Drag Experienced by a Composite Sphere in an Axisymmetric Creeping Flow of Micropolar Fluid

This paper concerns an analytical study of a steady axisymmetric uniform flow of an incompressible micropolar fluid past a permeable sphere that contains a solid sphere. The mathematical expression for the flow fields are obtained in terms of stream function by using modified Bessel’s function and Gegenbauer function. No-slip condition, zero microrotation components, continuity of normal velocity which is equal to the filtration velocity on the surface of the sphere are used as boundary conditions. It is assumed that the fluid obeys Darcy law at the permeable surface. The internal and external drag force exerted by the fluid on the sphere, flow rate and the relevant quantities such as pressures, microrotation vectors have been calculated. It is observed that drag is greater for impermeable sphere as compared to permeable sphere. As permeability parameter increases the flow rate also increases rapidly. Various useful results are obtained and compared with the previous particular cases.

Keywords:

Permeable sphere , Micropolar fluid , Darcy law , Drag force , stream function