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 $$\alpha = 1$$ .