Efficiencies for Partially Wetted Spine Fins: Uniform Cross Section, Conical, Concave Parabolic, and Convex Parabolic Spines

Abstract

In this study, efficiencies for partially wetted fins for the uniform cross section spine, conical spine, concave parabolic spine, and convex parabolic spine are presented using an analytical method. Depending on the set of boundary conditions, there are two methods for deriving the efficiencies of partially wet fins for each spine. The eight equations for fin efficiencies were investigated. Fin efficiency is a function of the length of the dry portion. Thus, the equations for calculating the length of the dry portion are also presented. The findings indicate that a larger crosssectional fin results in a higher conduction heat transfer rate. Contrarily, the fin efficiency is lower. This is different from the longitudinal fin, for which the trend lines of heat transfer rate and fin efficiency are the same. This converse relationship is due to the effect of the ratio of the crosssectional area to the surface area. Moreover, partially wet fin efficiencies decrease with increased relative humidity. For convenience, the approximate equation for efficiencies for partially wet fins, which is derived from the equations for fully wet and fully dry fin efficiencies, is also presented.