Flow of Two Immiscible Couple Stress Fluids between Two Permeable Beds

The paper deals with the flow of two immiscible couple stress fluids between two homogeneous permeable beds. The flow is considered in two zones: zone I and II contain free flow of two immiscible couple stress fluids between two permeable porous beds at the bottom and top. The flow in the free channel bounded by two permeable beds is assumed to be governed by Stokes’s couple stress fluid flow equations and that in the permeable beds by Darcy’s law. The continuity of velocity, vorticity, shear stress and couple stress are imposed at the fluid-fluid interface and Beavers-Joseph (BJ) slip boundary conditions are employed at the fluid-porous interface. The equations are solved analytically and the expressions for velocity, skin friction and volumetric flow rate are obtained. The effects of the physical governing parameters on velocity are investigated.

Keywords:

Beavers , Immiscible fluids , Couple stress fluid , Joseph (BJ) slip boundary condition , Permeable beds , Darcy’s law