Buoyancy-driven convection with a uniform magnetic field. Part 1. Asymptotic analysis

We study the convection of an electrically conducting liquid in a horizontal cylinder (horizontal Bridgman configuration). A uniform steady vertical magnetic field is externally imposed. The thermal and magnetic Prandtl numbers are assumed equal to zero. The thermal field is obtained assuming pure conduction and certain conditions at the boundaries, so that the heat flux is axial and uniform. The influence of the cylinder's cross-sectional shape is examined. In the high Hartmann number limit (Ha [Gt ] 1), an analytical solution is found for the fully established flow. With electrically insulating walls, the magnetically damped convective velocity varies as Ha-2 when the cross-section has a horizontal plane of symmetry, while it varies as Ha-1 for non-symmetrical shapes. When the walls are perfectly conducting, the damped velocity always varies as Ha-2.