Liquid Metal-Enabled Synergetic Cooling and Charging of Superhigh Current

Chuanke Liu; Maolin Li; Daiwei Hu; Yi Zheng; Lingxiao Cao; Zhizhu He

doi:10.1016/j.eng.2024.11.035

Engineering ›› 2025, Vol. 47 ›› Issue (4) :125 -138. DOI: 10.1016/j.eng.2024.11.035

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Liquid Metal-Enabled Synergetic Cooling and Charging of Superhigh Current

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Abstract

High-power direct current fast charging (DC-HPC), particularly for megawatt-level charging currents (≥ 1000 A), is expected to significantly reduce charging time and improve electric vehicle durability, despite the risk of instantaneous thermal shocks. Conventional cooling methods, which separately transmit current and heat, struggle to achieve both flexible maneuverability and high-efficiency cooling. In this study, we present a synergetic cooling and transmission strategy using a gallium-based liquid metal flexible charging connector (LMFCC), which efficiently dissipates ultra-high heat flux while simultaneously carrying superhigh current. The LMFCC exhibits exceptional flexible operability (bending radius of 2 cm) and transmission stability even under significant deformation owing to the excellent liquidity and conductivity of liquid metal (LM). These properties are markedly better than those of solid metal connector. A compact induction electromagnet-driven method is optimized to significantly increase the LM flow rate and the active cooling capacity, resulting in sudden low temperature (< 16 °C at 1000 A). This synergetic cooling and charging strategy are expected to enable ultrahigh-heat-flux thermal management and accelerate development of the electric vehicle industry.

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Keywords

Electric vehicle / Superhigh current charging / Liquid metal / Synergetic-cooling strategy / Flexible charging cable

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Chuanke Liu, Maolin Li, Daiwei Hu, Yi Zheng, Lingxiao Cao, Zhizhu He. Liquid Metal-Enabled Synergetic Cooling and Charging of Superhigh Current. Engineering, 2025, 47(4): 125-138 DOI:10.1016/j.eng.2024.11.035

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1. Introduction

As global energy structures evolve and environmental awareness increases, advanced electric vehicle (EV) technology has become crucial for reducing carbon emissions and addressing resource challenges [1], [2], [3], [4], [5], [6], [7], [8]. The International Energy Agency’s “World Energy Outlook 2023” report indicates that the number of EVs worldwide will increase nearly 10-fold by 2030 [9]. However, challenges such as range anxiety and long charging time continue to impede widespread EV adoption compared with traditional fuel vehicles [10], [11], [12], [13], [14]. High-power fast charging (HPC) technology has emerged as a promising solution to reduce charging time, making it comparable to conventional refueling [15], [16], [17], [18], [19], [20]. Recent innovations have boosted the peak charging power of direct-current (DC)-HPC systems from 43.5 to 450 kW, with new standards targeting 600 kW and even 1 MW [21], [22], [23], [24], [25]. These advancements enabled full charging in only 20 min, as illustrated in Fig. 1. However, future demands pose significant challenges for DC-HPC, particularly the need to fully charge EVs equipped with a 100 kWh battery in under five minutes. This challenge is further compounded by the requirement of ultrahigh-current charging exceeding 3000 A for electric trucks, aircraft, and ships. The resulting instantaneous large heat shock can potentially hinder the development of next-generation DC-HPC technology [26], [27], [28], [29].

As the charging currents in DC-HPC systems increase, the resulting Joule heating significantly increases the temperature of power lines, accelerating aging and increasing the risk of fire hazards [30], [31], [32], [33]. Although increasing the diameter of power lines can reduce Joule heat, it makes cables bulkier and less flexible owing to the rigidity of traditional copper conductors. Currently, leading companies in the global energy and automotive industries have introduced liquid-cooled HPC technology capable of handling ultra-large currents [34], [35], [36], as illustrated in Figs. 1(b) and (c). However, traditional water/oil-based cooling methods attempt to separate the current conduction and heat transfer processes, which are limited by the thermophysical properties of the cooling medium, flow channel structure, and overall thermal dissipation strategy. These limitations lead to complicated charging systems with short lifespans, high failure rates, and high maintenance costs. The emerging supercooled liquid-phase boiling cooling method [37], [38], which boasts significant heat absorption capabilities and can handle currents exceeding 2400 A, holds potential for reducing EV charging time to just five minutes. However, this approach faces significant limitations, including restricted cable lengths, poor reliability, and localized hot-spot-induced failures. Therefore, to meet the future demands of ultra-high charging currents, it is crucial to design DC-HPC charging systems with flexible maneuverability and highly efficient cooling.

Liquid metal (LM)-based cooling technology [39], [40], [41], [42], [43], [44], [45], [46], [47] has gained increasing importance in various industrial applications, including nuclear energy management, solar power generation, high-temperature thermal storage, and waste heat recovery. Compared to the hazardous sodium–potassium alloys and the high melting points of lead–bismuth alloys, room-temperature gallium-based LM offers several advantages, such as outstanding biocompatibility, high thermal conductivity (∼30 W·mK⁻¹), low viscosity (∼2 × 10⁻³ Pa·s), and high boiling point (∼2200 K) [48], [49], [50]. These properties make LM particularly appealing for cooling electronic devices with high heat fluxes, drawing significant interest from both academia and industry [51], [52], [53], [54]. Relevant studies [55], [56], [57] have demonstrated that the convective thermal transfer performance of LM is significantly superior to that of traditional cooling fluids such as water or oil, offering comprehensive benefits in high heat flux dissipation, particularly regarding pressure reduction (when used with microchannels) and cooling capacity enhancement. Additionally, LM-based cooling technology utilizes an advanced electromagnet-driven method in which fluid movement is controlled by the Ampère force generated through the interaction between the induced current and magnetic flux density [58], [59]. This method improves the operational reliability and eliminates issues such as blade wear and coolant leakage, which are common in LM owing to their high density and high surface tension. It differs fundamentally from the traditional mechanical pumping, which relies on interface driving (such as blade rotation) [60]. The emerging LM-based cooling technology presents promising opportunities for megawatt-level DC-HPC systems (> 1000A), particularly in addressing the need for operational flexibility and efficient cooling [61].

