Flow of a viscous fluid at small Reynolds number past a porous sphere with a solid core

Uniform flow of an incompressible viscous fluid at small Reynolds number past a porous sphere of radius a with a solid concentric spherical core of radius b has been discussed. The region of the porous shell is called zone I which is fully saturated with the viscous fluid, and the flow in this zone is governed by the Brinkman equation. The space outside the shell where clear fluid flows is divided into two zones (II and III). In these zones the flow is discussed following Proudman and Pearson's method of expanding Stokes' stream function in powers of Reynolds number and then matching Stokes' solution with Oseen's solution. The stream function of zone II is matched with that of zone I at the surface of the shell by the condition suggested by Ochoa - Tapia and Whitaker. It is found that the drag on the spherical shell increases with the increase of the lambda (=b/a) and also with the increase of the Darcy number. The graph of dimensionless drag against lambda for various values of Reynolds number shows that the drag increases with the increase of the Reynolds number for all values of lambda.