Exact Insulated-Tip Fin Length Correction for Tip Convection Compensation

This study details the derivation of a length correction term for computing the heat transfer performance of one-dimensional, straight, convecting-tip fins using the insulated-tip fin solution. Use of this corrected length in the insulated-tip fin solution produces the identical heat transfer rate and temperature profile as those computed using the more complex convecting-tip fin equations. The analysis derives the length correction equation from fundamental principles and produces a simple, closed-form expression valid for all fin cross-sectional shapes. Furthermore, the valid parameter range where this length correction is applicable, and outside of which no exact length correction is possible, is quantified.