Fin performance ratios greater than unity: Not just a theoretical aspiration

Previous work using the fin performance ratio has shown that it may not exceed unity. This study proves that this is not the case under certain conditions relating to the heat transfer from the tip of the fin. Equations for longitudinal rectangular fins have been used to demonstrate how this can be achieved and a performance ratio chart is provided showing performance ratios exceeding unity when the ratio of the heat transfer coefficient at the tip to that along the length of the fin exceeds the maximum effectiveness (a parameter of the problem). Under these conditions the maximum performance ratio is given by the ratio of the heat transfer coefficients (αe/α) divided by the maximum effectiveness. This has relevance for fins used in boiling and condensing systems where different heat transfer coefficients may exist on different parts of the fins due to the existence of different phases.