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.