Asymptotic analysis and symmetry in MHD convection

The motion of an electrically conducting fluid in the presence of a steady magnetic field is analyzed. For any non-uniform magnetic field and any non-electromagnetic driving force, a high Hartmann number asymptotic analysis is developed using curvilinear coordinates based on the magnetic field. This analysis yields the structure of the electric current density and velocity fields. In a second step, orthogonal planar symmetries lead to a significant simplification of the asymptotic structure, depending on the nature of the symmetry. The asymptotic solution is applied to some configurations, some of them corresponding to crystal growth from a melt. In the case of electrically insulating boundaries, the nature of the symmetry is found to govern the magnitude and structure of the damped velocity. copyright 1996 American Institute of Physics