Influence of the Homochronism Number of the Liquid in a Spherical Layer on the Heat Exchange in it and its Magnetic Hydrodynamics

Представлены результаты численного моделирования конвективного теплообмена электропроводящей жидкости между концентрическими сферами при подводе тепла к внутренней сфере. Исследовано влияние числа Грасгофа и джоулевой диссипации на структуру течения жидкости, поля температуры, магнитной индукции и распределение локальных чисел Нуссельта. Получено уравнение подобия теплообмена, когда ускорение свободного падения направлено к центру сферического слоя. 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.

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Simulation of the Convective Heat Exchange in the Spherical Layer of an Electrically Conducting Liquid

Journal of Engineering Physics and Thermophysics ◽

10.1007/s10891-019-01921-x ◽

2019 ◽

Vol 92 (1) ◽

pp. 183-195

Author(s):

S. V. Solov’ev

Keyword(s):

Heat Exchange ◽

Convective Heat ◽

Convective Heat Exchange ◽

Spherical Layer ◽

Conducting Liquid ◽

Electrically Conducting

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Heat Exchange and Magnetic Hydrodynamics of the Core of the Earth

Heat Transfer Research ◽

10.1615/heattransres.v32.i7-8.100 ◽

2001 ◽

Vol 32 (7-8) ◽

pp. 5

Author(s):

V. K. Bulgakov ◽

S. V. Solov'ev

Keyword(s):

Heat Exchange ◽

Magnetic Hydrodynamics ◽

The Core ◽

The Earth

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Temperature State of the Anisotropic Spherical Layer During Convective Heat Exchange with the Environment

Herald of the Bauman Moscow State Technical University Series Natural Sciences ◽

10.18698/1812-3368-2019-4-40-55 ◽

2019 ◽

pp. 40-55

Author(s):

V.S. Zarubin ◽

V.V. Leonov ◽

V.S. Jr. Zarubin

Keyword(s):

Heat Conduction ◽

Heat Exchange ◽

Convective Heat ◽

Outer Surface ◽

Heat Conduction Problem ◽

Convective Heat Exchange ◽

Spherical Layer ◽

Coating Material ◽

Temperature State ◽

Heat Shielding

The paper focuses on the process of steady heat conduction in a spherical layer of a heat-shielding coating made of anisotropic material. The inner surface of the layer is ideally heat-insulated but its outer surface is exposed to heating by convective heat exchange with the environment, the temperature of which varies along this surface. Based on the obtained solution of the linear heat conduction problem, we quantitatively assessed the influence of the degree of anisotropy of the coating material, its relative thickness, intensity of convective heat transfer, and uneven distribution of ambient temperature on the equalization of temperature distribution in the spherical layer. The results obtained can be used to select the characteristics of an anisotropic coating material in order to reduce the temperature of the outer surface of the spherical layer in the zone of the most intense heating.

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HEAT EXCHANGE OF ELECTRIC CONDUCTIVE LIQUID AT LARGE VALUES OF THE REYNOLD'S MAGNETIC NUMBER

Южно-Сибирский научный вестник ◽

10.25699/sssb.2021.36.2.023 ◽

2021 ◽

pp. 12-22

Author(s):

С.В. Соловьев ◽

Т.С. Соловьева

Keyword(s):

Heat Transfer ◽

Numerical Simulation ◽

Reynolds Number ◽

Fluid Flow ◽

Heat Exchange ◽

Spherical Layer ◽

Magnetic Reynolds Number ◽

Electrically Conductive ◽

Conductive Liquid ◽

Nusselt Numbers

Представлены результаты численного моделирования нестационарного конвективного теплообмена и магнитной гидродинамики электропроводной жидкости в сферическом слое при граничных условиях для температуры первого рода. Исследовано влияние величины магнитного числа Рейнольдса на эволюцию структуры течения жидкости, поле температуры, магнитной индукции и распределение чисел Нуссельта. The results of numerical simulation of unsteady convective heat transfer and magneto hydrodynamics of an electrically conductive fluid in a spherical layer under boundary conditions for a temperature of the first kind are presented. The influence of the value of the magnetic Reynolds number on the evolution of the structure of the fluid flow, the field of temperature, magnetic induction and the distribution of Nusselt numbers is investigated.

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