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Article information
2019 , Volume 24, ¹ 5, p.61-74
Solov`ev S.V.
Simulation of electrically conductive liquid convection in a spherical layer when heat is applied to the inner sphere
The Boussinesq approximation is used for modelling a large class of problems of convective heat transfer in spherical concentric layers in which the gravity vector is directed vertically downwards. But for problems of geophysics and astrophysics there is a fundamental difference, the gravity vector is directed along the radius to the center of the spherical layer. Therefore, the study of convective heat transfer in spherical layers, when the vector of gravitational acceleration is directed along the radius to the center of the spherical layer, is of independent interest. In this paper, the influence of the Grashof number, the Joule dissipation heat on the fluid flow structure, temperature field, magnetic induction, and the distribution of Nusselt numbers when heat is applied from below are studied. To solve the problem, the finite element method is used. In a dimensionless formulation, the problem is solved taking into account both the heat of the Joule dissipation, magnetic, inertial, viscous and lifting forces in a spherical coordinate system and the symmetry in longitude. The stationary fields of temperature, stream functions, vortex strength, radial and meridional components of magnetic induction and the distribution of local Nusselt numbers of electro conductive liquid in a concentric spherical layer for different Grashof numbers with and without accounting for the heat of Joule dissipation are obtained when heat is applied to the inner sphere. Two critical values of the Grashof number are numerically determined. The equation of heat exchange similarity is obtained, when the acceleration of gravity is directed to the center of the spherical layer. The mathematical model and the presented results may be useful for the study of convective heat exchange of electrically conducting fluid in space technologies and in the geophysical and astrophysical problems.
[full text]
Keywords: mathematical modeling, convective heat transfer, Joule dissipation, magnetic hydrodynamics, spherical layer, heat exchange similarity equation
doi: 10.25743/ICT.2019.24.5.006.
Author(s):
Solov`ev Sergey Viktorovich
Dr. , Professor
Position: Professor
Office: Pacific State University
Address: 680035, Russia, Khabarovsk, 136, Tikhookeanskaja street
Phone Office: (4212)-375188
E-mail: solovjovsv@rambler.ru
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Bibliography link:
Solov`ev S.V. Simulation of electrically conductive liquid convection in a spherical layer when heat is applied to the inner sphere // Computational technologies. 2019. V. 24. ¹ 5. P. 61-74
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