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Mathematical Problems in Engineering
Volume 2010, Article ID 765729, 19 pages
http://dx.doi.org/10.1155/2010/765729
Research Article

Thermal Characterizations of Exponential Fin Systems

Thermal Engineering and Desalination Technology Department, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

Received 14 December 2009; Accepted 7 April 2010

Academic Editor: Francesco Pellicano

Copyright © 2010 A.-R. A. Khaled. 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

Exponential fins are mathematically analyzed in this paper. Two types are considered: (i) straight exponential fins and (ii) pin exponential fins. The possibility of having increasing or decreasing cross-sectional areas is considered. Different thermal performance indicators are derived. The maximum ratio between the thermal efficiency of the exponential straight fin to that of the rectangular fin is found to be 1.58 at an effective thermal length of 2.0. This ratio is even larger when exponential fins are compared with triangular and parabolic straight fins. Moreover, the maximum ratio between the thermal efficiency of the exponential pin fin to that of the rectangular pin fin is found to be 1.17 at an effective thermal length of 1.5. However, exponential pin fins thermal efficiencies are found to be lower than those of triangular and parabolic pin fins. Moreover, exponential joint-fins may transfer more heat than rectangular joint-fins especially when differences between their senders and receivers portions dimensionless indices are very large. Finally, it is found that increasing the joint-fin exponential index may cause straight exponential joint-fins to transfer more heat than rectangular joint-fins.