The unsteady Hartmann flow of a conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal insulating porous plates is studied with heat transfer. A uniform pressure gradient which decays exponentially is imposed in the axial direction. An external uniform magnetic field and uniform suction and injection through the surface of the plates are applied in the vertical direction. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are considered in the energy equation. Numerical solutions for the governing momentum and energy equations are obtained using finite differences. The effect of the magnetic field, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions is investigated. and Obsahuje seznam literatury