Second law analysis of the flow of two immiscible couple stress fluids in four zones

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.

This work investigates the entropy generation 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, zone-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 plates of the channel are maintained at constant temperatures higher than that of the fluid. The closed form expressions for entropy generation number and Bejan number are derived in dimensionless form by using the expressions of velocity and temperature. The effects of relevant parameters on velocity, temperature, entropy generation number and Bejan number are analyzed and presented through graphs.