Flow Induced in a Porous Medium due to a three dimensional couette flow Adjacent to it

Abstract

The flow of a viscous fluid induced in a porous medium due to a uniform motion of a plate parallel to its surface has been discussed when there is a transverse sinusoidal injection of the fluid at the moving plate. The fluid fills the space between the plate and the porous medium which is fully saturated with the fluid. Due to this type of the injection velocity the flow in the clear fluid becomes three dimensional. It is assumed that the flow in the clear fluid region governed by Navier-Stokes equation and that in the porous medium by the Brinkman equation near the interface and by Darcy law far away from interface. It is found that with increase of the permeability of the porous medium the magnitude of the velocity component increase in both regions. In the porous region the velocity component parallel to motion of the plate is maximum at the interface and then decreases exponentially forming a boundary layer at the interface. Also the velocity component parallel to the motion of the plate decreases with the increase of injection Reynolds number Re and the magnitude of other velocity components increases with the increase of Re.