The Motion Induced by the Orthogonal Stretching of a Membrane Beneath a Quiescent Fluid-Saturated Porous Medium

The flow induced above an impermeable membrane undergoing orthogonal linear stretching beneath a quiescent fluid-saturated porous medium is investigated. The problem is governed by two parameters, a stretching ratio alpha and a dimensionless permeability parameter beta. Numerical solutions of the nonlinearly coupled governing ordinary differential equations are given for selected values of beta over a range of alpha and also for the case of radial stretching alpha = 1 over a range of beta. Results are plotted for the wall shear stresses and the velocity induced into the boundary layer from the far field. Asymptotics for large alpha at beta = 0 and large beta at alpha = 1 are presented. Sample velocity profiles at beta = 0, 2 are presented as are profiles for a radially stretching disk at alpha = 1.