Heat Dissipation System Based on Electromagnetic-Driven Rotational Flow of Liquid Metal Coolant

With the rapid advancement of electronic information technology, the integration degree of the semiconductor integrated circuit is growing up with its function strengthening. And the ever-increasing power density of the integrated circuit device will definitely lead to large temperature rise which reduces the stability and the lifetime of the device [1,2]. Empirical data show that the failure rate of microelectronic system doubles with every 10 °C increase in temperature [3]. Therefore, efficient heat dissipation is receiving more and more attention. Up to now, there are several main heat dissipation methods including air cooling [4], liquid cooling [5], heat pipe cooling [6], and semiconductor cooling [7]. Air cooling is the simplest heat dissipation method and is not suitable for high heat flow density chip cooling condition due to the large-size fins and the high thermal resistance [8,9]. Heat pipe cooling is a passive heat transfer method and contains liquid evaporation and gas condensation processes. There are various factors influencing the heat pipe performance including capillary limit, boiling limit, viscous limit, entrainment limit, vapor limit, and so on [10,11]. Semiconductor cooling method takes advantage of the Seeback, Peltier, and Thomson effects to implement active cooling. Water vapor condensation is easy to occur on the cold side of the semiconductor radiator and could lead to short-circuit fault. And the size of the semiconductor radiator becomes larger with the increase of the radiating power [12]. Liquid cooling is one of the most widely used heat dissipation strategies [13–15]. And the working medium can be various liquid including water [16], water-based nanofluids [17], liquid metal [18,19], and so on. Water is the most commonly used liquid cooling medium. Although it has a high heat capacity of 4.2 J/(g · °C), the low boiling point (100 °C at 1 atm) hinders its application in high temperature cooling environment. Compared with water or other liquid-phase working medium, liquid metal has the highest thermal conductivity in all the fluid materials. For example, Ga is a kind of room temperature liquid metal with melting point of 29.8 °C. And the thermal conductivity of Ga is about 50 times larger than that of water. In addition, the boiling point of Ga is 2403 °C and the liquid-phase range is 2373.2 °C [20]. The high thermal conductivity and the high boiling point of liquid metal enable it to be an ideal liquid cooling medium in various heat dissipation working conditions including chip cooling [21,22], laser diode array cooling [23], nuclear cooling [24,25], concentrated solar cooling [26,27], and so on. The application of liquid metal in chip cooling research has received more and more attention in recent years and many related heat dissipation coolants and techniques have been developed. Ma and Liu [28] proposed a concept of nano liquid metal coolant fabricated by addition of high thermally conductive nano particles into liquid metal. Deng and Liu [29] demonstrated a hybrid liquid metal–water cooling system combining the merits of both liquid metal and water. Yang and Liu [30] fabricated an electrically driven chip cooling device by using liquid metal and aqueous solution as the coolants. Yang et al. [31] demonstrated the flow and thermal model of liquid metal-based mini-channel heat sink. However, existing heat dissipation structures with hybrid coolants combining liquid metal and other fluids are relatively complex and are not conductive to effective integration. This paper is dedicated to introduce a new type of compact liquid metal cooling system with the rotational flow of liquid metal activated by electromagnetic field.

Ga_68.5In_21.5Sn₁₀ (melting point ∼11 °C, nontoxic) is selected as the liquid metal coolant and its weight is 17.9 g. The preparation process of Ga_68.5In_21.5Sn₁₀ is as follows: Gallium, indium and tin with purity above 99.99% purchased from Zhuzhou Keneng New Material Co., Ltd. were weighed according to the mass ratio of Ga: In: Sn = 68.5: 21.5: 10. And then they were put in a beaker. The beaker was placed under vacuum conditions and in 90 °C constant temperature water bath heated for about 2 h, followed by stirring the metals continuously and cooling to room temperature after uniform mixing.

A piece of annulus-shaped rubidium-iron-boron magnet is adopted to produce a uniform magnetic field. The size of the magnet is 40 mm inner diameter and 50 mm outer diameter and 5 mm length. The magnetic induction strength of the magnet is measured by a digital TESLA meter (YJT-100, Xi'an Qingcheng Electromechanical Equipment Co., Ltd.), and the measurement result is presented in Fig. 1(a). It can be seen that there is a uniform distribution of magnetic induction strength in the hollow part of the magnetic ring. And this guarantees a uniform Ampere force distribution subjected by liquid metal.

