Solutions of boundary layer equations governing free convective and magnetohydrodynamic flows through parametric differentiation

Abstract

The method of parametric differentiation has been used to obtain the solutions of a system of nonlinear equations governing two- and three-dimensional free convective boundary layer flows, and a two-dimensional magnetohydrodynamic boundary layer flow. The main advantage of this method is that the governing nonlinear equations are reduced to linear equations and the nonlinearity of the problem is confined to a set of first order equations which are much easier to solve compared to the original nonlinear equations. Another advantage of this method is that it provides a mean of obtaining the solution for the entire range of the parameter in a step-by-step manner from a known solution with a given value of the parameter. The results obtained by this method are in very close agreement with the corresponding results obtained by other numerical methods.