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Reduction of the 2-D Heat Equation for Straight Fins of Uniform Profile Into a Quasi 1-D Equation

[+] Author Affiliations
Antonio Campo

University of Vermont

Paper No. IMECE2005-81571, pp. 123-128; 6 pages
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Innovations in Engineering Education: Mechanical Engineering Education, Mechanical Engineering/Mechanical Engineering Technology Department Heads
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Mechanical Engineering Education
  • ISBN: 0-7918-4232-0 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME


Owing to the combined action of transverse convection and longitudinal conduction, the temperature in fins varies longitudinally since the transversal temperature change is practically insignificant. Textbooks on heat transfer widely employ the quasi one-dimensional approximation for the analysis of straight fins of uniform profile [1-6]. Unfortunately, justification of this simplistic approach has been based on the prevalent criterion of fins owing large slenderness ratios, i.e., large length and small thickness. This route is a mere geometric consideration that obviates the heat path implications that are inherent to fins. Beginning with the formulation with the 2-D heat conduction equation, the primary aim of this paper is to develop a systematic mathematical procedure for the validity of the quasi 1-D approximation in terms of two parameters: (1) the transverse Biot number and (2) the slenderness ratio.

Copyright © 2005 by ASME
Topics: Heat , Equations , Fins



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