Optimal Homotopy Asymptotic Method for solving viscous ow through expanding or contracting gaps with permeable walls

In this paper an analytical technique, namely Optimal Homotopy Asymptotic Method (OHAM), is implemented for solving the problem of two-dimensional viscous ow through expanding or contracting gaps with permeable walls. In addition, comparison of the OHAM results is presented with the Homotopy Analysis Method and numerical calculation by the shooting method coupled with a Runge-Kutta integration scheme results. By this technique, we have a convenient way to control the convergence of obtained series and adjust convergence regions when necessary. The eects of non-dimensional wall dilation rate  and permeation Reynolds number Re on the wall shear stress, velocity, normal pressure and the axial pressure distributions are discussed.

Permeable walls, Non-dimensional wall dilation rate, Permeation Reynolds number, Optimal Homotopy Asymptotic Method (OHAM), Homotopy Analysis Method (HAM)