Pulsatile flow between two coaxial porous cylinders with slip on inner cylinder for large frequency of pulsation.

Abstract

The unsteady component of axial flow of an incompressible fluid in the region lying between the annular spaces of two coaxial cylinders has been investigated. The outer cylinder is assumed to possess uniform permeability and the inner one is a naturally permeable tube obeying Darcy's Law. The flow is maintained by a periodic pressure gradient across the annulus. Making use of an appropriate set of similarity variables, the governing partial differential equations have been transformed to a set of a system of nonlinear ordinary differential equations. The solution of the resulting equations subject to appropriate boundary conditions has been obtained using a singular perturbation technique. The frequency of pulsation has been considered to be large. The effect of the flow parameters on the unsteady component of axial flow has been discussed. The analytical results have been compared with numerical solutions.