Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 568263, 15 pages
Research Article

Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity

1Young Researchers Club, Islamic Azad University, Arak Branch, P.O. Box 38149-54688, Arak, Iran
2Department of Mechanical Engineering, University of Isfahan, Isfahan 81746-73441, Iran

Received 25 October 2010; Accepted 30 December 2010

Academic Editor: J. Jiang

Copyright © 2010 A. Moradi and H. Ahmadikia. 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.


Three different profiles of the straight fin that has a temperature-dependent thermal conductivity are investigated by differential transformation method (DTM) and compared with numerical solution. Fin profiles are rectangular, convex, and exponential. For validation of the DTM, the heat equation is solved numerically by the fourth-order Runge-Kutta method. The temperature distribution, fin efficiency, and fin heat transfer rate are presented for three fin profiles and a range of values of heat transfer parameters. DTM results indicate that series converge rapidly with high accuracy. The efficiency and base temperature of the exponential profile are higher than the rectangular and the convex profiles. The results indicate that the numerical data and analytical method are in agreement with each other.