In this study, we report a novel synergetic cooling and charging strategy enabled by a gallium-based LM flexible charging connector (LMFCC) and specifically designed for DC-HPC systems. This approach represents a significant advancement in managing instantaneous large heat shocks while ensuring the efficient transmission of superhigh charging currents. We systematically investigated the flexibility and transmission stability of LMFCC relative to traditional solid metal connectors, even under extreme deformation conditions. Additionally, we developed a compact induction electromagnet-driven method, outlining the magnetohydrodynamics (MHD) generation process and identifying key performance factors to optimize the pumping capability and boost the active cooling capacity of the LMFCC system. Finally, we constructed a three-dimensional multi-physics numerical model and established a synergetic cooling and transmission test platform to comprehensively assess the adaptability of the LMFCC to superhigh charging currents across varying hydrodynamic and geometric parameters.

2. Experiments and methods

2.1. Working principle of synergetic cooling LMFCC

Fig. 2 illustrates the LMFCC synergetic cooling and charging system for superhigh currents, comprising DC+/DC− LM flexible cables (LMFCs), induction electromagnet-driven units, transition connection units, LM-enhanced heat dissipation units, and LM-based charging guns. The DC+ (or DC−) LMFC contains two charging cables filled with LM to form independent coolant-circulating loops through a channel within the transition connection unit. This unit connects the EVs and charging stations, facilitating the transfer of electrical energy from the grid power to the vehicle battery. The induction electromagnet-driven unit achieved by rotating permanent magnets (PM-EMP) can generate an Ampère force that effectively pumps the LM into the transition connection unit and subsequently through the DC+ and DC− coolant-circulating loops. Notably, DC-HPC enables the directional transmission of electrical energy accompanied by thermal generation, accumulation, and dissipation. This can lead to significant temperature increases in the LMFC, accelerating aging and posing fire safety risks, particularly at superhigh currents. The instantaneous large thermal shock is swiftly mitigated by the PM-EMP-driven LM, which transports heat to the radiator at the charging station, achieving efficient convection heat transfer between the coolant and air. Therefore, we developed a synergetic cooling and charging strategy enabled by the LMFCC for DC-HPC, where the LM serves as an excellent heat-carrying coolant and effective current-carrying conductor. This approach offers new opportunities for achieving a simple, reliable, lightweight charging system with low maintenance cost and outstanding cooling capacity, even for future ultrahigh charging power (> 1 MW). Furthermore, the fluid nature of the LM enables the LMFCC to have superior flexibility and transmission stability compared with traditional rigid copper cables.

Figs. 2(c) and (d) provide a detailed illustration of the integrated induction electromagnet-driven strategy for the LMFCC. The PM-EMP integrates an active-rotating magnetic system and LM pumping body. In this system, several internal permanent magnets are evenly distributed on the outer surface of a three-phase coil mounted on an inner yoke iron (YI) to form an active-rotating element. Additionally, outer permanent magnets are placed on the annular inner yoke, with a highly magnetoresistive layer separating them from the active driving element. The C-shaped pumping body, embedded in a rectangular LM channel, is supported by a stable base and support structure to ensure reliable operation. The outer YI, arranged on the outer surface of the pump body in a tile structure, provides a low-reluctance path for the magnetic field lines. When an alternating current is applied to the three-phase coil, a rotating magnetic field is generated, which induces a current within the LM. The interaction between the magnetic and current fields produces an electromagnetic force that effectively drives LM flow. PM-EMP offers significant advantages, including enhanced pumping reliability, elimination of issues related to blade wear and fluid leakage, and increased output power density.

2.2. Experiment setup of synergetic cooling LMFCC

To comprehensively evaluate the adaptability of the LMFCC to a superhigh charging current, we developed a bench test platform, as illustrated in Fig. 3. It mainly includes a synergetic cooling LMFCC, a DC high-power supply, and multisensing signal collection and acquisition systems. The LMFC is constructed from two highly elastic silicone tubes filled with LM, with inner diameters (D) ranging from 6 to 10 mm and lengths (L) from 0.5 to 2.0 m. To improve the electrical contact between the transition connection unit (T2 copper) and the LM coolant, the copper surface was electroplated to enhance wettability. The pump body, crafted from a high-temperature-resistant and high-toughness resin using advanced three-dimensional printing technology, is designed to minimize the shunt effect of induced currents in the LM and to enhance the driving capability. The permanent magnet used is an N54 NdFeB with a residual magnetic flux density of 1.4 T (T = Tesla), whereas the YI is made from 50W470 to reduce energy losses. The LM, which serves as both the current- and heat-carrying medium, is a Ga₆₈In₂₀Sn₁₂ alloy, prepared by mixing 68% Ga, 20% In, and 12% Sn at 200 °C for two hours. The positive and negative terminals of the DC power source (SSA-151000, Bufan, China) are connected to the LMFCC transition connectors to simulate a superhigh-current transmission. Four pressure sensors (CYYZ11A, Xingyi, China; measuring range 0–500 kPa, accuracy ±0.10%) are positioned at the LMFC inlet (P_in; P means pressure) and outlet (P_out) to measure pressure loss (ΔP = P_in − P_out). Multiple temperature sensors (PT-100, Kepai, China; measuring range 10–150 °C, accuracy ±0.15%) are placed at the LMFC inlet (T_in; T means temperature), outlet (T_out), and radiator outlet (T_r-out) to monitor the heat generation, accumulation, and dissipation characteristics of the LMFCC, respectively. Additionally, two flow rate sensors (test range 0.3–5.0 L·min⁻¹, accuracy ±3.00%) are located at the PM-EMP outlet to measure the LMFCC system flow rate (G). An uncertainty analysis [62] of the LMFCC system is presented in Note S1 and Table S1 in Appendix A. The thermophysical parameters [54], [59], [63] of all components are listed in Table S2 in Appendix A.

2.3. Numerical method

2.3.1. Three-dimensional multi-physics model for integrated PM-EMP

To enhance the LM driving efficiency and improve the LMFCC thermal control capacity, we developed a fully coupled multi-physics numerical model for the PM-EMP. This model provides a comprehensive analysis of the MHD generation process, encompassing electromagnetics, hydrodynamics, instability, and end effects, while systematically exploring the factors that influence the performance. The Reynolds number (Re) calculation of the LM within the PM-EMP is presented in Note S2 in Appendix A. Consequently, the complex and highly nonlinear constitutive equation of the PM-EMP is defined as follows:

(1)

\{\begin{matrix} \nabla \times H_{m} = J \\ B = \nabla \times A \\ E = - \frac{\partial A}{\partial t} \\ \nabla \cdot B = 0 \\ J = σ (E + U_{L M} \times B) \end{matrix}

(2)

\{\begin{matrix} \frac{\partial U_{L M}}{\partial t} + (U_{L M} \cdot \nabla) U_{L M} = - \frac{1}{ρ} \nabla P + \frac{1}{ρ} J \times B + μ \nabla^{2} U_{L M} \\ \nabla \cdot U_{L M} = 0 \end{matrix}

where

B

A

, and

H_{m}

represent the flux density, vector potential, and field strength of the magnetic field, respectively.

