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RESEARCH PAPERS

A Least Weight Circular Cooling Fin

[+] Author and Article Information
S. Güçeri

Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, N. C.

C. J. Maday

Department of Engineering Science and Mechanics, North Carolina State University, Raleigh, N. C.

J. Eng. Ind 97(4), 1190-1193 (Nov 01, 1975) (4 pages) doi:10.1115/1.3438726 History: Received June 06, 1975; Online July 15, 2010

Abstract

The design of the least weight circular cooling fin is obtained through an application of the Minimum Principle. The fin temperature, thickness, and heat flux are considered to be functions only of the radius. Solutions are obtained for the exact one-dimensional representation and also for the approximate case where the profile curvature is neglected in the convection calculation. A regularization technique is used to avoid computational difficulties, especially near the tip where the fin thickness becomes vanishingly small. In the exact case, an additional degree of freedom allows the selection of the fin root dimension. This flexibility suggests the possibility of optimization in a parameter, the root dimension; this was done by using a pattern search technique. Closed form results are given for the approximate case. For kθo /qo = 100, the fin design obtained in the exact case is about 20 percent shorter and contains about 1 percent to 2 percent less material than the fin obtained in the approximate case.

Copyright © 1975 by ASME
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