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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 269420, 11 pages
http://dx.doi.org/10.1155/2013/269420
Research Article

Lie Group Analysis and Similarity Solutions for Mixed Convection Boundary Layers in the Stagnation-Point Flow toward a Stretching Vertical Sheet

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Malaysia
2Nuclear Science Research School, Nuclear Science and Technology Research Institute (NSTRI), P.O. Box 14395-836, Tehran, Iran
3Institute of Mathematical Research, Universiti Putra Malaysia, 43400 Serdang Selangor, Darul Ehsan, Malaysia
4Department of Mathematics, Islamic Azad University, Bushehr Branch, 7514763448 Bushehr, Iran
5Department of Applied Mathematics and Computer Science, Eastern Mediterranean University, Famagusta, Northern Cyprus via Mersin 10, Turkey

Received 16 December 2012; Revised 18 January 2013; Accepted 18 January 2013

Academic Editor: Nail Migranov

Copyright © 2013 Sarkhosh Seddighi Chaharborj 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.

Abstract

An analysis for the mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet is carried out via symmetry analysis. By employing Lie group method to the given system of nonlinear partial differential equations, we can obtain information about the invariants and symmetries of these equations. This information can be used to determine the similarity variables that will reduce the number of independent variables in the system. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using fifth-order Improved Runge-Kutta Method (IRK5) coupled with shooting method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. This paper' results in comparison with known results are excellent.