E

and

J

denote the electric field intensity and current density, respectively, and μ is the dynamic viscosity.

σ

is the electrical conductivity;

U_{L M}

velocity of LM flow;

ρ

is the density.

\nabla

is the the nabla operator and

t

is the time. Bidirectional coupling between the electromagnetic and fluid fields is achieved by introducing a volume force (the vector product of the current and magnetic flux density) as an external term in the Navier–Stokes equation, whereas the fluid velocity is reintegrated into the electromagnetic field as a negative influence. The no-slip condition is applied at the fluid walls. The flow rate (Q) and pressure boundary (P₀ = 0 kPa, representing relative pressure) are set at the inlet and outlet, respectively. To ensure the accuracy of the numerical calculations, grid independence verification for the PM-EMP was performed, as presented in Table S3 in Appendix A. The results indicate that the grid 4 division method is uniformly applied to all simulation working conditions of the PM-EMP.

2.3.2. Fully coupled model of current–heat–fluid for LMFC

To address the significant engineering challenges associated with megawatt-level (> 1000 A) DC-HPC, we developed a three-dimensional fully coupled numerical model of an LMFC to explore the factors influencing performance. First, for a cylindrical channel, Re varies from 12 171 to 101 430, implying that the k₀-ε turbulent flow model was applied to simulate the hydrodynamic characteristics. Additionally, the operation of an LMFC involves complex multi-physics processes, including current flow, electromagnetic heating, fluid dynamics, heat transfer, and nonisothermal flow, all of which can be described by the following equations:

(3)

\{\begin{matrix} \nabla \cdot J_{L M F C} = 0 \\ \nabla \cdot E_{L M F C} = 0 \\ J_{L M F C} = σ E_{L M F C} \\ ρ C_{p} (\frac{\partial T}{\partial t} + U_{L M} \cdot ▱ T) = \nabla \cdot (k \nabla T) + J_{L M F C} \cdot E_{L M F C} \\ ρ (\frac{\partial U_{L M}}{\partial t} + U_{L M} \cdot ▱ U_{L M}) = - \nabla P + \nabla \cdot [(μ + μ_{t}) (\nabla U_{L M} + {(\nabla U_{L M})}^{T})] \\ \frac{\partial (ρ k_{0})}{\partial t} + \nabla \cdot (ρ k_{0} U_{L M}) = \nabla \cdot [(μ + \frac{μ_{t}}{σ_{k_{0}}}) \nabla k_{0}] + μ_{t} (\nabla U_{L M} : \nabla U_{L M} - \frac{2}{3} {(\nabla \cdot U_{L M})}^{2}) - ρ ε \\ \frac{\partial (ρ ε)}{\partial t} + \nabla \cdot (ρ ε U_{L M}) = \nabla \cdot [(μ + \frac{μ_{t}}{σ_{ε}}) \nabla ε] + C_{ε 1} \frac{ε}{k_{0}} μ_{t} (\nabla U_{L M} : \nabla U_{L M} - \frac{2}{3} {(\nabla \cdot U_{L M})}^{2}) - C_{ε 2} \frac{ε^{2}}{k_{0}} \\ \nabla \cdot U_{L M} = 0 \end{matrix}

where

J_{L M F C}

and

E_{L M F C}

represent the current density and electric field intensity of the LMFC, respectively. μ_t, k₀, and ε represent the viscosity, kinetic energy, and dissipation rate of turbulence, respectively, and C_ε1 and C_ε2 denote the model constants.

C_{p}

is the specific heat capacity; k is the thermal conductivity;

▱ T

and

▱ U_{L M}

are the gradient of temperature and LM velocity, respectively.

σ_{k_{0}}

and

σ_{ε}

are the Prandtl numbers of turbulent kinetic energy and turbulent dissipation rate, respectively. The constant temperature (T₀ = 30 °C), flow rate (G ranging from 2 to 10 L·min⁻¹), and ground boundary are set at the inlet of the LMFC. The open, ground, and pressure boundary (P₀ = 0 kPa) are applied to the outlet of the LMFC. Additionally, the current boundary (I ranging from 100 to 1500 A) conditions are set at the mid-section of the LMFC. Owing to the low thermal conductivity of the silicone tube, the adiabatic boundary conditions are set on other outer surfaces of the LMFC. Furthermore, the grid independence verification of the LMFC is performed, as presented in Table S4 in Appendix A. The results indicate that the grid four partitioning method applies to all the simulation conditions for the LMFC.

2.4. Method validity

To validate the effectiveness of our method, we conducted a comparative analysis of the PM-EMP performance and LMFCC heat transfer characteristics using both numerical simulations and experiments, which are presented in Note S3 and Fig. S1 in Appendix A. As shown in Fig. S1(a), a comparison between the experimental and simulation data reveals a strong correlation, confirming the validity and accuracy of the PM-EMP numerical simulation. For instance, at a flow rate of Q = 0.2 L·min⁻¹ and n = 150 r∙min⁻¹, the experimental pressure head values were 47.8 kPa, while the simulation results yielded 44.9 kPa, indicating deviations of 6.5%. Fig. S1(b) shows a consistent relationship between the numerical and experimental data, demonstrating the accuracy of the LMFC model. For instance, at I = 1000 A, the maximum temperature deviations of the LMFC were 5.2% (L = 1.0 m) and 3.3% (L = 2.0 m).

3. Results and discussion

3.1. Driving performance optimization of synergetic cooling LMFCC

3.1.1. Magnetic field

We systematically discuss the MHD generation process and driving performance optimization of the synergetic cooling LMFCC. YI and SBS represent the yoke iron and short-circuit bar structure, respectively. According to a previous study [64], the equation for estimating the maximum pressure of the PM-EMP (ΔP_max) is as follows:

(4)

\{\begin{matrix} Δ P_{max} = \frac{σ B^{2} s {\bar{U}}_{B} l_{ch} K_{l}}{2} \\ s = 1 - \frac{{\bar{U}}_{LM}}{{\bar{U}}_{B}} \end{matrix}

(5)

\{\begin{matrix} K_{l} = R [\frac{α^{2}}{λ^{2}} (1 - \frac{t h (\frac{λ W}{2})}{\frac{λ W}{2}})] \\ λ^{2} = α^{2} (1 + i ε_{0}) \\ ε_{0} = \frac{σ μ_{0} {\bar{U}}_{B} s τ H}{π H_{ng}} \\ α = \frac{π}{τ} \end{matrix}

where s,

{\bar{U}}_{B}

, l_ch, and K_l denote the slip rate, magnetic field travel average velocity, effective length, and lateral end effect attenuation coefficient, respectively, and ε₀, H_ng, and τ represent the magnetic action parameter, nonmagnetic gap, and magnetic pole distance, respectively.

