Brinkman Flow of a Viscous Fluid Through a Spherical Porous Medium Embedded in Another Porous Medium

An analytical investigation for a two-dimensional steady, viscous, and incompressible flow past a permeable sphere embedded in another porous medium is presented using the Brinkman model, assuming a uniform shear flow far away from the sphere. Semi-analytical solutions of the problem are derived and relevant quantities such as velocities and shearing stresses on the surface of the sphere are obtained. The streamlines inside and outside the sphere and the radial velocity are shown in several graphs for different values of the porous parameters sigma(1) = (mu/(mu) over bar)(a/root K-1) and sigma(2) = (mu/(mu) over bar)(a/root K-2), where a is the radius of the sphere, mu is the dynamic viscosity of the fluid, (mu) over bar is an effective or Brinkman viscosity, while K-1 and K-2 are the permeabilities of the two porous media. It is shown that the dimensionless shearing stress on the sphere is periodic in nature and its absolute value increases with an increase of both porous parameters sigma(1) and sigma(2).