Homotopy Perturbation Analysis of Steady Free Convective Flow over a Nonlinearly Stretching Sheet in an Extended Darcy-Forchheimer Porous Medium with Viscous Dissipation

This study conducts an analysis to investigate the steady free convective flow over a nonlinearly stretching sheet immersed in an Extend-Darcy-Forchheimer porous medium with viscous dissipation. The governing nonlinear partial differential equations are converted into self-similar nonlinear ordinary differential equations through the application of similarity transformations. Subsequently, these transformed equations are solved using He's Homotopy Perturbation Method (HPM), a semi-exact method with the notable advantage of not necessitating a small parameter in the equations, thus circumventing the limitations associated with traditional perturbation methods. In this paper, we begin by providing a concise introduction to the fundamental principles of HPM for addressing nonlinear differential equations, followed by its application to obtain solutions for the nonlinear governing equations governing the flow, including the nonlinear term. The study also presents and discusses the effects of various relevant physical parameters on the flow.