Optimum Profile of Thin Fins With Volumetric Heat Generation: A Unified Approach

[+] Author and Article Information
B. Kundu

Department of Mechanical Engineering, Jadavpur University, Kolkata 700 032, Indiabkundu123@rediffmail.com

P. K. Das

Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, Indiapkd@iitkgp.ernet.in

J. Heat Transfer 127(8), 945-948 (Jan 18, 2005) (4 pages) doi:10.1115/1.1929784 History: Received May 20, 2004; Revised January 18, 2005

In this paper, a generalized methodology for the optimum design of thin fins with uniform volumetric heat generation is described. Using variational calculus, the optimum profiles of longitudinal, annular, and pin fins are determined from the basic fin equation under the constraint of specified fin volume. From a common optimality criteria, a generalized closed form expression for the fin thickness is obtained for the above three types of fins. Closed-form expressions are also obtained for the optimum profiles of longitudinal and pin fins. As a special case, both the temperature profile and the shape of optimum fins without heat generation are determined.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Geometrical configurations of three typical fins

Grahic Jump Location
Figure 2

Optimum profiles as a function of dimensionless heat generation rate Ng: (a) longitudinal fin, (b) pin fin, and (c) annular fin



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