A micro high temperature ceramic electric heater is used for the heat source which is presented as the inset of Fig. 1(b). The size of the electric heater is 10 mm × 10 mm × 1 mm. Figure 1(b) shows its temperature–time, heating power–time, and heating voltage–time relationships. The temperature of the electric heater was measured by a T-type thermocouple attached to its surface with the temperature detection error within 0.1 °C. The measurement was performed two times under room temperature of 22.1 °C. And the standard deviation of the two measurements is 10.02 °C with the data acquisition points of 187. It can be seen from Fig. 1(b) that there is a better consistency between the two measurements as the time is less than about 21 s and the temperature is less than about 131 °C. As the temperature continues to rise, the measurement error intermittent increases while the two measurement results turn out to be quite consistent at the points indicated by the red arrows. Such law of change may be due to the heat transfer characteristics of the electric heater itself. In addition, it can also be seen that the heating power and the temperature gradually tend to be stabilized at constant applied voltage, and the time constant of the heating power is approximately the same as the stable time of the temperature. Generally speaking, there is a corresponding relationship between heating power and temperature of the electric heater, and the heating power of 4.2 W corresponds to the temperature of about 230 °C.

Graphite is selected as the electrode material. It is a kind of nonmetal conductor with electrical conductivity of 3 × 10³ S/m. The anode is a cylinder with diameter of 5 mm and length of 8 mm, while the cathode is a ring-shaped object with 30 mm internal diameter, 40 mm external diameter, and 10 mm height, respectively. As liquid metal has a poor wettability on the surface of graphite electrode, the low motion resistance enables its smoothly moving under electromagnetic actuation force [32].

The schematic diagram and the external appearance of the experimental device are presented in Figs. 2(a) and 2(b), respectively. The electric heater is attached to the bottom surface of a piece of square shaped AlN ceramic plate by using thermal silicone grease. And on the upper surface of the ceramic plate, there is a pair of dual ring-shaped graphite electrodes. Liquid metal is located between the cylindrical-shaped anode and the annulus-shaped cathode. Magnetic field is provided by an annulus-shaped permanent magnet located on the top of the cathode, and its direction is perpendicular to the top surface of liquid metal. Liquid metal can be driven by Ampere force to rotate around its central axis when the electrodes are electrified. In order to conduct the heat to air environment timely, a piece of copper fin is attached to the ceramic plate. To detect real-time temperature of the heat dissipation system, seven temperature monitoring points have been set up on the experimental device which are indicated as numbers 1–7 presented in Fig. 1. The points 1–5 represent different positions on the surface of liquid metal. And the points 6 and 7 represent the temperature of the electric heater and the radiator, respectively. In order to fix the junction of the thermocouple firmly at point 6, a piece of copper plate with a slot was set between the electric heater and the ceramic plate, and the junction was put in the slot. Then the surface temperature of the electric heater will thus be measured. Seven T-type thermocouples were placed in the graphite electrodes or the liquid metal to perform the temperature monitoring in real time, and the temperature measurement error is within ±0.1 °C. These thermocouples were fabricated with copper and constantane wires which were purchased from Shanghai Sanguang Electric Alloy Co., Ltd. In addition, an Agilent 34970A is used to monitor and collect the real-time information of temperature and voltage at a sample rate of 2 samples/s.

The initial and boundary conditions of the numerical simulation are shown in Table 1.

A simulation model is developed to present the velocity distribution of the liquid metal after electrifying the electrodes. The numerical model was implemented in COMSOL Multiphysics 5.4 which is a powerful software platform for investigating the multi-physical coupled fields.

