A Singular Perturbation Solution for Couette Flow Over a Semi-Infinite Porous Bed

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Abstract
An analysis has been performed to study conjugate Couette flows in a channel over a packed-spheres bed of semi-infinite extent. The Brinkman model is used as the momentum equation in the porous bed with the variation of porosity approximated by an exponential function. An approximate expression for the permeability of the bed, applicable for a wide range of porosity, is constructed. A singular perturbation solution is obtained for the velocity distribution in the packed-spheres bed. The streamwise velocity and the shearing stress of the conjugate flows in the channel and in the packed-spheres bed are matched at the fluid/porous bed interface. An explicit analytical expression for the slip coefficient is obtained by comparing the results based on the present formulation with those based on Beavers and Joseph’s formulation. It is shown that the value of the slip coefficient decreases as a result of the variable porosity effect.

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