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Mathematical Problems in Engineering
Volume 2013, Article ID 724385, 5 pages
Research Article

Prandtl's Boundary Layer Equation for Two-Dimensional Flow: Exact Solutions via the Simplest Equation Method

1Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South Africa
2Department of Mathematical Science, International Institute of Symmetry Analysis and Mathematical Modeling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa

Received 12 March 2013; Accepted 18 March 2013

Academic Editor: H. Jafari

Copyright © 2013 Taha Aziz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.