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

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Abstract

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 \(\alpha = 1\).

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  1. Department of Mechanical Engineering, University of Colorado, Boulder, CO, 80309-0427, USA

    Patrick D. Weidman

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  1. Patrick D. Weidman
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Correspondence to Patrick D. Weidman.

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Weidman, P.D. The Motion Induced by the Orthogonal Stretching of a Membrane Beneath a Quiescent Fluid-Saturated Porous Medium. Transp Porous Med 110, 533–542 (2015). https://doi.org/10.1007/s11242-015-0571-0

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  • DOI: https://doi.org/10.1007/s11242-015-0571-0

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