In this study, the transient generalized Couette flow with heat transfer of a dusty viscous incompressible electrically conducting fluid is studied under the influence of a constant pressure gradient and considering the ion slip. An external uniform magnetic field is applied perpendicular to the plates which are kept at constant temperatures. A numerical
solution for the governing momentum and energy equations are obtained using the method of finite differences. The influence of various magnetic field parameters (magnetic field intensity, Hall parameter, ion slip parameter) on the velocity and temperature fields of both the fluid and dust particles phases is demonstrated.