Couette flow of micropolar fluid in a channel filled with anisotropic porous medium

Abstract

This paper presents a mathematical model for the flow of micropolar fluid in a horizontal channel filled with an anisotropic porous medium, bounded by two parallel plates—where the upper plate is stationary, and the lower plate moves at a constant velocity. The flow, driven by both a constant pressure gradient and the movement of the lower plate, is governed by the Darcy-Brinkman equation. Using no-slip and no-spin boundary conditions, we analytically derive expressions for the velocity, microrotational velocity, and stress distributions. The study provides a graphical analysis of the flow behavior influenced by key parameters such as the Darcy number, porous medium anisotropy, anisotropy angle, and the micropolar fluid’s material parameters. Furthermore, the effects of the material parameters and Darcy number on shear stress and couple stress are thoroughly investigated. The findings have applications in modeling fluid flow in striated or fractured rock formations.