聚变堆和电磁冶金中存在大量的磁场和流动方向不平行或不垂直的情况,本文针对环形方管内液态金属在倾斜磁场作用下的三维自驱动热电磁流动与传热行为开展了数值研究,系统考察磁场倾角（0°~90°）对流场结构、电流分布及传热性能的影响规律。磁场倾角改变了热电电流分布,引发流动的非单调响应：平均流速随倾角增大单调下降,但最大驱动速度在45°出现峰值,该角度下的磁阻尼处于极小值附近,且流场角部集中的洛伦兹力产生了最大局部驱动力。同时流动与传热呈现显著的非同步变化：大倾角虽降低整体流量,但流场角部射流诱导的剪切混合作用使上热壁面平均努塞尔数显著上升,并在竖直磁场下达到了最大。本研究揭示了通过磁场取向可实现对局部存在高热流密度的器件附近进行被动冷却优化,为液态金属热电磁流动的被动热管理系统设计提供了参考。
In applications such as fusion reactors and electromagnetic metallurgy, magnetic fields and flow directions are often neither parallel nor perpendicular. Addressing this, this paper presents a numerical study on the three-dimensional self-driven thermoelectric magnetohydrodynamic (TEMHD) flow and heat transfer of liquid metal in a toroidal square duct under inclined magnetic fields. The influence of the magnetic inclination angle (0°-90°) on flow structures, current distributions, and heat transfer performance is systematically investigated. The results indicate that magnetic inclination alters the thermoelectric current distribution, triggering a non-monotonic flow response: while the average velocity decreases monotonically with increasing inclination, the maximum driving velocity exhibits a peak around 45°. Mechanism analysis reveals that at this angle, the magnetohydrodynamic (MHD) damping is near its minimum, and the highly concentrated Lorentz force at the corners generates the maximum local driving force. Furthermore, a distinct non-synchronous variation between flow and heat transfer is observed; although high inclination angles reduce the overall flow rate, the shear mixing induced by corner jets significantly increases the average Nusselt number on the upper heated wall, which reaches its maximum under a vertical magnetic field. This study demonstrates that optimizing passive cooling near components with local high heat flux can be achieved by adjusting the magnetic field orientation, providing a reference for the design of liquid metal passive thermal management systems based on TEMHD flow.
[1] Merola M, Loesser D, Martin A, et al.ITER plasma-facing components[J]. Fusion Engineering and Design, 2010, 85(10/11/12): 2312-2322. DOI:10.1016/j.fusengdes.2010.09.013.
[2] Brauer T, Klinger T, Bosch H S.Progress, challenges, and lessons learned in the construction of Wendelstein 7-X[J]. IEEE Transactions on Plasma Science, 2012, 40(3): 577-583. DOI:10.1109/TPS.2011.2174658.
[3] Xu W Y, Curreli D, Ruzic D N.Computational studies of thermoelectric MHD driven liquid lithium flow in metal trenches[J]. Fusion Engineering and Design, 2014, 89(12): 2868-2874. DOI:10.1016/j.fusengdes.2014.06.008.
[4] Abdou M A, Team T A, Ying A, et al.On the exploration of innovative concepts for fusion chamber technology[J]. Fusion Engineering and Design, 2001, 54(2): 181-247. DOI:10.1016/S0920-3796(00)00433-6.
[5] Deng Y G, Jiang Y, Liu J.Low-melting-point liquid metal convective heat transfer: A review[J]. Applied Thermal Engineering, 2021, 193: 117021. DOI:10.1016/j.applthermaleng.2021.117021.
[6] Modestov M, Kolemen E, Fisher A E, et al.Electromagnetic control of heat transport within a rectangular channel filled with flowing liquid metal[J].Nuclear Fusion, 2018, 58(1): 016009. DOI:10.1088/1741-4326/aa8bf4.
[7] Pourkiaei S M, Ahmadi M H, Sadeghzadeh M,et al.Thermoelectric cooler and thermoelectric generator devices: a review of present and potential applications, modeling and materials[J].Energy, 2019, 186:115849.1-115849.17.DOI:10.1016/j.energy.2019.07.179.
[8] Shercliff J A.Thermoelectric magnetohydrodynamics[J]. Journal of Fluid Mechanics, 1979, 91(2): 231-251. DOI:10.1017/s0022112079000136.
[9] Kiflemariam R, Lin C X.Numerical simulation of integrated liquid cooling and thermoelectric generation for self-cooling of electronic devices[J]. International Journal of Thermal Sciences, 2015, 94: 193-203.DOI:10.1016/j.ijthermalsci.2015.02.012.
[10] Nolas G S, Sharp J, Goldsmid H J.Thermoelectrics: Basic Principles and New Materials Developments[M]. Berlin, Heidelberg: Springer, 2001 DOI:10.1007/978-3-662-04569-5.
[11] Chen Z Q, Wang Z H, Chen L.Magnetic field control of three‐dimensional self‐driven multi‐physical thermoelectric system in metal energy storage[J]. International Journal of Energy Research, 2022, 46(8): 11250-11264. DOI:10.1002/er.7925.
[12] Chen Z Q, Wang Z H, Chen L.Heat transfer enhancement of liquid metal thermal convection affected by the seebeck effect and magnetic field[J]. International Journal of Energy Research, 2023, 2023(1): 5159687. DOI:10.1155/2023/5159687.
[13] Zhang D K, Wang Z H, Meng X, et al.Self-driven thermoelectric cooling contraption for liquid metals under the static magnetic field[J]. Physics of Fluids, 2023, 35(7) : 077112. DOI:10.1063/5.0155822.
[14] Xue L, Chen L, Ni M J.Controlling heat transport and flow structure in vertical convection using the thermoelectric effect[J]. Journal of Fluid Mechanics, 2025, 1015: A31. DOI:10.1017/jfm.2025.10310.
[15] Bond O G, Howell P D.Thermoelectric magnetohydrodynamic flow in a liquid metal-infused trench[J].Journal of Fluid Mechanics, 2025, 1004: A2. DOI:10.1017/jfm.2024.1130.
[16] Zhang X J, Mao J, Chen Y J, et al.Investigations of liquid metal magnetohydrodynamic rectangular duct flows under inclined transversal magnetic fields[J]. Nuclear Fusion, 2019, 59(5): 056018. DOI:10.1088/1741-4326/ab0b46.
[17] Wang L, Zhang X J, Sun Z C.Effects of inclined gradient magnetic field on the liquid metal flow states through coupled conducting ducts[J]. Journal of Fusion Energy, 2023, 42(2): 54. DOI:10.1007/s10894-023-00391-7.
[18] Davidson P A.Introduction to Magnetohydrodynamics[M]. 2nd ed. Cambridge: Cambridge University Press, 2017.
[19] Wang J.Etude de l'effect thermoélectrique magnétique en solidification directionnelle d'alliages Al-Cu[D]. Grenoble: Université de Grenoble, 2013.
