Second law analysis for Poiseuille flow of immiscible micropolar fluids in a channel

In this paper, the problem of steady Poiseuille flow of two immiscible incompressible micropolar fluids between two horizontal parallel plates of a channel with constant wall temperatures is studied in terms of entropy generation. The flow is assumed to be governed by Eringen's micropolar fluid flow equations. The flow region is divided into two zones, the flow of the heavier fluid taking place in the lower zone-I. No slip condition is taken on the plates and at the interface continuity of velocity, micro-rotation, temperature, heat flux and shear stresses is imposed. The velocity, micro-rotation and temperature fields are derived analytically. The dimensionless quantities-entropy generation number (Ns), Bejan number (Be) and irreversibility ratio (ϕ) are analytically derived. The effects of material parameters like micropolarity (ci), couplestress (si) on the velocity, micro-rotation and temperature are investigated. The derived equation for the dimensionless entropy generation number is used to interpret the relative importance of frictions to conduction by varying viscous dissipation parameter. The entropy generation near the plates increases more rapidly in fluid I than in fluid II as viscous dissipation effects become more important in zone I. The velocity and temperature profiles are found to be in good agreement with the distributions of the dimensionless entropy generation number (Ns).