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Abstract

Straight or longitudinal fins of variable profile are explained in most textbooks on heat transfer, but unfortunately annular or circular fins of variable profile are not. Owing to this limitation, the present article addresses an elemental approximate analytic solution for treating the governing quasi 1-D heat equation descriptive of an annular fin of hyperbolic profile. To solve this equation approximately, usage of the mean radius of the annular fin is made. The transformed ordinary differential equation with constant coefficients is equivalent to the quasi 1-D heat equation for the straight fin of uniform profile that appears in all heat transfer textbooks. Within the framework of engineering analysis and design, the estimates of approximate temperatures and companion heat transfer rates for the annular fin of hyperbolic profile owing realistic values of the parameters give evidence of good quality and minimal errors. The transformation procedure is carried out in a step-by-step manner and can be readily comprehended by undergraduate students in mechanical engineering programs.

Keywords

Annular fin of hyperbolic profile mean radius equivalent straight fin of uniform profile temperature distribution heat transfer rate fin efficiency

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Elemental approximate analytic procedure for the annular fin of hyperbolic profile amenable to a heat transfer course

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