According to practical sizes of the constituent parts of the experimental setup, a 3D finite element method model based on self-adaption grid division was established to simulate the multi-physical fields coupled together including electromagnetic field, thermal field and flow field. Since the heat transfer process and the fluid flow process are all unsteady, a transient solver was used during the calculation. And segregated algorithm and conjugate gradient iterative procedure were carried out to solve the conservation equations. A grid independence test was performed and is presented in Fig. 4. The temperature of the electric heater was monitored when the grid number is 20169, 35712, 67387, 171213, 276106, and 661177, respectively. It can be seen from Figs. 4(a) and 4(b) that the temperature of the electric heater gradually decreased to a nearly stable value with the increase of grid number. And there is an approximately linear relationship between computational time and grid number. Considering the factors of calculating accuracy and computational time, grid number of 661177 was finally selected for simulation. The computational domain and the grid structure of the simulation model of the experimental setup are shown in Fig. 4(c) and 4(d), respectively. And the statistical information of the model grid is listed in Table 2.

To validate the numerical results, a comparison between numerical and experimental steady temperature results of the monitor points 6 (the heater) and 4 (the liquid metal) is presented in Fig. 5. The heat flow density of the heater is 12.276 W/cm² and the values are acquired at 300 s. As to the monitor points 6 and 4, the percentage errors between the numerical and experimental results are, respectively, 1.62% and 1.64%, which shows a good consistency. And the numerical results can be considered reliable.

Let us analyze qualitatively the velocity and temperature distribution of the experimental device. It can be seen from Fig. 6(a) that the velocity is generally centrosymmetric distributed around the central cylinder anode. And the maximum velocity appears near the anode. The velocity decreases with the increase of the distance from the anode and gradually increases near the cathode. The reason can be elucidated that the current density has the maximum value in the region near the anode, and the magnetic induction intensity in the region near the cathode is higher than that in other regions.

As can be seen from Fig. 6(b), the minimum velocity appears in the regions near the bottom of the electrodes. It is due to the high friction force between the liquid metal and the graphite electrodes. In the middle area between the two electrodes, the velocity in the upper region is large than that in the lower region. It can be attributed to the surface oxidation layer which increases the moving resistance of the liquid metal.

The temperature distribution of the heat dissipation device is shown in Figs. 6(c) and 6(d). It can be seen that the temperature decreases gradually from the electric heater to the surrounding areas. And the temperature in the area above the top edge of the electric heater is much higher than that in the area below the bottom edge of the electric heater. Therefore, the role of the rotated liquid metal is to distribute the temperature evenly throughout the heat dissipation system.

The transient thermal resistance–time changing curve is characteristic of nonlinearity in the heating process of the heater. Figure 7(a) are the total radiating power–time, R_total-time, R_heater-lm-time, R_lm-rad-time, and R_rad-amb-time curves when the heating power is set as 7.1 W and the electric power of the liquid metal is set as 0.87 W. It can be seen that the heating power increases sharply at the beginning and then keeps steady with the time. R_total(t), R_heater-lm(t), R_lm-rad(t), and R_rad-amb(t) are in exponential relationship with the time.

By fitting the experimental data with the analytic model, R_i and C_i for R_total(t), R_heater-lm(t), R_lm-rad(t), and R_rad-amb(t) are presented in Table 3.

Figure 8 shows the changing relationship among R_heater-lm-time, R_lm-rad-time, and R_rad-amb-time curves when the heating power/voltage are set as typical values including 0.083 W/0.904 V, 0.331 W/1.809 V, 0.738 W/2.716 V, 3.755 W/6.386 V, 5.913 W/8.252 V, and 13.641 W/13.949 V, respectively. It can be seen that when the heating power is 0.083 W, R_heater-lm is a negative value which is about –0.37 °C/W (Fig. 8(a)), and as the heating power increases to 0.331 W, R_heater-lm changes from a negative to a positive value which is about 0.23 °C/W (Fig. 8(b)). As the heating power is set as 0.738 W, R_heater-lm is larger than R_lm-rad but lower than R_rad-amb (Fig. 8(c)). The stable value of R_heater-lm becomes larger and larger with the increase of the heating power (Fig. 8(d)). It equals to that of R_rad-amb when the heating power is 5.913 W (Fig. 8(e)), and it becomes the maximum value of the three parts thermal resistances as the heating power continues to increase (Fig. 8(f)).

