Simulation of non-stationary heat exchange of electro-conductive liquid in a spherical layer

Background. In the paper, unsteady convective heat transfer of an electrically conductive liquid between two isothermal concentric spheres is investigated when the acceleration vector of gravity is directed along the radius to the center of the spherical layer. The effect of Grasgof's number on the structure of fluid flow, temperature field, magnetic induction and the distribution of Nusselt numbers is investigated. Materials and methods. To solve the problem, a finite element method is used. In a dimensionless formulation the problem is solved by taking into account the magnetic, inertial, viscous and lifting forces in a spherical coordinate system, taking into account symmetry in longitude. Results. Non-stationary and stationary temperature fields, stream functions, vortex strength, radial and meridional components of magnetic induction, and the distribution of Nusselt local numbers of an electrically conducting liquid in a spherical layer for various Grashof numbers are obtained. Conclusions. It is shown how the fields of temperature, magnetic induction, the distribution of Nusselt numbers and the structure of fluid flow in a spherical layer change with increasing convection intensity.