Fins with a prescribed temperature at the tip: Efficiency and effectiveness expressions

•Expressions of the fin efficiency and effectiveness for fins with a prescribed temperature at the tip.•The fin efficiency is reduced when for certain values of mL.•An alternative analysis if proposed using the expressions of the fins with an adiabatic tip.

This paper presents an analysis of extended surfaces with constant cross-sectional area and a prescribed temperature at the tip. The expressions of the fin efficiency and effectiveness for extended surfaces with a constant cross-sectional area can be found in the literature for a boundary condition of an insulated or convective tip but not for a prescribed temperature at the tip. In this case, there are two different expressions for efficiency and effectiveness depending on the value of the non-dimensional parameter mL with respect to the critical value mL∗.The results indicate that for excess temperature ratios θL/θb≳0.25θL/θb≳0.25, the fin efficiency decreases for certain values of mL. This region should be avoided for proper fin design.