Couple stress fluid flow enclosing a solid sphere in a porous medium: Effect of magnetic field

Abstract

The present research explores the Stokesian flow of an axisymmetric, incompressible couple stress fluid through a porous material enclosing a solid sphere in the presence of a uniform magnetic field. Utilizing the separation of variables technique, the problem is solved analytically. Expressions for the stream function, velocity components, vorticity component, fluid pressure, stress tensors, and couple stresses are obtained, which involved modified Bessel functions, trigonometric functions, and algebraic functions. Impenetrability, no-slip, and nil-vorticity conditions have been applied at the interface. A novel result for the drag force experienced by a solid sphere enclosed in porous material under the applied uniform magnetic field is reported. The evidence already in place leads to the identification and validation of our results for flow past the impermeable sphere. Tangential velocity and normal velocity, drag force, and streamline patterns are displayed for different values of flow parameters, which incorporate the Hartmann number, permeability parameter, and couple stress parameter.