that the leakage would be not easy to happen in the cooling system. What is more, liquid metal has high boiling point and low vapor pressure, so the evaporation problem of

coolant could be better avoided, making the system more reliable.

However, corrosion behavior happened between liquid metal and the micro channel with T2 copper as the material, and the filter screen could be blocked by some sort of foamy substance, which might be the oxidation products of liquid metal or probably the corrosion products, and this need to be further confirmed.

CONCLUTION Liquid metal’s density is higher than water, but its

viscosity is smaller at the same temperature level. In the same flow geometric condition and the same volume flow, the flow resistance when liquid metal flows through micro channel would be higher than that of water. In the experiment, under low-velocity condition, the measured pressure difference ratio of liquid metal and water was about 2. With the increase of velocity, pressure difference ratio of liquid metal and water would raise higher. It is further inferred that when the flow becomes vigorous turbulent flow, the measured pressure difference ratio of liquid metal and water will gradually approach their density ratio, but this conclusion needs further experimental confirmation.

Liquid metal has much higher thermal conductivity than water, but its heat capacity is relatively smaller. In the low-velocity region, the dominant factor is the heat capacity, and the convective heat transfer coefficient of liquid metal may be smaller than that of water. However, when the velocity is relatively higher, liquid metal’s high thermal conductivity will have obvious advantage in the convective heat transfer. Therefore, taking into further consideration that liquid metal can be driven by a silent and nonmoving electromagnetic pump efficiently, when using liquid metal as the coolant, more compact and energy-saving micro channel cooling devices with better cooling capability may come into reality.

Using liquid metal as the coolant of micro channel cooing devices, the leakage and evaporation problems could be better avoided. Moreover, the liquid metal can be driven efficiently by an electromagnetic pump without any moving parts. So the cooling system would run more stable. However, corrosion and blocking problems did exist in the liquid metal based micro channel, which would greatly affect the performance or even endanger the running of cooling system. These issues still need to be further studied.

ACKNOWLEDGMENTS This work is partially supported by the National Natural

Science Foundation of China under grant 50576103.

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