Heat transfer by laminar flow between parallel plates under the action of transverse magnetic field

Solutions of the energy equation of magnetohydrodynamics are obtained for the heat-transfer problem corresponding to Hartmann's velocity profile for forced flow between two infinite parallel plates. The semi-infinite plates z=+L, x≤0, are kept at a constant temperature T0 and the plates z=±L, x≥0, are kept at a different temperature Ts (constant). Solutions are found which are valid for the regions x≤0 and x≥0 respectively. These are joined smoothly at the plane x=0 by imposing certain continuity conditions. Asymptotic solutions for large M≥10 are presented. A simplified case valid for large Peclet numbers is worked out numerically and the mean mixed temperature and local total Nusselt numbers are tabulated and shown graphically. These are compared with the corresponding values for the heat-transfer problem in which the magnetic field is absent and the fluid is electrically non-conducting. It is found that due to ionic-conductivity the mean mixed temperature at any point is decreased and consequently the local total Nusselt number is increased