alexa Lie Group Method for Studying the Heat Generation Effec
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
Open Access

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Research Article

Lie Group Method for Studying the Heat Generation Effect on Freeconvection Laminar Boundary-layer Flow Over a Vertical Flat Plate

Abd-el-Malek MB1,3*, Badran NA1, Hassan HS2 and Abbas HH2

1Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt

2Department of Basic and Applied Science, Arab Academy for Science, Technology and Maritime Transport, P.O. BOX 1029 Alexandria, Egypt

3Department of Mathematics and Actuarial Science, The American University in Cairo, New Cairo 11835, Egypt

*Corresponding Author:
Abd-el-Malek MB
Department of Engineering Mathematics and Physics
Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt
Tel: 01000066496
E-mail: [email protected]

Received date: August 10, 2015; Accepted date: October 06, 2015; Published date: October 12, 2015

Citation: Abd-el-Malek MB, Badran NA, Hassan HS, Abbas HH (2015) Lie Group Method for Studying the Heat Generation Effect on Free-convection Laminar Boundary-layer Flow Over a Vertical Flat Plate. J Generalized Lie Theory Appl 9:232. doi:10.4172/1736-4337.1000232

Copyright: © 2015 Abd-el-Malek MB, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 

Abstract

The nonlinear equations of heat and mass transfer in two-dimensional free-convection, laminar, boundary layer flow of a viscous incompressible fluid over a vertical plate with thermophoresis and heat generation effect have been considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Liegroup method starts out with a general infinitesimal group of transformations under which the given partial differential equations are invariant. The determining equations are a set of linear differential equations, the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equations may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables of the system. The effect of the heat generation parameter He, the Prandtl number Pr, the Schimted number Sc, the thermophoretic parameter τ, the solutal Grashof number Gc and the thermal Grashof number Gr on velocity, concentration and temperature have been studied and the results are plotted.

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