Study of natural convection in the presence of magnetic field (cylindric enclosure)

Abstract

Buoyancy-driven magneto hydrodynamic flow in a liquid-metal filled cylindrical enclosure is investigated by numerical simulations, the finite volume method was applied to solve the mass, momentum and energy equations. The numerical result obtained shows the disappearance of the vortex break down under the effect of an axial temperature gradient between the bottom heated and the top cooled of cylinder. In the case of the natural convection with and without magnetic field for fluid with low Prandtl number, the instability appears in the form of regular oscillations for high values of the critical Grashof number, corresponding to the Hartmann numbers. These oscillations are produced by the multicellular mode of the flow. Diagrams of stability show the dependence of the critical Grashof number and critical frequency with the increase of the Hartmann number. we note that, the action of the magnetic field has a stabilizing effect on the flow.