An idealized induction furnace, in which the motion is due to thermal buoyancy, is analysed by the simultaneous solutions of the Maxwell, Navier–Stokes and energy equations commonly used in magnetohydro-dynamics. Temperature and velocity profiles are obtained, and an understanding of the coupling between electromagnetic, thermal and mechanical phenomena is gained. It is shown that, for a given applied magnetic field produced by the exciting coil and a given furnace width, there is an optimum frequency of exciting current which produces maximum motion of the molten charge.