Purpose-The purpose of this paper is to examine the flow, heat transfer and entropy generation characteristics for an inclined channel of two immiscible micropolar fluids. Design/methodology/approach-The flow region consists of two zones, the flow of the heavier fluid taking place in the lower zone. The flow is assumed to be governed by Eringen's micropolar fluid flow equation. The resulting governing equations are then solved using the homotopy analysis method. Findings-The following findings are concluded: first, the entropy generation rate is more near the plates in both the zones as compared to that of the interface. This indicates that the friction due to surface on the fluids increases entropy generation rate. Second, the entropy generation rate is more near the plate in Zone I than that of Zone II. This may be due to the fact that the fluid in Zone I is more viscous. This indicates the more the viscosity of the fluid is, the more the entropy generation. Third, Bejan number is the maximum at the interface of the fluids. This indicates that the amount of exergy (available energy) is maximum and irreversibility is minimized at the interface between the fluids. Fourth, as micropolarity increases, entropy generation rate near the plates decreases and irreversibility decreases. This indicates an important industrial application for micropolar fluids to use them as a good lubricant. Originality/value-The problem is original as no work has been reported on entropy generation in an inclined channel with two immiscible micropolar fluids.

In this work, we present the theoretical investigation of the transient rotating electro-osmotic flow of a couple stress fluid in a microchannel, through the Laplace transform technique. The analysis is dependent on the Debye–Hückel linear approximation for electrical potentials. The governing equations of the couple stress fluid are taken to address the flow field in a rotating environment. The mathematical formulation of these governing equations provides a system of ordinary differential equations, which are then solved to achieve analytical solutions for electrostatic potential, axial and transverse velocity distribution, and volumetric flow rate. A comparison was made for the present analytical solution with data available in the literature. There was excellent matching. The characteristics of different influential parameters on axial and transverse velocity distributions, volume, and angle flow rates are pictorially deliberated. The study reveals that the rise in the couple stress parameter accelerates the axial electro-osmotic flow velocity inside the electrical double layer.

An attempt has been made to study the entropy generation analysis of couple stress fluid flow in an annulus between two concentric rotating vertical cylinders. There is a porous lining attached to the inside of an outer cylinder. The flow is under the influence of a radial magnetic field. The flow in the annular gap is caused by rotation of the cylinders. The Stokes couple stress flow model is employed. The flow in the porous sleeve is governed by Darcy's law. The velocity, temperature, entropy generation number, Bejan number, wall shear stress and heat transfer rate at the inner and outer cylinders are obtained numerically by employing a finite difference scheme with vanishing of couple stresses on the boundary. The effect of relevant parameters on the flow and entropy generation rate are discussed and depicted through graphs.

The paper aims the heat transfer analysis for the flow of two immiscible micropolar fluids inside a horizontal channel, by the first and second laws of thermodynamics under the action of an imposed transverse magnetic field. The plates of the channel are maintained at constant 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. The condition of hyper-stick is taken on the plates and continuity of velocity, micro-rotation, temperature, heat flux, shear stress and couple stress are imposed at the interface. The velocity, micro-rotation and temperature profiles 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 walls.

MSC Classification: 76A05; 35Q79; 80A20The present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. The dimensionless fluid equations are solved by using homotopy analysis method (HAM) and validated with Runge-Kutta shooting method (RKSM). The convergent series solution is then used for the irreversibility analysis in the flow domain. The effects of thermal conductivity and viscosity variation parameters, couple stress parameter, Reynolds number, Grashof number, Hartmann number on the velocity profile, temperature distribution, entropy production, and heat irreversibility ratio are presented through graphs, and salient features of the solutions are discussed. The computations show that the entropy production rate decreases with increased magnetic field and thermal conductivity parameters, whereas it rises with increasing values of couple stress parameter, Brinkman number, viscosity variation parameter, and Grashof number. The study is relevant to lubrication theory.

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