Stokes and Rayleigh layers in presence of naturally permeable boundaries

Unsteady flow of viscous incompressible fluid caused by oscillations of a naturally permeable wall bounding the fluid is examined in this theoretical paper. Solutions of the governing Navier-Stokes equations, subject to slip condition at a porous interface, have been obtained by considering oscillatory solutions and an initial value problem. The effect of the permeability of the porous medium enters through a slip grouping parameter, whose influence on the structure of the Stokes' layer has been shown graphically. As a particular case of an initial value problem we have obtained Rayleigh layer over a naturally permeable wall and compared it with the classical Rayleigh layer for a range of nondimensional parameter.