Abstract
The coupled equations of thermal convection and of thermoelectric magnetohydrodynamics in the high Hartmann number approximation are solved for motions inside a thin-walled conducting sphere, where the interfacial temperature and the surface heat transfer rates are both quadratic functions of the Cartesian coordinates. In this case the motion is pure rotation about an axis inclined at an arbitrary angle to the uniform magnetic field. To reduce the complexity of the problem some two- and four-parameter variants are considered. These reveal multiple non-uniqueness, bifurcation and catastrophe-type behaviour when the problem is specified in terms of known heat transfer rates. The stability of solutions is only briefly discussed. The implications for cells of liquid lithium in fusion reactor blankets and possible experiments are outlined.