Analytical and Numerical Investigation of Second Grade Magnetohydrodynamics Flow over a Permeable Stretching Sheet

Abstract

In this paper, the steady laminar boundary layer flow of non-Newtonian second grade conducting fluid past a permeable stretching sheet, under the influence of a uniform magnetic field is studied. Three different methods are applied for solving the problem; numerical Finite Element Method (FEM), analytical Collocation Method (CM) and 4th order Runge-Kutta numerical method. The FlexPDE software package is used for modeling and solving the problem by FEM. In most new analytical methods used for solving nonlinear equations, it is impossible to solve problems with infinity boundary conditions. In this article by using a special technique, the infinity boundary condition transformed to a finite one, then the governing equation solved analytically. In the physical aspect, the effects of the non-Newtonian, magnetic and permeability parameters on the velocity distribution have been investigated. As a result, the present suggested technique can be used for the analytical solution of many such problems with infinite boundary conditions. Moreover, the comparison between the results obtained from our modified analytical method and numerical solutions shows an excellent agreement.