Pulsatile flow between two coaxial porous cylinders with slip on inner cylinder
Hamza, Elsadig A. | 2011-10-13
A fully developed, axisymmetric, pulsatile motion of an incompressible Newtonian fluid,under the action of an oscillatory pressure gradient, has been considered in this work. The fl ow is assumed to take place in the annular space between two coaxial circular cylinders, the outer one a porous cylinder of uniform permeability and the inner one a naturally permeable tube. There arises a coupled flow, which has been analysed by solving the Navier-Stokes equations in the free fluid region and the Darcy's equation in the porous region, together with the Beavers-Joseph slip condition at the free fl uid-porous medium
interface. Using an appropriate set of similarity variables, the governing partial differential
equations have been transformed to a system of nonlinear ordinary differential equations. The solution of the resulting system, together with appropriate boundary conditions, has been obtained, for a special case, by a perturbation approach. It has been assumed that the frequency of pulsation and the suction parameter are small (<< 1). The variation of velocity pro les, pressure drop and skin friction has been illustrated in a number of cases of interest. The analytical results have been compared with numerical solution for small values of suction parameter.