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An unsteady flow formation in Couette motion of an electrically conducting fluid subject to transverse magnetic field has been analyzed in the presence of suction/injection through the porous plates when one of the porous plates is in ramped motion. It is assumed that the porous plates are uniformly permeable and the fluid is entering the flow region through one of the porous plates at same rate as it is leaving through the other porous plate. The resulting boundary value problem has been solved exactly under the assumption of a negligible induced magnetic field, external electric field and pressure gradient. Unified closed form expressions for the velocity field and skin-friction corresponding to the case of a magnetic field fixed relative to the fluid or to the moving porous plate have been presented. In order to highlight the impact of the ramp motion of the porous plate on the fluid flow, it has also been compared with Couette flow between porous plates when one of the porous plates has been set into an impulsive motion.

Unsteady hydromagnetic couette flow due to ramped motion of one of the porous plates