Heat transfer and magnetic hydrodynamics of liquid in a spherical layer. Part 1

Abstract

Background. The processes of heat transfer of an electrically conductive liquid in closed volumes (in particular, in spherical concentric layers) play an important role for a wide range of problems in space technology, nuclear energy, geophysics and astrophysics. These studies have been studied in sufficient detail for the case when in the Navier-Stokes equation in the expression for the lift force the gravity vector is directed vertically downwards. When studying the heat transfer of an electrically conductive fluid, there are a number of problems when there is a fundamental difference in the Navier-Stokes equation in the expression for the lifting force − the gravity vector is directed along the radius to the center (or away from the center) of the spherical layer, and not vertically down. Such work is still not enough. Therefore, the study of the convective heat transfer of an electrically conductive fluid in a spherical layer (the gravity vector is directed along the radius towards or away from the center of the spherical layer) and its evolution, taking into account the dissipation of the Joule heat, inertial, viscous, lifting and magnetic forces, is an actual task. Materials and methods. The finite element method is used to solve the problem. In a dimensionless form, the problem in variables vortex, stream function, temperature and magnetic induction is solved in a spherical coordinate system, taking into account symmetry in longitude. Results. The influence of small values of the magnetic Reynolds number on the evolution of the temperature fields, the current function, the vortex, the radial and meridional components of the magnetic induction, and the distribution of local Nusselt numbers in a spherical layer of an electrically conductive liquid is studied. It has been found that the influence of Joule heat dissipation on heat transfer and magnetic hydrodynamics of the fluid increases with decreasing magnetic Reynolds number. The threshold value of the magnetic Reynolds number and the time at which the intensity of heat transfer on the surfaces of the spherical liquid layer changes occur are determined. Conclusions. The results obtained can be used in the design of thermal and magnetohydrodynamics processes in power apparatuses, devices and objects, when it is necessary to provide a maximum heat flux on the inner or outer surface (depending on the task) of a spherical liquid layer.

Keywords

• mathematical modeling
• unsteady convective heat transfer
• magnetohydrodynamics
• spherical layers