B

is the magnetic flux density; W is the channel width of PM-EMP; H is the channel height of PM-EMP;

{\bar{U}}_{LM}

is the average velocity of LM;

R

is the the real part of a complex number;

α

is the number of pole pairs within a distance of 2π;

λ

is a new complex parameter;

t h

is the hyperbolic tangent function (tanh);

i

is the imaginary unit, and μ₀ denotes the magnetic permeability of air. Therefore, B² is proportional to the PM-EMP driving capacity. The magnetic field variations and enhancement mechanisms of the PM-EMP are analyzed, as shown in Fig. 4. As shown in Figs. 4(a)–(c), the radial magnetic flux density (B_r) along the LM flow direction exhibited a non-sinusoidal distribution, particularly in the absence of YI. This occurs because the magnetic loop (first magnetic path) between adjacent magnets is weakened, whereas the path (second magnetic circuit) from the N to the S poles of the magnet itself is strengthened because of the low reluctance of air. With the introduction of YI, the non-sinusoidal distribution significantly improved, and the amplitude of B_r increases by approximately 65%. This improvement indicates that YI provides a low-reluctance path, which enhances the first magnetic loop and weakens the second path. The attenuation of B_r occurs in the width direction (Z) from 14 to 0 mm or from 42 to 55 mm, indicating an edge effect near the LM wall (Fig. 4(d)). Notably in the structural design, the width of the permanent magnet should be at least 10% larger than that of the channel.

3.1.2. Electric field

Fig. 5 illustrates the current density distribution, optimization mechanism, and lateral-end effect of PM-EMP. As shown in Fig. 5(a), the vertical component of the induced current density (I_Z), which is primarily concentrated at the center of the LM channel, exhibits good uniformity and is favorable for generating an effective electromagnetic force. In contrast, the tangential component (I_T), which occurs near the channel wall, gradually increases and contributes to transverse end effects, thereby reducing the stability of the MHD process. The current density can be optimized significantly by incorporating the SBS and YI, as shown in Fig. 5(b). The arrows near the wall are completely confined within the SBS, providing a low-resistance path that effectively mitigates the lateral-end effect. This results in a more uniform distribution across the LM channel, enhancing the generation of effective electromagnetic force. Furthermore, increasing the rotational speed (n) markedly enhances the magnitude of I_Z, as is evident from the comparison between Figs. 5(b) and (c). As shown in Fig. 5(d), I_Z exhibits a non-sinusoidal distribution with four subpeaks, indicating a secondary current closure phenomenon within the LM. This is because strengthening of the second magnetic path weakens the radial magnetic B_r between adjacent magnetic poles, thereby promoting short closed paths. The waveform of I_Z is shown to be optimized, particularly at n = 350 r∙min⁻¹, indicating that the secondary current closure effect is significantly reduced by the SBS. The amplitude of I_Z increased by 123.9% (2.53 × 10⁶ A·m⁻² at n = 150 r∙min⁻¹) and 441.6% (6.12 × 10⁶ A·m⁻² at n = 350 r∙min⁻¹) with YI and SBS, respectively, compared to the baseline without YI and SBS (1.13 × 10⁶ A·m⁻² at n = 150 r·min⁻¹). This indicates that the MHD effect can be optimized by utilizing SBS and increasing the rotational speed.

3.1.3. Fluid field

The electromagnetic force (F) applied to the LM generates an internal pressure gradient within the PM-EMP, with its distribution, variation, and optimization, as illustrated in Fig. 6. As shown in Fig. 6(a), the tangential component (F_T) of electromagnetic force density, which directly influences the driving capacity and flow stability, is primarily concentrated in the middle region of the LM channel. Meanwhile, the vertical component (F_Z) of electromagnetic force density, which significantly contributes to local pressure drops and lateral end effects, intensifies as it moves from the center toward the channel walls. This is primarily because of the non-sinusoidal distribution of the electromagnetic parameters and the increasing proportion of the tangential component of current density (particularly near the walls). The near-wall distribution and negative effect of F are significantly improved by the addition of an SBS, as shown in Figs. 6(b) and (c). Specifically, compared with the configuration without SBS, F_T is greatly enhanced and optimized, showing a more uniform distribution along the channel width when SBS is applied. This improvement is because of the enhanced distribution of I_T near the wall, where the SBS provides a low-resistance path. Additionally, a negative F_T is generated along the flow direction owing to the secondary current-closure effect. For example, at n = 150 r∙min⁻¹ without YI and SBS, F_T = −1.28 × 10³ N·m⁻³ at an arc length (l) of 19.5 mm, as shown in Fig. 6(d). The negative F_T is reduced by 87.4% (−1.61 × 10² N·m⁻³ at n = 150 r∙min⁻¹) and by 97.6% (−3.01 × 10¹ N·m⁻³ at n = 350 r∙min⁻¹) with YI and SBS, respectively, compared to the case without YI and SBS (−1.28 × 10³ N·m⁻³ at n = 150 r∙min⁻¹). The maximum value of F_T has been increased from 1.68 × 10⁵ N·m⁻³ (without YI and SBS at n = 150 r∙min⁻¹) to 6.38 × 10⁵ N·m⁻³ (with YI and SBS at n = 150 r∙min⁻¹) and 1.51 × 10⁶ N·m⁻³ (with YI and SBS at n = 350 r∙min⁻¹), representing increases of 279.8% and 798.8%, respectively. Additionally, the size and density of the arrows visually represent these changes.

