An optimum profile of a special pin fin: full solutions

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.