Journal of Applied Mathematics
Volume 2012 (2012), Article ID 671548, 13 pages
http://dx.doi.org/10.1155/2012/671548
Research Article

Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem

R. J. Moitsheki1 and M. D. Mhlongo2

1Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
2Department of Mathematical Sciences, Mangosuthu University of Technology, P.O. Box 12363, Jacobs, Umlazi 4026, South Africa

Received 23 August 2011; Accepted 12 October 2011

Academic Editor: Jacek Rokicki

Copyright © 2012 R. J. Moitsheki and M. D. Mhlongo. 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

We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.