Entropy generation analysis of the flow of twoimmiscible couple stress fluids between two porous beds

Abstract

This paper investigates the entropy generation analysis in a steady flow of two immiscible couple stress fluids in a horizontal channel bounded by two porous beds at the bottom and top. The flow is considered in four zones: zone IV contains the flow of viscous fluid in the large porous bed with low permeability at the bottom, zones I and II contain free flow of two immiscible couple stress fluids, and zone III contains the flow of viscous fluid in the thin porous bed with high permeability at the top. The flow is assumed to be governed by Stokes’s couple stress fluid flow equations in the free channel. In zone IV, Darcy’s law together with the Beavers-Joseph (B-J) slip condition at the interface is used, whereas in zone III Brinkman’s model is used for flow. The walls of the channel are maintained at constant and different temperatures higher than that of the fluid. The closed-form expressions for velocity and temperature are derived analytically, and these are used to compute the dimensionless expressions for the entropy generation number and Bejan number. The effects of relevant parameters on velocity, temperature, entropy generation number, and Bejan number are analyzed and presented through graphs. It is observed that the porous plates act as smooth surfaces and reduce the viscous friction.