Abstract
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.
Highlights
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
Esmaeilpour and Ganji [2] presented the problem of forced convection over a horizontal flat plate and employed the homotopy perturbation method (HPM) to compute an approximation to the solution of the system of nonlinear differential equations governing the problem
The results reveal that the HPM is very effective such that the analytical solution, obtained by using only two terms from HPM solution, coincides well with the homotopy analysis method (HAM) solution
Summary
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. Many semianalytical methods have been used to solve the boundary layer flow problems 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. Liao [7] solved the boundary-layer flow over a stretched impermeable wall by means of another semianalytic technique, namely, the homotopy analysis method (HAM) He [8] compared the HAM with the HPM and stated that the difference is clear just as the Taylor series method is different from the perturbation methods. The results reveal that the HPM is very effective such that the analytical solution, obtained by using only two terms from HPM solution, coincides well with the HAM solution
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