An analysis of a fully developed forced and free convective magnetohydrodynamic flow between two electrically conducting vertical plates has been carried out taking into account the external circuit and the thermal conductance ratio of the plates. Derived are approximate solutions to the nonlinear integro-differential equations governing the velocity, the temperature, the skin friction, and the Nusselt number. It is observed that an increase in the thermal conductance ratio leads to both an increase in velocity and temperature.