A comparison of two formulations of the fin efficiency for straight fins

A formulation of the fin efficiency based on Newton's law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the surrounding fluid to the heat conducted through the base. The first formulation requires that the solution of the nonlinear fin equations for constant heat transfer coefficient and constant thermal conductivity is known, whilst the second formulation of the fin efficiency requires only that a first integral of the model equation is known. This paper shows the first formulation of the fin efficiency contains approximation errors as only power series and approximate solutions to the nonlinear fin equations have been determined. The second formulation of the fin efficiency is exact when the first integrals can be determined.