The pumping efficiency and flow stability of the PM-EMP are influenced by the motion state of the LM and the internal pressure distribution, as shown in Fig. 7. In Figs. 7(a)–(c), multiple large-scale vortices, defined as lateral end effects, form near the channel walls. This occurs because the uneven distribution of the induced current density (I) generates a vertical force component (F_Z) near the walls, which intensifies flow instability and pressure loss. Notably, in the numerical calculations, the outlet boundary condition of the PM-EMP is set to P₀ = 0 kPa. The oscillatory increase in pressure along the flow direction indicates the presence of pressure pulsations (ΔP₁, ΔP_2, and ΔP₃) during PM-EMP operation, as shown in Fig. 7(d). The unsteady flow is exacerbated by increased rotational speed (n) or YI and SBS usage. For example, the pressure pulsations increase from 2.7 kPa (ΔP₁ at n = 150 r∙min⁻¹ without YI and SBS) to 23.3 kPa (ΔP₂ at n = 150 r∙min⁻¹ with YI and SBS) and 27.7 kPa (ΔP₃ at n = 350 r∙min⁻¹ with YI and SBS), representing improvements of 763.0% and 925.9%, respectively. However, compared to the configuration without YI and SBS (ΔP_h = 16.7 kPa at n = 150 r∙min⁻¹), the pressure head (ΔP_h) of PM-EMP is significantly enhanced by 412.6% (ΔP_h = 85.6 kPa at n = 150 r∙min⁻¹) and 1087% (ΔP_h = 198.2 kPa at n = 350 r∙min⁻¹) when YI and SBS are used. This indicates a tradeoff between pressure pulsation and performance improvement, which can be addressed by increasing the number of magnetic poles to modify the period of F_T changes.

3.1.4. Performance optimization

Fig. 8 presents a comprehensive analysis of the factors influencing the driving performance of the PM-EMP. As shown in Fig. 8(a), the pressure head varies smoothly with the Q, demonstrating superior driving characteristics compared to a mechanical pump. The performance of the PM-EMP is significantly enhanced by the inclusion of SBS. This enhancement is primarily because of the confinement of I_T within the SBS, which effectively reduces the lateral end effect and negative electromagnetic forces, thereby increasing the magnitudes of I_Z and F_T. The pumping capability of the PM-EMP is further improved using YI, which provides a low-reluctance path for the magnetic field lines, strengthening B_r, I_Z, and F_T, as illustrated in Fig. 8(b). A smaller channel height of PM-EMP (H) is better suited for applications requiring high sensitivity to pressure heads, while a larger H is more appropriate for scenarios demanding a constant pressure head and higher flow rates. The channel width of PM-EMP (W) has a more significant impact on the lateral end-effect coefficient (K_l) than H, as presented in Figs. 8(c) and (d). Based on Eq. (5), Table 1 lists the effect of W on the lateral end-effect coefficient (K_l) at Q = 0.2 L·min⁻¹, n = 150 r·min⁻¹, and H = 2 mm. As W increases, K_l improves, indicating a reduction in the lateral-end effect, particularly for larger widths. Notably, the longitudinal end effect significantly impacts the pumping capacity and flow characteristics of the PM-EMP, which are presented in Note S4 and Fig. S2 in Appendix A.

3.2. Characterization of flexibility and maneuverability of synergetic cooling LMFCC

To assess the effectiveness of the LMFC in real-world settings and its potential to enhance the user experience, we visually compared the flexibility and operability of conventional copper cables with those of the multifield cooperative LM power line, as shown in Fig. 9. Compared with copper solid properties at specific gravity of 8.9 g·cm⁻³, LM offers excellent flow conductivity and lower density of 6.4 g·cm⁻³ (28.1% improvement, Fig. 9(a)), making it a promising material for the development of next-generation liquid-cooled power lines that are both lightweight and convenient, even for ultra-high current charging. Figs. 9(b)–(e) demonstrate that the LMFC exhibits complete flexibility under stretching and torsion conditions. It shows exceptional dynamic adaptability and operability, particularly in bending scenarios (d is the curvature diameter of LMFC in the bent state, d = 4 cm). Even under extreme folding conditions, the LMFC maintains good electrical conductivity and fully recovers to its original state after deformation. In contrast, copper-based wires exhibit significant resistance to these deformation requirements.

The impact of the dynamic deformation on the multi-energy field transmission of the LMFC is illustrated in Figs. 9(f)–(i). The LM power line, with an initial length (l₀) of 0.12 m and an inner diameter (D) varying from 4 to 10 mm, was tested under different conditions. For a strain rate (ε_s) of 50%, the LMFC resistance increased from 2.99 × 10⁰ mΩ, 1.31 × 10⁰ mΩ, 7.69 × 10⁻¹ mΩ, and 4.74 × 10⁻¹ mΩ to 6.98 × 10⁰ mΩ, 2.93 × 10⁰ mΩ, 1.69 × 10⁰ mΩ, and 1.09 × 10⁰ mΩ, representing increases of 133.4% (D = 4 mm), 123.7% (D = 6 mm), 119.8% (D = 8 mm), and 130.0% (D = 10 mm), respectively. The LMFC demonstrated good electrical stability under torsional and bending conditions. Even with a torsion deformation of 720°, the resistance increased by only 5.0% (D = 4 mm), 5.5% (D = 6 mm), 6.3% (D = 8 mm), and 5.8% (D = 10 mm). For a bending radius of d = 4 cm, the resistance increased by 5.3% (D = 4 mm), 5.1% (D = 6 mm), 5.1% (D = 8 mm), and 5.9% (D = 10 mm). However, folding the LMFC by half significantly increases its resistance. Unlike copper-based conductors, LM can be directly recycled as a conductor without requiring additional processing.

3.3. Integrated transmission performance of synergetic cooling LMFCC

Liquid-cooled power lines that offer both exceptional cooling performance and operational flexibility are critically important for meeting the engineering demands of megawatt-level (≥ 1000 A) DC-HPC systems. The adaptability of the synergetic cooling LMFCC for superhigh current transmission is thoroughly evaluated, as shown in Fig. 10. A key aspect of this evaluation is determining whether an electrical crosstalk exists between the dispersion current (I_d) and the charging current (I), which could potentially impact the driving performance and charging efficiency of the system, which are presented in Note S5 and Fig. S3 in Appendix A. Furthermore, the temperature consistency between the DC+ and DC− LMFCs is within 1.5 °C; hence, the data from the DC + LMFC is used for subsequent system performance analysis. Fig. 10(a) illustrates the heat generation, accumulation, and dissipation characteristics of the system under different charging current levels (50–1000 A). For L = 2.0 m, D = 10 mm, and G = 3.0 L·min⁻¹, the temperature difference (ΔT = T_max−T_a, T_a is the environment temperature) between the maximum temperature (T_max) and the external environment remains at 54.3 °C even at 1000 A, demonstrating the excellent heat extraction and dissipation capabilities of LM. For I ranging from 400 to 600 and 800 A, ΔT increases from 9.9 to 19.8 and 34.7 °C, respectively. This indicates that the system achieves efficient cooling primarily through heat conduction, effectively integrating the current and heat transfer processes. Additionally, the radiator outlet temperature and LMFC inlet temperature gradually increases with rising current, suggesting that the system effectively dissipates large amounts of heat through superior convective heat transfer between the air and LM, outperforming traditional water- or oil-based systems. For example, as the current increases from 600 to 800 and 1000 A, T_r-out rises modestly from 28.0 to 30.6 and 34.4 °C, corresponding to temperature rises of 2.6 and 6.4 °C, respectively.

Figs. 10(b)–(d) presents the influences of the LMFC length (L), diameter (D), and system flow rate (G) on the active cooling performance of the system. It is observed that the variation in temperature difference (ΔT) with increasing L becomes more pronounced, especially at 1000 A. For currents from 600 to 800 and 1000 A, ΔT rises from 14.9 to 26.3 and 42.0 °C with L = 1.5 m, compared to 7.8 to 13.5 and 20.1 °C with L = 0.5 m, corresponding to increases of 7.1, 12.8 and 21.9 °C, respectively. Additionally, the thermal control capability is significantly improved by increasing D, particularly at higher charging currents. For example, at 1000 A, ΔT decreases from 86.8 (D = 6 mm) to 67.6 (D = 8 mm) and 54.3 °C (D = 10 mm), enhancing temperature control by 22.1% and 37.4%, respectively. Similarly, at 600 and 800 A, the cooling performance improves by 17.8% and 29.5% (ΔT decreases from 28.1 to 23.1 and 19.8 °C), and by 21.1% and 33.9% (ΔT weakens from 52.5 to 41.4 and 34.7 °C), respectively. This observation is explained by the relationship between heat generation and resistance. The heat generated (q = I²R) is directly proportional to L and inversely proportional to D², where the resistance (R) is defined as

R = \frac{L}{σ A_{0}}

and the cross-sectional area of the fluid channel (A₀) is

\frac{π D^{2}}{4}

. Increasing the G significantly reduces ΔT, highlighting the strong dependence of cooling performance on the driving capability of the PM-EMP. For I = 1000 A, ΔT changes from 91.7 (G = 1.5 L∙min⁻¹) to 71.2 (G = 2.0 L·min⁻¹), 60.2 (G = 2.5 L·min⁻¹), and 54.3 °C (G = 3.0 L·min⁻¹), corresponding to a decrease of 22.4%, 34.4%, and 40.8%, respectively. However, the rate of improvement in cooling performance slows as G increases. For I from 800 to 1000 A, the change of ΔT is from 35.4 (G = 1.5 L∙min⁻¹) to 27.0 (G = 2.0 L∙min⁻¹), 22.3 (G = 2.5 L∙min⁻¹), and 19.6°C (G = 3.0 L∙min⁻¹).

These trends can be understood by examining the heat transport, as shown in Figs. 10(e)–(g). The thermal resistance of the heat capacity (R_capacity =

\frac{1}{m C_{p}}

, where m is the mass flow rate) reflects the thermal carrying performance of the LM. The heat transfer capacity of the LMFCC system can be significantly improved by increasing D or G. As D increases from 6 to 8 and 10 mm, R_capacity decreases from 1.11 × 10⁻² to 1.00 × 10⁻² and 9.63 × 10⁻³ °C·W⁻¹, showing reductions of 9.9% and 13.2%, respectively. This trend is consistent with directly affected by the negative correlation between C_p and T. For G increasing from 1.0 to 3.0 L·min⁻¹, R_capacity decreases from 3.15 × 10⁻² to 2.00 × 10⁻², 1.47 × 10⁻², 1.16 × 10⁻², and 9.63 × 10⁻³ °C·W⁻¹, corresponding to a reduction of 36.5%, 53.3%, 63.2%, and 69.4%, respectively. This implies that thermal-carrying capacity is gradually reduced (explained in Fig. 10(d)). Additionally, the pressure loss (ΔP) of the system is significantly strengthened by reducing D and increasing L and G, particularly for smaller D. This indicates higher demand on PM-EMP driving capability. For example, when D changes from 6 to 8 and 10 mm, ΔP changes from 161 to 45 and 16 kPa, corresponding to a reduction of 72.0% and 90.1%, respectively. Applying the LMFCC technology to rapidly recharge EVs requires balancing the active cooling capabilities, driving performance, and system cost.

Fig. 10(h) shows the influence of D (at G = 6 and 10 L·min⁻¹) on the cooling performance and hydrodynamic characteristics of the LMFCC using numerical methods. For I = 1000 A, L = 3 m, and G = 10 L·min⁻¹, the ΔT of the system can be as low as 46.9 (D = 6 mm), 32.5 (D = 7 mm), 25.4 (D = 8 mm), 19.5 (D = 9 mm), and 15.9 °C (D = 10 mm), with corresponding ΔP values of 1894, 930, 480, 280, and 167 kPa. These values demonstrate for a strong driving performance to achieve an excellent cooling capability. A comparative analysis of the LMFC and copper cables (under natural convection and active liquid-cooling conditions) is shown in Fig. 10(i). Compared with natural convection copper cables, LMFCC exhibits outstanding thermal control capabilities, particularly for higher charging currents. For example, for I = 1500 A, with 419.3 (D = 10 mm) and 191.6 °C (D = 14.14 mm), ΔT becomes 65.6 °C, and the corresponding temperature control performance is increased to 84.4% and 65.8%, respectively. Moreover, for I = 1500 A, the system cooling capacity is enhanced to 26.7% compared to the active cooling copper cable ΔT = 89.5 °C. This indicates that traditional separated heat dissipation methods are not only inefficient but also complex and unreliable.

4. Conclusions

We report a novel synergetic cooling and charging strategy enabled by LMFCC for DC-HPC, particularly for superhigh currents. The LMFCC demonstrated exceptional performance in both flexible operability and transmission stability, even at considerable deformation. We also developed an advanced compact induction electromagnetic-driven system that promotes the LMFCC active-cooling capability by optimizing the current and magnetic flux distribution to suppress end effects. Compared with other methods, the proposed LMFCC exhibited excellent practical potential, remarkable lightweight design, and substantial cooling improvement (> 26% at 1500 A). Our synergetic cooling strategy represents a breakthrough in fundamental theory and applied research on ultrahigh heat flux thermal management, contributing to the rapid advancement of the EV industry.

Acknowledgments

The authors would like to acknowledge the National Natural Science Foundation of China (NSFC) (52076213) and the 2115 Talent Development Program of China Agricultural University for the financial coverage of this work.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2024.11.035.

