Application of He’s Method in Solving a System of Nonlinear Coupled Equations Arising in Non-Newtonian Fluid Mechanics

Abstract

In this paper, Hes homotopy perturbation method is successfully employed to solve a nonlinear coupled system of ordinary differential equations that arises in the fully developed natural convection flow of a third grade fluid between two vertical parallel walls. The same problem is also solved by a numerical method (Runge-Kutta method of order 4) using the software MAPLE. The numerical results obtained by these methods are then compared and an excellent agreement is observed. This comparative study confirms the wide range applicability of HPM for nonlinear boundary value problems in different areas of science and engineering.