First and Second Law Analysis for the MHD Flow of Two Immiscible Couple Stress Fluids between Two Parallel Plates

This paper aims to analyze the heat transfer by the first and second laws of thermodynamics for the flow of two immiscible couple stress fluids inside a horizontal channel under the action of an imposed transverse magnetic field. The plates of the channel are maintained at constant and different temperatures higher than that of the fluid. The flow region consists of two zones, the flow of the heavier fluid taking place in the lower zone. No slip condition is taken on the plates and continuity of velocity, vorticity, shear stress, couple stress, temperature, and heat flux are imposed at the interface. The velocity and temperature distributions are derived analytically and these are used to compute the dimensionless expressions for the entropy generation number and Bejan number. The results are presented graphically. It is observed that the imposed magnetic field reduces the entropy production rate near the plates.