Effect of induced magnetic field and heat transfer on nonstationary magnetohydrodynamic flow around a porous plate

A. A. Megakhed

Abstract
A study is made of the problem of the nonstationary flow of a conducting viscws incompressible liquid around a flat porous plate taking into accwnt the induced magnetic field and the heat transfer. An exact solution is obtained for the flow rate and the induced magnetic field for constant suction and magnetic Prandtl number equal to unity when the free flow rate is a function of time and it is shown that it is possible to obtain such a solution only at an Alfven speed smaller than the suction rate. When the free flow rate is constant or is a periodic function of time, an explicit solution is obtained. A solution is also obtained for the nonstationary equation for the heat flux taking into account the viscous energy dissipation and Joule heating. In this case exact solutions for the temperature field are obtained when a) there is no heat transfer at the plate, and b) the temperature of the plate is a given function of time.