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An optimum profile of a special pin fin: full solutions

Mustafa Turkyilmazoglu (Department of Mathematics, Hacettepe Universitesi, Ankara, Turkey)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 6 March 2020

Issue publication date: 15 October 2020

102

Abstract

Purpose

This paper aims to present an elegant exact solution in terms of elementary functions for a special pin fin without the classical length-of-arc approximation.

Design/methodology/approach

The temperature distribution along the fin and the surface function, both being the functions of a shape parameter, is inversely proportional to each other. The specialty of the spine is such that its shape and temperature profile are linked for a given Biot number.

Findings

Exact formulas for the pin fin tip temperature, pin fin base heat transfer rate, surface area of the spine and thermal fin efficiency are also given.

Originality/value

Without the traditional arc length assumption, the pin fin is shown to be an effective extended surface to remove the excessive heat from the hot surface it is pinned to. Optimum pin fin dimensions leading to the maximum base heat transfer rate are also worked out for a specified fin volume.

Keywords

Citation

Turkyilmazoglu, M. (2020), "An optimum profile of a special pin fin: full solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 11, pp. 4945-4954. https://doi.org/10.1108/HFF-11-2019-0801

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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