In the present study, the unsteady Couette flow with heat transfer of a dusty viscous incompressible electrically conducting fluid under the influence of an exponential decaying pressure gradient is studied without neglecting the Hall effect. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field is applied perpendicular to the plates. The governing equations are solved numerically using finite differences to yield the velocity and temperature distributions for both the fluid and dust particles.