Stokes flow of an incompressible micropolar fluid past a porous spheroidal shell

Abstract

Consider a pair of confocal prolate spheroids S0 and S1 where S0 is within S1. Let the spheroid S0 be a solid and the annular region between S0 and S1 be porous. The present investigation deals with a flow of an incompressible micropolar fluid past S1 with a uniform stream at infinity along the common axis of symmetry of the spheroids. The flow outside the spheroid S1 is assumed to follow the linearized version of Eringen’s micropolar fluid flow equations and the flow within the porous region is assumed to be governed by the classical Darcy’s law. The fluid flow variables within the porous and free regions are determined in terms of Legendre functions, prolate spheroidal radial and angular wave functions and a formula for the drag on the spheroid is obtained. Numerical work is undertaken to study the variation of the drag with respect to the geometric parameter, material parameter and the permeability parameter of the porous region. An interesting feature of the investigation deals with the presentation of the streamline pattern.