MHD Effects on the Flow of Second-Grade Fluid Sandwiched between Two Newtonian Fluid Layers through Porous Medium

The present problem is associated with the flow of second-grade fluid which is sandwiched between two Newtonian fluid layers through the horizontal porous channels. The fluids are immiscible, incompressible and the flow in both regions are unsteady. Flow of electrically conducting fluids in horizontal porous channels is governed by the Brinkman equation under the assumption that effective viscosity and dynamical viscosity of fluids are equal. The flow is caused due to a time dependent pressure gradient and a uniform magnetic field acting in perpendicular direction to the fluid flow. No-slip conditions and interface conditions (velocity continuity, shearing stress continuity) have been employed as boundary conditions. Analytical expressions for flow velocities and volumetric flow rate are obtained. Influence of magnetic field and other various parameters such as viscosity ratio, elasticity parameter, density ratio, electrical conductivity ratio and permeability on the fluid velocity and flow rate are explained graphically. Present study can be used to solve the real-life problems where multicomponent flow exists, such as flow of various industrial fluids, flow in the rivers, flow of various immiscible oils through the bed of rocks or soils, flow of bloods in the arteries, flow of immiscible chemicals, etc.