Abstract
The heat transfer equation for a two-dimensional magnetohydrodynamic channel flow has been solved using boundary conditions of the third kind considering a discontinuity in the “ambient” temperature. The boundary conditions of the third kind indicate that the normal temperature gradient at a particular point in the boundary is assumed to be proportional to the difference between the fluid temperature and the externally prescribed ambient temperature. The presence of an external circuit is also considered to permit the flow of an electric current in the direction perpendicular to the plane of analysis. The resistance of the external circuit is varied from zero (closed circuit) to infinity (open circuit). Temperature fields far away from and near to the discontinuity are found separately and then added in order to obtain the temperature in the whole flow region. The solutions in the limits where the boundary conditions become first (Dirichlet) or second (Neumann) kind are discussed and the influence of the external resistance and the Hartmann, Peclet and Biot numbers on the temperature distribution is investigated.
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