The analogy between a problem of magnetohydrodynamics and the Benard problem in the Boussinesq approximation

It is shown that the equations of motion written in a longitudinal plane of symmetry of a liquid-metal current-carrying conductor of rectangular cross section are identical with the equations that describe heat conduction in a flat layer of liquid heated from below in the Boussinesq approximation. The main parameters that determine the threshold of the convective instability that develops under the action of Lorentz forces in a current-carrying liquid metal are found. (C) 1999 American Institute of Physics. [S1063-7850(99)01705-X].