Viscous Fluid Flows Induced by Translational-Oscillatory Motion of a Submerged Porous Sphere

Abstract

Viscous fluid flows induced by a translational-oscillatory motion of a submerged porous sphere are determined. The fluidmotion inside and outside the sphere is considered in amoving noninertial reference frame fitted to the sphere. Exact analytical solutions of the Navier–Stokes equation outside the sphere and the nonstationary Brinkman equation inside the sphere are found. Examples of streamline patterns for some values of governing parameters are presented. It is shown that the results obtained earlier for particular cases of viscous flow around an impermeable solid sphere can be obtained from the solution presented.