A study of creeping magnetohydrodynamic viscous flow past a viscous fluid sphere placed in a porous medium

Resumo

This paper presents the steady flow of an incompressible magnetohydrodynamic viscous fluid past a viscous fluid sphere placed in a porous medium. The dynamics of fluid motion are determined by the Stokes equation within the fluid domain, accompanied by the Lorentz force resulting from an external magnetic field. The flow is assumed to exhibit uniform characteristics when situated at a certain distance from the fluid sphere, and the no-slip boundary condition is applied at the fluid sphere surface. The solution is obtained by applying these boundary conditions. Expressions for the stream functions and fluid sphere's drag force are derived using an analytical method. We provide a graphical presentation and discuss the relationship among the coefficient of drag, Hartmann number, and porosity parameter. It is noted that a raise in the porosity parameter and Hartmann number values raises the drag. It is also noticed that the drag in magnetohydrodynamic viscous fluid flow past a fluid sphere in a porous medium is more significant than in magnetohydrodynamic flow past a fluid sphere without a porous medium. This is attributed to the combined resistance of Lorentz forces and the permeability of the porous medium. The current study subsequently obtains some findings that correspond with previous research.