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Technical Briefs

# Temperature/Heat Analysis of Annular Fins of Hyperbolic Profile Relying on the Simple Theory for Straight Fins of Uniform Profile

[+] Author and Article Information
Antonio Campo1

Department of Mechanical Engineering, The University of Vermont, Burlington, VT 05405acampo@uvm.edu

Jianhong Cui

Department of Mechanical Engineering, The University of Vermont, Burlington, VT 05405

The same result is obtainable from the application of the arithmetic mean of the two extreme ordinates $R=c$ and $R=1$ in [$c$, 1].

1

Corresponding author.

J. Heat Transfer 130(5), 054501 (Apr 08, 2008) (4 pages) doi:10.1115/1.2885162 History: Received November 02, 2006; Revised December 01, 2007; Published April 08, 2008

## Abstract

This technical brief addresses an elementary analytic procedure for solving approximately the quasi-1D heat conduction equation (a generalized Airy equation) governing the annular fin of hyperbolic profile. The importance of this fin configuration stems from the fact that its geometrical shape and heat transfer performance are reminiscent of the annular fin of convex parabolic profile, the so-called optimal annular fin. To avoid the disturbing variable coefficient in the quasi-1D heat conduction equation, usage of the mean value theorem for integration is made. Thereafter, invoking a coordinate transformation, the product is a differential equation, which is equivalent to the quasi-1D heat conduction equation for the simple straight fin of uniform profile. The nearly exact analytic temperature distribution is conveniently written in terms of the two controlling parameters: the normalized radii ratio $c$ and the dimensionless thermogeometric parameter $M2$, also called the enlarged Biot number. For engineering analysis and design, the estimates of temperatures and heat transfer rates for annular fins of hyperbolic profile owing realistic combinations of $c$ and $M2$ give evidence of good quality.

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## Figures

Figure 1

Sketch of an annular fin of hyperbolic profile

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