Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 826819, 13 pages
doi:10.1155/2011/826819
Research Article

Steady Heat Transfer through a Two-Dimensional Rectangular Straight Fin

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

Received 9 December 2010; Accepted 14 February 2011

Academic Editor: Reza Jazar

Copyright © 2011 Raseelo J. Moitsheki and Atish Rowjee. 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

Exact solutions for models describing heat transfer in a two-dimensional rectangular fin are constructed. Thermal conductivity, internal energy generation function, and heat transfer coefficient are assumed to be dependent on temperature. We apply the Kirchoff transformation on the governing equation. Exact solutions satisfying the realistic boundary conditions are constructed for the resulting linear equation. Symmetry analysis is carried out to classify the internal heat generation function, and some reductions are performed. Furthermore, the effects of physical parameters such as extension factor (the purely geometric fin parameter) and Biot number on temperature are analyzed. Heat flux and fin efficiency are studied.