Magnetohydrodynamic Stokes flow of couple stress fluid past a viscous liquid drop in a porous medium

Abstract

This article analyzes the steady flow of couple stress fluid past a viscous liquid droplet embedded
in a porous medium under the influence of a magnetic field, employing a no-slip condition. The Stokes and
Brinkman equations examine the flow dynamics within and around the liquid drop. The influence of an
external magnetic field on fluid flow is characterized by Lorentz’s force in the transverse direction. Analytical
expressions for stream functions and drag force on a liquid drop are derived. The analysis yields specific cases,
such as viscous fluid flow past a viscous liquid drop and a solid sphere, with results in strong agreement with
established literature. Graphical analysis illustrates the relationship among the coefficient of drag, couple
stress parameter, and Hartmann number. At low couple stress parameter values, strong couple stress effects
result in higher drag. The drag also increases with the rising Hartmann number. Streamline patterns are
analyzed about different couple stress parameters and Hartmann numbers.