Analysis of a concave parabolic fin with vertically cutting fin tip and variable fin base thickness

Abstract

A concave parabolic fin with vertically cutting fin tip and variable fin base thickness is analyzed using a two-dimensional analytic method. Heat loss is presented as a function of the actual fin length, the ratio of the actual fin length to the imaginary fin length, the fin base height, and the convection characteristic number. Also, heat loss is shown as a function of the fin base thickness for both the fixed actual fin length and the fixed actual fin tip length. For equal amounts of heat loss, the relationships are presented between 1) the convection characteristic number and the fin base height, 2) the fin base thickness and the fin base height, and 3) the fin base thickness and the actual fin tip length. One of the results shows that the heat loss for the fixed actual fin tip length decreases more remarkably than that for the fixed actual fin length as the fin base thickness increases.