The flow between a rotating disk and a stationary porous disk of finite thickness

Abstract

The flow of a viscous incompressible fluid between a rotating disk and a stationary disk is studied. The two disks are impermeable. There is a layer of porous medium over the stationary disk. The generalized Darcy law is used to represent the fluid motion in the porous medium and the Navier-Stokes equations in the pure fluid medium. The nonlinear equations representing the motion, together with the boundary conditions and the matching conditions at the interface, constitute a two point boundary value problem. In view of the sensitive nature of the problem to the choice of missing initial conditions required for the forward integration, a shooting method in conjunction with the continuation method is used to produce the numerical solution. The response of the velocity profiles and stresses on the boundaries to the increase in the thickness of the porous layer is studied.