Thermally coupled magnetohydrodynamics flow

摘要

This paper deals with the questions of existence and uniqueness of solutions to the equations of stationary, incompressible magnetohydrodynamics (MHD) when bouyancy effects due to temperature differences in the flow cannot be neglected. To that effect we couple the MHD equations to the heat equation and employ the well-known Boussinesq approximation. We consider the equations posed on a bounded three-dimensional domain. We point out that these equations model such phenomena as the cooling of nuclear reactors by electrically conducting fluids, continuous metal casting, crystal growth, and semiconductor manufacture.