Notes on the perturbation solutions of the boundary layer flow of nanofluids past a stretching sheet

Abstract

Boundary value problems arise in fluid mechanics, physics and engineering are usually of complex type and can not be solved analytically in general, hence, applied mathematicians resort to the numerical methods or solver codes to search for the solutions. In this note, the applicability of the perturbation method to the mathematical model describing the boundary layer flow of nanofluids past a stretching sheet has been analyzed. The mathematical model is governed by a system of nonlinear ordinary differential equations and the solutions are obtained in closed form via a straightforward perturbation method. As a well known fact, the perturbation method is based on the existence of a small parameter and accordingly, the thermophoresis parameter is used as a perturbation parameter. Several plots are introduced to explore the validity of the suggested method. The current numerical results agree with those obtained by using an implicit finite-difference method. Accordingly, the perturbation method can be used with highly trust to solve similar problems.