On a Homotopy Perturbation Treatment of Steady Laminar Forced Convection Flow over a Nonlinearly Stretching Porous Sheet

The steady two-dimensional laminar forced convection boundary layer flow of an incompressible viscous Newtonian fluid over a nonlinearly stretching porous (permeable) sheet with suction is considered. The sheet’s permeability is also considered to be nonlinear. The boundary layer equations are transformed by similarity transformations to a nonlinear ordinary differential equation (ODE). Then the homotopy perturbation method (HPM) is used to solve the resultant nonlinear ODE. The dimensionless entrainment parameter and the dimensionless sheet surface shear stress are obtained for various values of the suction parameter and the nonlinearity factor of sheet stretching and permeability. The results indicate that the dimensionless sheet surface shear stress decreases with the increase of suction parameter. The results of present HPM solution are compared to the values obtained in a previous study by the homotopy analysis method (HAM). The HPM results show that they are in good agreement with the HAM results within 2% error. 1. Introduction Boundary-layer flow of an incompressible fluid over a stretching sheet has many applications in engineering such as in liquid film condensation process, aerodynamic extrusion of plastic sheets, cooling process of metallic plate in a cooling bath, and glass and polymer industries. In the last decade, many semianalytical methods have been used to solve the boundary layer flow problems. For example, He [1] proposed a new perturbation technique coupled with the homotopy technique, which requires no small parameters in the equations and can readily eliminate the limitations of the traditional perturbation techniques. He named this method as the homotopy perturbation method (HPM). Esmaeilpour and Ganji [2] presented the problem of forced convection over a horizontal flat plate and employed the HPM to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. Xu [3] obtained an approximate solution of a boundary layer equation in unbounded domain by means of He’s homotopy perturbation method (HPM). Fathizadeh and Rashidi [4] solved the convective heat transfer equations of boundary layer flow with pressure gradient over a flat plate using the HPM. They studied the effects of Prandtl number and pressure gradient on both temperature and velocity profiles in the boundary layer. Raftari and Yildirim [5] obtained by means of the HPM an approximate analytical solution of the magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a permeable