Slow Flow Past Porous Shell of Variable Permeability with Cavity at the Centre

In this paper slow flow of a viscous, incompressible fluid past a heterogeneous porous spherical shell with cavity is discussed. The permeability of porous sphere is varying with radial distance. Flow outside the porous spherical shell and inside the central cavity region is governed by the Stoke's equation. Brinkman equation is used to analyze the flow inside the porous region. The boundary conditions used at the interface of porous and clear region are the continuity of velocity and stress. Exact solution of the problem is obtained and relevant quantities such as stream lines, velocity, pressure and drag on surface of the spherical shell are evaluated and exhibited graphically. The effect of various parameters on the flow has been discussed. Obtained results are useful for the flow past porous particles of variable permeability.