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Harper G, Sommerville R, Kendrick E, Driscoll L, Slater P, Stolkin R, et al.Recycling lithium-ion batteries from electric vehicles.Nature 2019; 575(7781):75-86.

[2]	Cano ZP, Banham D, Ye S, Hintennach A, Lu J, Fowler M, et al.Batteries and fuel cells for emerging electric vehicle markets.Nat Energy 2018; 3(4):279-289.

[3]	Ren Y, Sun X, Wolfram P, Zhao S, Tang X, Kang Y, et al.Hidden delays of climate mitigation benefits in the race for electric vehicle deployment.Nat Commun 2023; 14(1):3164.

[4]	Kendall K, Ye S, Liu Z.The hydrogen fuel cell battery: replacing the combustion engine in heavy vehicles.Engineering 2023; 21:39-41.

[5]	Wang Z, Zhou J, Rizzoni G.A review of architectures and control strategies of dual-motor coupling powertrain systems for battery electric vehicles.Renew Sustain Energy Rev 2022; 162:112455.

[6]	Wassiliadis N, Steinsträter M, Schreiber M, Rosner P, Nicoletti L, Schmid F, et al.Quantifying the state of the art of electric powertrains in battery electric vehicles: range, efficiency, and lifetime from component to system level of the Volkswagen ID.3.eTransportation 2022; 12:100167.

[7]	Cuma MU, Koroglu T.A comprehensive review on estimation strategies used in hybrid and battery electric vehicles.Renew Sustain Energy Rev 2015; 42:517-531.

[8]	Manzetti S, Mariasiu F.Electric vehicle battery technologies: from present state to future systems.Renew Sustain Energy Rev 2015; 51:1004-1012.

[9]	Yang H, Fulton L.Decoding US investments for future battery and electric vehicle production.Transport Res Pt D 2023; 118:103693.

[10]	Xu C, Behrens P, Gasper P, Smith K, Hu M, Tukker A, et al.Electric vehicle batteries alone could satisfy short-term grid storage demand by as early as 2030.Nat Commun 2023; 14(1):119.

[11]	Xu Y, Kara EC, Moura SJ, González MC.Planning for electric vehicle needs by coupling charging profiles with urban mobility.Nat Energy 2018; 3(6):484-493.

[12]	Yang Z, Chang Z, Zhang Q, Huang K, Zhang X.Decorating carbon nanofibers with Mo₂C nanoparticles towards hierarchically porous and highly catalytic cathode for high-performance Li-O₂ batteries.Sci Bull 2018; 63(7):433-440.

[13]	Ruan J, Walker P, Zhang N.A comparative study energy consumption and costs of battery electric vehicle transmissions.Appl Energy 2016; 165:119-134.

[14]	Yuan X, Li L, Gou H, Dong T.Energy and environmental impact of battery electric vehicle range in China.Appl Energy 2015; 157:75-84.

[15]	Li Y, Vasileiadis A, Zhou Q, Lu Y, Meng Q, Li Y, et al.Origin of fast charging in hard carbon anodes.Nat Energy 2024; 9(2):134-142.

[16]	Heenan TMM, Mombrini I, Llewellyn A, Checchia S, Tan C, Johnson MJ, et al.Mapping internal temperatures during high-rate battery applications.Nature 2023; 617(7961):507-512.

[17]	Tomaszewska A, Chu Z, Feng X, O'Kane S, Liu X, Chen J, et al.Lithium-ion battery fast charging: a review.eTransportation 2019; 1:100011.

[18]	Zhu GL, Zhao CZ, Huang JQ, He C, Zhang J, Chen S, et al.Fast charging lithium batteries: recent progress and future prospects.Small 2019; 15(15):1805389.

[19]	Yang X, Wang C.Understanding the trilemma of fast charging, energy density and cycle life of lithium-ion batteries.J Power Sources 2018; 402:489-498.

[20]	Yang X, Zhang G, Ge S, Wang C.Fast charging of lithium-ion batteries at all temperatures.Proc Natl Acad Sci USA 2018; 115(28):7266-7271.

[21]	Parlikar A, Schott M, Godse K, Kucevic D, Jossen A, Hesse H.High-power electric vehicle charging: low-carbon grid integration pathways with stationary lithium-ion battery systems and renewable generation.Appl Energy 2023; 333:120541.

[22]	Muratori M, Elgqvist E, Cutler D, Eichman J, Salisbury S, Fuller Z, et al.Technology solutions to mitigate electricity cost for electric vehicle DC fast charging.Appl Energy 2019; 242:415-423.

[23]	Saldaña G, San JI Martin, Zamora I, Asensio FJ, Oñederra O.Electric vehicle into the grid: charging methodologies aimed at providing ancillary services considering battery degradation.Energies 2019; 12(12):2443.

[24]	Rubino L, Capasso C, Veneri O.Review on plug-in electric vehicle charging architectures integrated with distributed energy sources for sustainable mobility.Appl Energy 2017; 207:438-464.

[25]	Azadfar E, Sreeram V, Harries D.The investigation of the major factors influencing plug-in electric vehicle driving patterns and charging behaviour.Renew Sustain Energy Rev 2015; 42:1065-1076.

[26]	Barman P, Dutta L, Bordoloi S, Kalita A, Buragohain P, Bharali S, et al.Renewable energy integration with electric vehicle technology: a review of the existing smart charging approaches.Renew Sustain Energy Rev 2023; 183:113518.

[27]	Du J, Liu Y, Mo X, Li Y, Li J, Wu X, et al.Impact of high-power charging on the durability and safety of lithium batteries used in long-range battery electric vehicles.Appl Energy 2019; 255:113793.

[28]	Ahmed S, Bloom I, Jansen AN, Tanim T, Dufek EJ, Pesaran A, et al.Enabling fast charging-a battery technology gap assessment.J Power Sources 2017; 367:250-262.

[29]	Oc Płoń, Cisek P, Pilarczyk M, Taler D.Numerical simulation of heat dissipation processes in underground power cable system situated in thermal backfill and buried in a multilayered soil.Energy Convers Manage 2015; 95:352-370.

[30]	Liu Y, Zhu Y, Cui Y.Challenges and opportunities towards fast-charging battery materials.Nat Energy 2019; 4(7):540-550.

[31]	Thakur AK, Ahmed MS, Kang H, Prabakaran R, Said Z, Rahman S, et al.Critical review on internal and external battery thermal management systems for fast charging applications.Adv Energy Mater 2023; 13(11):2202944.

