Flow of Couple-Stress and Micropolar Immiscible Liquid Layers Between Permeable Beds with Entropy Generation

Document Type : Full Length Research Article

Authors

Department of Mathematics, VIT-AP, Guntur, 522237, India

Abstract

The study explores heat and mass transfer characteristics of micropolar and couple stress liquids under the influence of an inclined magnetic field between two permeable beds. Viscous and Darcy dissipations have been accounted for in this model. In this model, the flow is divided into three regions: Region-B contains a micropolar liquid, while Region-A and C are occupied by couple stress liquids. Liquid injection occurs through the lower bed, with extraction from the upper bed at the same velocity. The Beavers-Joseph slip boundary conditions govern the liquid-permeable bed interface. The equations that govern the flow are solved numerically using the RK-4th order method in conjunction with the shooting method in Mathematica. Graphical results have been presented to illustrate the effects of pertinent parameters on velocity, microrotation, temperature, concentration, Nusselt number, entropy generation, Bejan number, and stress distribution. Our results reveal that the flow is suppressed by the Hartmann number, slip, permeability, and frequency parameters. When the Brinkman number, inclination angle, and micropolar material parameter increase, the temperature distribution also rises. However, higher Schmidt and Soret numbers contribute to a decrease in concentration, whereas a greater diffusivity ratio results in a rise in concentration. Entropy generation rises with an increase in the Brinkman number but falls with the growth of the slip parameter. Furthermore, with the rise of the permeability parameter and Hartmann number, the Nusselt number decreases at the lower permeable bed, and it shows a reverse trend at the upper permeable bed. A comparative analysis of our results with those of Nikodijevic et al. [1] and Pramod et al. [2] shows excellent agreement.

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©2025 The Author(s). Journal of Heat and Mass Transfer Research published by Semnan University Press.

This is an open access article under the CC-BY-NC 4.0 license. (https://creativecommons.org/licenses/by-nc/4.0/)

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History

  • Receive Date: 02 April 2025
  • Revise Date: 25 July 2025
  • Accept Date: 02 August 2025

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