Multiphase flow of Newtonian fluid sandwiched between non-Newtonian fluids through a composite porous channel

The present study is concerned with the flow of a Newtonian fluid through a composite rectangular porous channel sandwiched between two non-Newtonian fluids (micropolar and couple stress fluids). The horizontal composite porous channel is divided into three porous channels of uniform width and flow is induced due to a constant pressure gradient. The governing Brinkman equation is used to describe the motion of the middle porous channel, while governing equations of micropolar and couple stress fluids are used to describe the motion of lower and upper porous channels, respectively. Expressions of linear velocity, microrotations, stresses (shear and couple) and flow rate are obtained analytically. Continuity of velocity, continuity of tangential stresses, no slip, no spin and no couple stress conditions are used at interfaces and outer surfaces of the composite porous channel as boundary conditions. Effect of various parameters on flow rate and fluid velocity are discussed and presented graphically.