OSCILLATORY FLOWOF AN INCOMPRESSIBLE COUPLE STRESS FLUID BETWEEN PERMEABLE BEDS WITH AN IMPOSED UNIFORM MAGNETIC FIELD

In this paper, we investigate the oscillatory flow of an incompressible couple stress fluid between permeable beds. The fluid is driven by an unsteady oscillatory pressure gradient. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. It is assumed that a uniform magnetic field is imposed in a direction normal to the flow. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy's law. The Beavers-Joseph (BJ) slip boundary conditions are used at fluid-permeable bed interfaces. The equations are solved analytically and the expressions for velocity and mass flux are obtained. The effects of Hartmann number, couple stress parameter, porosity parameter, slip parameter, frequency parameter, and the oscillatory component of the pressure gradient on the velocity are studied numerically and the results are presented through graphs.