Control of MHD Flow and Heat Transfer of a Micropolar Fluid through Porous Media in a Horizontal Channel

Abstract

The problem considered in this paper is a steady micropolar fluid flow in porous media between two plates. This model can be used to describe the flow of some types of fluids with microstructures, such as human and animal blood, muddy water, colloidal fluids, lubricants and chemical suspensions. Fluid flow is a consequence of the constant pressure gradient along the flow, while two parallel plates are fixed and have different constant temperatures during the fluid flow. Perpendicular to the flow, an external magnetic field is applied. General equations of the problem are reduced to ordinary differential equations and solved in the closed form. Solutions for velocity, microrotation and temperature are used to explain the influence of the external magnetic field (Hartmann number), the characteristics of the micropolar fluid (coupling and spin gradient viscosity parameter) and the characteristics of the porous medium (porous parameter) using graphs. The results obtained in the paper show that the increase in the additional viscosity of micropolar fluids emphasizes the microrotation vector. Moreover, the analysis of the effect of the porosity parameter shows how the permeability of a porous medium can influence the fluid flow and heat transfer of a micropolar fluid. Finally, it is shown that the influence of the external magnetic field reduces the characteristics of micropolar fluids and tends to reduce the velocity field and make it uniform along the cross-section of the channel.