Three-dimensional buoyant convection in a rectangular cavity with differentially heated walls in a strong magnetic field

Three-dimensional buoyant convection in a rectangular cavity with a horizontal temperature gradient in a strong, uniform magnetic field is considered. The walls of the cavity are electrically insulating. An asymptotic solution to the problem in the inertialess approximation is obtained for high values of the Hartmann number, Ha. In the presence of either the vertical or the horizontal longitudinal fields, the three-dimensional flow is characterised by high-velocity jets at the walls of the cavity parallel to the magnetic field. The velocity of the jets is O(Ha) times higher than in the bulk of the fluid. On the other hand, in the presence of the horizontal transverse magnetic field, the velocity in the core is O(Ha) times higher than in the other two cases. However, no jets are present in the parallel layers. The analysis of the convective heat transfer for low values of the Peclet number shows that either the vertical, or the longitudinal field is the most efficient in damping of the convective heat transfer, depending on the dimensions of the cavity.