Unsteady Flow of Two Immiscible Viscous Fluids Over a Naturally Permeable Bed

Abstract

The unsteady flow of two viscous, incompressible and immiscible fluids in a long parallel channel of which the upper one is impervious and lower one is porous of infinite thickness is considered by taking a pressure gradient of the form Pe/sup ct/, where P and c are constants. Beavers and Joseph's slip condition at the permeable interface and the generalised Darcy's law in the porous region have been used. The analysis reveals that the flow depends upon the Reynolds number for the upper and lower fluids, slip parameter and the porous parameter. The effect of slip parameter alpha and the porous parameter neta on the flow are studied in detail.