It can be seen from Fig. 9 that all the measured curves are approximately linear with different slope values. As to T_heater, the slope value is about 1.033 °C/W. When 0 < m < 1, T_heater can be lower than the average temperature of liquid metal, and R_heater-lm can be a negative value which is mentioned above. The demarcation point between R_heater-lm > 0 and R_heater-lm < 0 is m = 1 which corresponds to Q_heater = 0.92 W. And if the temperature of the electric heater is to be controlled within 80 °C which corresponds to Q_heater = 12.32 W, then the heating power of the electric heater should be less than 12.32 W. The system presented above exhibits excellent heat dissipation performance compared with liquid metal-based heat dissipation systems introduced in related references as shown in Table 4. As the heat flow density of the heating source are, respectively, set as 3.15 W/cm² and 3.5 W/cm², the temperature of the heating source can be controlled within 38.6 °C and 39.8 °C which is a great improvement compared with previous works [5,36].

In summary, we have presented an electromagnetic driven liquid metal-based heat dissipation system. Liquid metal is situated between the dual ring-shaped electrodes and rotates around the anode by an electromagnetic field. The velocity profile throughout the liquid metal is demonstrated and the results show that the velocity is distributed unevenly along longitudinal section. The temperature profile of the experimental device shows that high temperature region is located on the electric heater side and liquid metal plays an important role in the flatting of temperature distribution. The thermal resistance model of the heat dissipation system is established. The total thermal resistance R_total of the system contains three parts and the size relationship between each part is analyzed. And R_total tends to be a stable value of 4.42 °C/W. As to the heat dissipation system, there is an approximately linear relationship between the temperature of the electric heater and the heating power. And the heating power should be less than 12.32 W when the temperature of the electric heater is to be controlled within 80 °C. Liquid metal-based thermal management introduced in the paper serves as an effective solution for the electronic heating systems with limited space.

This work was partially supported by the National Science Foundation for Young Scientists of China (Grant No. 51706234) and CAS Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry (CRYOQN201909).

There are no conflicts of interest.

The authors attest that all data for this study are included in the paper.

c =

speed of light (m/s)

h =

convective heat transfer coefficient (W/(m² · °C))

i =

subscript index

j =

subscript index

m =

ratio

q =

heat flux (W)

t =

time (s)

v =

velocity (m/s)

w =

enthalpy per unit mass (J/kg)

L =

size (m)

P =

pressure (Pa)

Q =

the radiating power of the heat transfer system (W)

R =

transient thermal resistance (°C/W)

T =

temperature (°C)

U =

wind velocity (m/s)

q =

energy flow density (W/m²)

v =

velocity vector (m/s)

B =

magnetic induction intensity vector (mT)

E =

electrical filed intensity vector (V/m)

F =

Lorentz force (N)

H =

magnetic field intensity vector (A/m)

J =

electrical current density vector (A/m²)

c_P =

heat capacity at constant pressure (J/(kg · °C))

C_i =

heat capacity of the heat transfer model (J/(kg · °C))

Q_{heating power} =

the total radiating power of the heat transfer system (W)

Q_{total power} =

the total radiating power of the heat transfer system (W)

R_{AlN plate-lm} =

the convective thermal resistance between AlN plate and liquid metal (°C/W)

R_{AlN plate-rad} =

the contact thermal resistance between AlN plate and fan radiator (°C/W)

R_{heater-AlN plate} =

the contact thermal resistance between heater and AlN plate (°C/W)

R_heater-lm =

the thermal resistance between heater and liquid metal (°C/W)

R_i =

thermal resistances of the heat transfer model (°C/W)

R_{lm-AlN plate} =

the convective thermal resistance between AlN plate and liquid metal (°C/W)

R_lm-rad =

the thermal resistance between liquid metal and fan radiator (°C/W)

R_rad-amb =

the thermal resistance between fan radiator and ambient (°C/W)

R_total =

total thermal resistance (°C/W)

T_amb =

the temperature of ambient (°C)

T_heater =

the temperature of the electric heater (°C)

T_lm =

the temperature of liquid metal (°C)

T_p1, T_p2, T_p3, T_p4, T_p5 =

the temperature of the five system monitoring points (°C)

T_rad =

the temperature of fan radiator (°C)

Pr =

Prandtl number

ɛ =

internal energy per unit mass (J/kg)

η =

dynamic viscosity (N · s/m²)

λ =

thermal conductivity (W/m · °C)

μ =

magnetic susceptibility

ν =

kinetic viscosity (m²/s)

ρ =

density (kg/m³)

σ =

electric conductivity (S/m)