Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field

Abstract We propose an analytical solution to the equations of magnetohydrodynamics that can be used to model the effect of a transverse magnetic field on buoyancy driven convection in a two-dimensional cavity. In the high Hartmann number limit, the velocity gradient in the core is constant outside of the two Hartmann layers at the vicinity of the walls normal to the magnetic field. We show that this core solution is correct everywhere in the cavity except in a boundary layer of extent Ha − 1 2 at the cold wall. The recirculating part of the flow is studied by means of a series expansion that allows for the computation of the stream function. We also present the variation of both components of velocity as a function of Ha, along with a discussion of the validity of our assumptions.

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