This article describes an analytical study of the steady flow of an incompressible micropolar fluid past a porous stationary sphere with a non-zero spin boundary condition for the microrotation vector. The problem is modeled by the Stokes equations for micropolar fluids in the exterior region, while the Brinkman equations are used to model the flow in the porous region. An appropriate stream function formulation in spherical coordinates is used to transform the governing equations into a set of coupled ordinary differential equations, which are solved analytically using special functions. Closed-form solutions for the velocity field, microrotation, and drag force are derived. The effects of various physical parameters, such as the coupling number, micropolar parameter, permeability parameter, and spin boundary parameter, on the hydrodynamic drag are studied in detail. The results show that the effect of microrotation on the drag characteristics is substantial compared to the Newtonian fluid, and the drag on the porous sphere is reduced due to the non-zero spin boundary condition. Various limiting cases are obtained from the current formulation, and the results are found to match with the existing literature, thus validating the analysis.
Priyadarsini et al. (Fri,) studied this question.