Evaluation of closed-form solutions based on the HPM and HAM approaches for the steady flow of third grade fluids in a porous half space

Abstract

In this paper, a closed-form solution for the steady flow of a third grade fluid in a porous half-space is presented. The governing non-linear ordinary differential equation is solved in closed form by means of the homotopy perturbation method (HPM), and it is shown that just two terms in the series expansion is sufficient to obtain a highly accurate solution which is valid for the whole domain. The results obtained are compared with numerical results obtained using a fourth-order Runge–Kutta method and the homotopy analysis method (HAM). Close agreement of the two sets of results is observed thus demonstrating the accuracy of the HPM approach for the particular problem considered.