Implementation of Homotopy Analysis Method on circular permeable slider containing of incompressible Newtonian fluid

The aim of this paper is to examine the classical problem of an incompressible Newtonian fluid through the porous of a circular slider which is moving laterally on a horizontal plan. Employing the similarity variables, the governing differential equations have been reduced to ordinary ones and solved via Homotopy Analysis Method (HAM). The analytical solution for the coupled Nonlinear Ordinary Differential Equations resulting from the momentum equation is obtained and Velocity fields have been computed and discussed for different values of the Reynolds number. Also the fourth-order Runge-Kutta numerical method (NUM) is used for the validity of these analytical methods and excellent agreement are observed between the solutions obtained from HAM and numerical results.