Magnetohydrodynamics stability of a rotating flow with heat transfer

We study the magnetohydrodynamic stability of an axisymmetric rotating flow in a cylindrical enclosure filled with a liquid metal (Pr = 0.015), having an aspect ratio equal to 2, and subjected to a vertical temperature gradient and an axial magnetic field. The finite volume method is used in order to solve the equations of continuity, momentum, energy, and electric potential. Without magnetic field, the critical Reynolds number is a decreasing function of the Richardson number owing to the destabilizing contribution of natural convection. In the presence of a vertical magnetic field, the flow stability is preserved for higher values of the Reynolds number. The stability diagram which is established shows the dependence of the critical Reynolds number with the increase of the Hartmann number, Ha, for various values of the Richardson number. This study confirms the possibility of stabilization of a liquid metal flow in mixed convection by application of an axial magnetic field.