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.

Issue Section:
Technical Briefs
Keywords:
Annular Fin, Calculus of Variation, Heat Generation, Longitudinal Fin, Optimum Profile, Pin Fin, variational techniques, heat conduction, convection
Topics:
Fins, Heat, Temperature profiles, Heat transfer, Variational techniques
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Copyright © 2005
 by American Society of Mechanical Engineers
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