Numerical solutions for the problem of the boundary layer flow of a Powell–Eyring fluid over an exponential sheet using the spectral relaxation method

Abstract

The spectral relaxation method is a very powerful tool which was applied in this paper to get the numerical solution for the system of nonlinear ordinary differential equations which describe the problem of fluid flow of a Powell–Eyring model past an exponentially shrinking sheet with the presence of magnetic field and thermal radiation. The introduced method is based on the spectral relaxation method, which is successfully used to solve this type of equations. Also, this method is developed from the Gauss–Seidel idea of reducing the governing nonlinear system of ordinary differential equations into smaller systems of linear equations. Likewise, the influences of the governing parameters on the velocity and temperature profiles are studied graphically. Results of this study shed light on the accuracy and efficiency of the proposed method in solving this type of the nonlinear boundary layer equations.