Buoyancy-driven MHD flow in electrically insulated rectangular ducts

A fully developed buoyant flow in a straight, horizontal rectangular duct with an axial temperature gradient in an arbitrary oriented, transverse magnetic field is investigated. The walls of the duct are electrically insulating. It is known that in the vertical magnetic field the flow is weak in the middle of the duct with high velocities near the walls parallel to the magnetic field. In the horizontal field, the velocity profile is more uniform, while the damping is weaker. The transition between the two cases is studied. It is shown that as the angle a between the magnetic field and the vertical co-ordinate increases, the flow becomes topologically similar to that in the horizontal field even for small values of a. This is due to the change in the closure pattern of the electric current. The electric current has to complete its loop at the walls of the duct, all of which become the Hartmann walls. The Hartmann-layer current induces an electric potential in the core, which leads to high velocities in the bulk of the flow.