Analytical approach for solving two-dimensional laminar viscous flow between slowly expanding and contracting walls

In this article, an analysis has been performed to study the two dimensional viscous flow between slowly expanding and contracting walls with weak permeability. The governing equations for the base fluid of this problem are described by dimensionless parameters wall dilation rate (α) and permeation Reynolds number (Re). The nonlinear differential equation is solved using two different analytically approaches by Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Then, the results are compared with numerical solution by fourth order Runge-Kutta-Fehlberg technique. Furthermore, the effects of dimensionless parameters on the velocity distributions are investigated in this research. As an important outcome, it is observed that, great agreement was found between the obtained results from the analytical and the numerical models.