A reliable treatment of a homotopy analysis method for two-dimensional viscous flow in a rectangular domain bounded by two moving porous walls

This study investigates the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions. The basic equations governing the flow are reduced to a highly nonlinear ordinary differential equation. This equation is solved analytically by using the homotopy analysis method (HAM). The analytic solutions of non-linear differential equation are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. The convergence analysis elucidates that the homotopy perturbation method (HPM) does not give the accurate results for the large values of the permeation Reynolds number Re. Graphical results are presented to investigate the influence of the nondimensional wall dilation rate αα and permeation Reynolds number on the velocity, normal pressure distribution and wall shear stress. It is noted that the behavior of the HAM solution for the velocity, normal pressure distribution and wall shear stress is in good agreement with the numerical solution.