A singular perturbation problem of non-newtonian flow between porous disks

Abstract

The non-Newtonian flow between parallel porous stationary disks due to uniform suction at the disks is considered for both small and large suction Reynolds numbers. In the case of small suction Reynolds number the Navier-Stokes equations have been solved by a regular perturbation technique. The solution obtained is valid for both suction and injection Reynolds numbers. The velocity, pressure and shear distributions have been obtained and are compared with those of the Newtonian flow. We find, in the case of injection, that the combined effect of cross viscosity and visco-elastic co-efficients is to increase the maximum velocity at the centre of the channel and to decrease the magnitude of the velocity gradient at the disks. Whereas in the case of suction, velocity profile is flatter with higher magnitude for the velocity gradients at the disks. In the case of large suction, the Navier-Stokes equations have been solved by the method of matched asymptotic expansions. We find that the effect of large suction at the disks is to flatten the velocity profiles considerably and thereby to push the boundary layer towards the disks. The combined effect of visco-elastic and cross-viscosity terms is to decrease the radial velocity and to increase the axial velocity distributions.