Abstract In this project we have considered the unsteady couette flow of an electrically conducting viscous, incompressible fluid bounded by two parallel porous plates. The external uniform magnetic field and a uniform suction and injection are applied to the plates. The fluid is subjected to an exponential decaying with time pressure gradient. The two plates are kept at different temperature and the joule and viscous dissipations are included in the energy equation. A numerical solution for the governing momentum and energy equations are obtained using the finite difference.