Magnetohydrodynamic couple stress fluid flow past a partially contaminated liquid drop embedded in a porous medium

Abstract This article provides an analytical framework for magnetohydrodynamic (MHD) couple stress fluid (CSF) flow around a partially contaminated liquid drop within a porous medium, utilizing the interfacial slip condition. The Brinkman and Stokes' equations are utilized to investigate the flow dynamics within and surrounding the porous region. The external magnetic field on the fluid flow, which is in the transverse direction, is represented by Lorentz's force. The boundary value problem addresses the continuity of the velocity components and stress distributions. Analytical expressions for stream functions are derived using the variable separable method, drag force on a liquid drop are calculated using the integration method. Specific cases are analyzed, including viscous fluids under both slip and no‐slip conditions, as well as rigid spheres and liquid drops. The findings are consistent with existing literature. Graphical analysis illustrates the relationship among the drag coefficient, couple stress viscosity ratio, and porosity parameter. Couple stress effects enhance rigid sphere drag more than liquid drop drag when the couple stress viscosity ratio increases. As the porosity parameter increases, drag also increases. The inner and outer streamlines get more disturbed as the couple stress viscosity ratio increases, creating more internal streamlines. Furthermore, a comparison investigation discovered that the drag of MHD couple stress fluid flow past a contaminated liquid drop in a porous media is larger than that of MHD viscous flow under the same conditions. This study enables improved control for geothermal and drug delivery applications.