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Solutions of the Blasius and MHD Falkner-Skan boundary-layer equations by modified rational Bernoulli functions

Velinda Calvert (Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi, USA)
Mohsen Razzaghi (Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 7 August 2017

Abstract

Purpose

This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner-Skan equations are third-order nonlinear boundary value problems on the semi-infinite domain.

Design/methodology/approach

The approach is based upon modified rational Bernoulli functions. The operational matrices of derivative and product of modified rational Bernoulli functions are presented. These matrices together with the collocation method are then utilized to reduce the solution of the Blasius and MHD Falkner-Skan boundary-layer equations to the solution of a system of algebraic equations.

Findings

The method is computationally very attractive and gives very accurate results.

Originality/value

Many problems in science and engineering are set in unbounded domains. One approach to solve these problems is based on rational functions. In this work, a new rational function is used to find solutions of the Blasius and MHD Falkner-Skan boundary-layer equations.

Keywords

Acknowledgements

The authors wish to express their sincere thanks to anonymous referees for their valuable suggestions that improved the final manuscript.

Citation

Calvert, V. and Razzaghi, M. (2017), "Solutions of the Blasius and MHD Falkner-Skan boundary-layer equations by modified rational Bernoulli functions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 8, pp. 1687-1705. https://doi.org/10.1108/HFF-05-2016-0190

Publisher

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Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited