One-Dimensional Versus Two-Dimensional Behavior of Isachenko's Optimal Straight Fin with Quarter-Circle Profile

Abstract

A study was conducted to investigate the behavior of the 2-D temperature distributions in a straight fin with a quarter-circle profile through the powerful finite element method. The computed numerical 2-D temperatures were post-analyzed to clarify in a natural way the circumstances under which the general 2-D heat equation degraded into a simple quasi 1-D heat equation for modeling Isachenko's optimal straight fin. This realistic interconnectivity was presented in graphs and in a table containing the transverse biot number (Bit). The structured finite element mesh was constructed with three-noded isoparametric triangular elements. Smaller three-noded isoparametric triangular elements were also constructed in the vicinity of the curved surface extending from the fin base to the fin tip for enhanced accuracy. Numerical calculations of the 2-D dimensionless temperatures for representative transverse Bit were performed with an in-house finite element code.