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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 947160, 16 pages
Research Article

Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles

1Defence, Peace, Safety and Security, Landward Sciences, Council for Scientific and Industrial Research, P.O. Box 395, Pretoria 0001, South Africa
2Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

Received 19 March 2014; Accepted 2 April 2014; Published 8 May 2014

Academic Editor: Oluwole Daniel Makinde

Copyright © 2014 M. D. Mhlongo and R. J. Moitsheki. 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.


One-dimensional steady-state heat transfer in fins of different profiles is studied. The problem considered satisfies the Dirichlet boundary conditions at one end and the Neumann boundary conditions at the other. The thermal conductivity and heat coefficients are assumed to be temperature dependent, which makes the resulting differential equation highly nonlinear. Classical Lie point symmetry methods are employed, and some reductions are performed. Some invariant solutions are constructed. The effects of thermogeometric fin parameter, the exponent on temperature, and the fin efficiency are studied.