[32]	Zeng Y, Chalise D, Lubner SD, Kaur S, Prasher RS.A review of thermal physics and management inside lithium-ion batteries for high energy density and fast charging.Energy Storage Mater 2021; 41:264-288.

[33]	Wang Q, Jiang B, Li B, Yan Y.A critical review of thermal management models and solutions of lithium-ion batteries for the development of pure electric vehicles.Renew Sustain Energy Rev 2016; 64:106-128.

[34]	Chou C, Fortin PA., assignee.Liquid-cooled charging connector. United States patent US 11084390. 2021 Aug 10.

[35]	Sasaridis D, Sukup MJ, Hastings C, Priestley DW, Zalan D, Szafer DG, et al., assignee.Liquid cooled charging cable and connector. United States patent US 20200282851. 2020 Sep 10.

[36]	Nagel T, Remisch D.Ing.h.c. F. Porsche Aktiengesellschaft (Stuttgart), assignees. Charging station having a charging cable with electric contact within a fluid duct. United States patent US 10081262. 2018 Sep 25.

[37]	Devahdhanush VS, Lee S, Mudawar I.Experimental investigation of subcooled flow boiling in annuli with reference to thermal management of ultra-fast electric vehicle charging cables.Int J Heat Mass Transf 2021; 172:121176.

[38]	Devahdhanush VS, Lee S, Mudawar I.Consolidated theoretical/empirical predictive method for subcooled flow boiling in annuli with reference to thermal management of ultra-fast electric vehicle charging cables.Int J Heat Mass Transf 2021; 175:121224.

[39]	Dai D, Zhou Y, Liu J.Liquid metal based thermoelectric generation system for waste heat recovery.Renew Energy 2011; 36(12):3530-3536.

[40]	Sun P, Liu C, He Z.A compact double-spiral electromagnetic pump for liquid metal cooling.Ann Nucl Energy 2023; 180:109486.

[41]	Cheng K, Wang Y, Xu J, Qin J, Jing W.A novel liquid metal MHD enhanced closed-brayton-cycle power generation system for hypersonic vehicles: thermodynamic analysis and performance evaluation with finite cold source.Energy Convers Manage 2022; 268:116068.

[42]	Arias I, Cardemil J, Zarza E, Valenzuela L, Escobar R.Latest developments, assessments and research trends for next generation of concentrated solar power plants using liquid heat transfer fluids.Renew Sustain Energy Rev 2022; 168:112844.

[43]	Vignarooban K, Xu X, Arvay A, Hsu K, Kannan AM.Heat transfer fluids for concentrating solar power systems—a review.Appl Energy 2015; 146:383-396.

[44]	Liu C, He Z.Liquid metal-enhanced thermoelectric generator for high-temperature thermal harvesting.Appl Therm Eng 2024; 247:123098.

[45]	Kabeel AE, El-Said EMS, Dafea SA.A review of magnetic field effects on flow and heat transfer in liquids: present status and future potential for studies and applications.Renew Sustain Energy Rev 2015; 45:830-837.

[46]	Ho CK, Iverson BD.Review of high-temperature central receiver designs for concentrating solar power.Renew Sustain Energy Rev 2014; 29:835-846.

[47]	Pacio J, Wetzel T.Assessment of liquid metal technology status and research paths for their use as efficient heat transfer fluids in solar central receiver systems.Sol Energy 2013; 93:11-22.

[48]	Wang L, Lai R, Zhang L, Zeng M, Fu L.Emerging liquid metal biomaterials: from design to application.Adv Mater 2022; 34(37):2201956.

[49]	Lin Y, Genzer J, Dickey MD.Attributes, fabrication, and applications of gallium-based liquid metal particles.Adv Sci 2020; 7(12):2000192.

[50]	Zhang M, Gao Q, Zhao Z, Guo L, Li X, Zhang C, et al.Liquid metal manifold microchannel heat sink for ultra-high heat flux cooling.Appl Therm Eng 2024; 248:123117.

[51]	Deng Y, Jiang Y, Liu J.Low-melting-point liquid metal convective heat transfer: a review.Appl Therm Eng 2021; 193:117021.

[52]	Qian Z, Li Y, Rao Z.Thermal performance of lithium-ion battery thermal management system by using mini-channel cooling.Energy Convers Manage 2016; 126:622-631.

[53]	Deng Y, Zhang M, Jiang Y, Liu J.Two-stage multichannel liquid-metal cooling system for thermal management of high-heat-flux-density chip array.Energy Convers Manage 2022; 259:115591.

[54]	Zhang X, Yang X, Zhou Y, Rao W, Gao J, Ding Y, et al.Experimental investigation of galinstan based minichannel cooling for high heat flux and large heat power thermal management.Energy Convers Manage 2019; 185:248-258.

[55]	Laube T, Dietrich B, Marocco L, Wetzel T.Conjugate heat transfer of a turbulent tube flow of water and GaInSn with azimuthally inhomogeneous heat flux.Int J Heat Mass Transf 2024; 221:125027.

[56]	Kalkan O.Multi-objective optimization of a liquid metal cooled heat sink for electronic cooling applications.Int J Therm Sci 2023; 190:108325.

[57]	Zhang Z, Lei J, Li F, Li L, Li S, Huang Y, et al.Investigation of the heat transfer characteristics of galinstan liquid metal driven by electromagnetism.Appl Therm Eng 2023; 230:120776.

[58]	Liu C, He Z.High heat flux thermal management through liquid metal driven with electromagnetic induction pump.Front Energy 2022; 16(3):460-470.

[59]	Zhang X, Zhou Y, Liu J.A novel layered stack electromagnetic pump towards circulating metal fluid: design, fabrication and test.Appl Therm Eng 2020; 179:115610.

[60]	Amy C, Budenstein D, Bagepalli M, England D, DeAngelis F, Wilk G, et al.Pumping liquid metal at high temperatures up to 1673 kelvin.Nature 2017; 550(7675):199-203.

[61]	Sun P, Zhang H, Jiang F, He Z.Self-driven liquid metal cooling connector for direct current high power charging to electric vehicle.eTransportation 2021; 10:100132.

[62]	Holman JP.Experimental methods for engineers.(5th ed.), McGraw-Hill, New York city (1989)

[63]	Bergman TL, Lavine AS, Incropera FP, DeWitt DP.Fundamentals of heat and mass transfer.(8th ed.), John Wiley & Sons, Inc., Hoboken (2011)

[64]	Hvasta MG, Nollet WK, Anderson MH.Designing moving magnet pumps for high-temperature, liquid-metal systems.Nucl Eng Des 2018; 327:228-237.

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