An approximate solution of the MHD flows of UCM fluids over porous stretching sheets by rational Legendre collocation method

Abstract

Purpose

The purpose of this paper is to develop an efficient method for solving the magneto-hydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid over a porous isothermal stretching sheet.

Design/methodology/approach

The paper applied a collocation approach based on rational Legendre functions for solving the third-order non-linear boundary value problem, describing the MHD boundary layer flow of an UCM fluid over a porous isothermal stretching sheet. This method solves the problem on the semi-infinite domain without transforming domain of the problem to a finite domain.

Findings

This approach reduces the solution of a problem to the solution of a system of algebraic equations. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem. The authors also compare the results of this work with some recent results and show that the new method is efficient and applicable.

Originality/value

The method solves this problem without use of discrete variables and linearization or small perturbation. Also it was confirmed by the theorem and figure of absolute coefficients that this approach has exponentially convergence rate.

Citation

Saadatmandi, A. and Sanatkar, Z. (2016), "An approximate solution of the MHD flows of UCM fluids over porous stretching sheets by rational Legendre collocation method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 7, pp. 2218-2234. https://doi.org/10.1108/HFF-05-2015-0176