Analytical solution of a couple stress fluid saturated in a porous medium through a Reiner–Rivlin liquid sphere

Abstract

The objective of the present investigation is to provide a theoretical analysis of the flow of an incompressible couple stress fluid through a Reiner–Rivlin liquid which is covered by a permeable medium. On the surface of the sphere, the boundary conditions, such as nil couple stress condition, impenetrability condition, continuity of velocities, and continuity of stresses, are applied. This research aims to analyze the flow behavior which has been evaluated under the influence of dimensionless parameter, couple stress parameter, and parameter impacting viscosity. The essential components that influenced the couple stress parameter in relation to couple stress viscosity are physically interpreted and presented. The analysis concludes with a graphical representation of flow pattern and drag under the effects of the couple stress parameter, couple stress viscosity ratio, permeability parameter, etc. The findings demonstrate that the Reiner–Rivlin liquid parameter (S) has an increasing function in the non-dimensional drag case but a decreasing function in the pressure case. Moreover, the stress viscosity of the couple is a significant component that impacts the drag and the pressure. Also, the streamline pattern shows that the couple stress fluid was completely penetrated by the Reiner–Rivlin liquid.