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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 417098, 7 pages
http://dx.doi.org/10.1155/2014/417098
Research Article

Comparison of Exact Solutions for Heat Transfer in Extended Surfaces of Different Geometries

Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South Africa

Received 17 January 2014; Accepted 19 February 2014; Published 19 March 2014

Academic Editor: Mariano Torrisi

Copyright © 2014 K. J. Moleofane 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.

Abstract

We consider a steady state problem for heat transfer in fins of various geometries, namely, rectangular, radial, and spherical. The nonlinear steady state problem is linearizable provided that the thermal conductivity is the differential consequence of the term involving the heat transfer coefficient. As such, one is able to construct exact solutions. On the other hand, we employ the Lie point symmetry methods when the problem is not linearizable. Some interesting results are obtained and analyzed. The effects of the parameters such as thermogeometric fin parameter and the exponent on temperature are studied. Furthermore, fin efficiency and heat flux along the fin length of a spherical geometry are also studied.