DRAG ON A POROUS SPHERE ENCLOSED IN A SOLID CORE EMBEDDED IN COUPLE STRESS FLUID

Abstract

In this paper, the problem of steady and axisymmetrical creeping flow of couple stress fluid past a permeable sphere enclosed by a solid core is analyzed. The continuous case of normal velocity and tangential velocity, stress jump boundary condition, and couple stress to be vanishing conditions are applied on the surface of the porous sphere, and the nonpenetrability boundary condition is applied for solid sphere. The problem is expressed by using the Stokes and Brinkman equations, which describe both the flow outside and inside the porous sphere, respectively. Expressions for the couple stress tensor and velocity fields are obtained in terms of Gegenbauer polynomials and Macdonald functions. Both the pressure distribution and the stream function solution for the axially symmetric motion are explicitly solved. An analytical determination for the flow field in terms of stream function is examined by wielding the method of separation of variables. The drag force felt by a permeable sphere due to the external and internal flow is calculated. The impact of the viscosity coefficients and couple stress parameter on drag is investigated numerically, and the findings are displayed in graphical form. The findings show that the uniform flow of a couple stress fluid past a porous sphere enclosed by a solid core with stress jump condition has less drag than the flow of a couple stress fluid through a porous sphere with continuous case of shear stress, and the presence of stress jump coefficients reduces the drag force, pressure, and couple stresses. With reference to earlier, well-known cases, some unique cases of flow past a porous sphere have been validated.