Reproduction of the Fin Efficiency Diagram for Annular Fins of Uniform Thickness by Solving Systems of up to Four Algebraic Equations

Abstract

This paper addresses a simple finite-difference procedure for solving the modified Bessel equation that governs the temperature variation along annular fins of uniform thickness with constant thermal conductivity and a uniform convection coefficient. After performing several numerical experiments for critical cases related to large radii ratios, c, and reasonable values of the enlarged Biot numbers, γ², it was found that heat transfer rates of good quality can be obtained by solving systems of up to four algebraic equations with the spreadsheet software Excel. Later, with the numerical fin efficiencies, η, gathered for all practical combinations of c and γ², the entire fin efficiency diagram can be easily reproduced.