Results of numerical simulation of the unsteady heat exchange in a layer of an electrically conducting liquid between two concentric spheres and of the magnetic hydrodynamics of this liquid at small magnetic Reynolds numbers (Rem = 10–1, 10–2, 10–3, 10–4, 10–5, and 10–6) and the homochronicity numbers Ho = 0.1 and 10 are presented. The influence of the Joule heat dissipation in this layer on the evolution of the liquid flow structure, the temperature and magnetic-induction fields, and the distributions of local Nusselt numbers in it, depending on the values of Rem and Ho, was investigated.
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F. Krause and K. K. Radler, Mean-Field Magnetohydrodynamics and Dynamo Theory [Russian translation], Mir, Moscow (1984).
Yu. B. Ponomarenko, On the hydrodynamic dynamo theory, Prikl. Mat. Teor. Fiz., 6, 47–51 (1973).
D. D. Sokolov, R. A. Stepanov, and P. G. Frik, Dynamo: In the way from the astrophysical models to the laboratory experiment, Usp. Fiz. Nauk, 184, No. 3, 313–335 (2014).
D. D. Sokolov, Modern state and prospects of the laboratory dynamo experiment, Soros Obrasovat. Zh., 7, No. 4, 111–115 (2001).
D. D. Sokolov, R. A. Stepanov, and P. G. Frik, Cosmic magnetism comes to the laboratory, in: Etudes on Mechanic, Red. Izd. Otdel Ural Otd. RAN, Ekaterinburg (2017), pp. 7–16.
A. V. Perminov and I. L. Nikulin, Mathematical model of the processes of heat and mass transfer and diffusion of the magnetic field in an induction furnace, J. Eng. Phys. Thermophys., 89, No. 2, 397−409 (2016).
M. I. Elkhazen, W. Hassen, R. Gannoun, A. K. Hussein, and M. N. Borjini, Numerical study of electroconvection in a dielectric layer between two cofocal elliptical cylinders subjected to unipolar injection, J. Eng. Phys. Thermophys., 92, No. 5, 2358–2370 (2019).
S. B. Kashevskii, B. E. Kashevskii, and A. L. Khudolei, An experimental model for investigating the dynamics of magnetic dispersion in a gradient magnetic field, J. Eng. Phys. Thermophys., 91, No. 1, 172–180 (2018).
N. Ahmed, Heat and mass transfer in MHD Poiseuille flow with porous walls, J. Eng. Phys. Thermophys., 92, No. 1, 128–136 (2019).
V. D. Borisevich and E. P. Potanin, Magnetohydrodynamics and heat transfer in rotating flows, J. Eng. Phys. Thermophys., 92, No. 1, 176–182 (2019).
S. V. Fedorov, Intensification of the magnetic field in jet flows of conducting materials: Collisions of two such flows, J. Eng. Phys. Thermophys., 94, No. 3, 654–665 (2021).
L. A. Kovaleva and G. I. Mukhariamova, Effect of electromagnetic treatment and rheological properties of oil: Experiment and application, J. Eng. Phys. Thermophys., 94, No. 3, 714–719 (2021).
J. Belabid, Hydromagnetic natural convection from a horizontal porous annulus with heat generation or absorption, J. Eng. Phys. Thermophys., 94, No. 4, 960–965 (2021).
S. V. Solov’уоv, Simulation of unsteady heat exchange in a spherical electrically conducting liquid layer, Part 1, Yuzhno-Sib. Nauch. Vestn., No. 3, 54–59 (2018).
S. V. Solov’уоv, Investigation of unsteady heat exchange in a spherical electrically conducting liquid layer, Izv. Vyssh. Uchebn. Zaved., Povolzhskii Region, Ser. Fiz. Mat. Nauk,, No. 4, 20–32 (2018).
S. V. Solov’уоv, Simulation of convection in a spherical electrically conducting liquid layer in the case where heat is supplied to the inner sphere, Vych. Tekhnol., 24, No. 5, 61–74 (2019).
S. V. Solov’уоv and T. S. Solov’уоva, Heat exchange in an electrically conducting liquid at small Reynolds numbers, Yuzhno-Sib. Nauch. Vestn., No. 2, 71–79 (2021).
S. V. Solov’уоv, Heat transfer modeling of an electrically conducting fluid in a spherical layer, Numer. Anal. Appl., 88, Issue 4, 351–364 (2015).
S. V. Solov’уоv, Simulation of convective heat exchange in the electrically conducting liquid in a spherical cavity. Algorithm of solution, J. Eng. Phys. Thermophys., 88, No. 6, 1416–1431 (2015).
S. V. Solov’уоv, Influence of joule dissipation on heat exchange and magnetic hydrodynamics of liquid in a spherical layer. Part I, J. Eng. Phys. Thermophys., 90, No. 5, 1251–1265 (2017).
S. V. Solov’уоv, Influence of joule heat dissipation on heat exchange and magnetic hydrodynamics of liquid in a spherical layer. Part II, J. Eng. Phys. Thermophys., 92, No. 4, 976–986 (2019).
S. V. Solov’уоv, Influence of the homochronism number of the liquid in a spherical layer on the heat exchange in it and its magnetic hydrodynamics, J. Eng. Phys. Thermophys., 93, No. 3, 567–575 (2020).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 95, No. 6, pp. 1432–1447, November–December 2022.
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Solov’ev, S.V. Heat Exchange and Magnetic Hydrodynamics of a Liquid in a Spherical Layer at Small Magnetic Reynolds Numbers. J Eng Phys Thermophy 95, 1406–1420 (2022). https://doi.org/10.1007/s10891-022-02609-5
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DOI: https://doi.org/10.1007/s10891-022-02609-5