Mathematical Extrapolating of Highly Efficient Fin Systems

Abstract

Different high-performance fins are mathematically analyzed in this work. Initially, three types are considered: (i) exponential, (ii) parabolic, and (iii) triangular fins. Analytical solutions are obtained. Accordingly, the effective thermal efficiency and the effective volumetric heat dissipation rate are calculated. The analytical results were validated against numerical solutions. It is found that the triangular fin has the maximum effective thermal length. In addition, the exponential pin fin is found to have the largest effective thermal efficiency. However, the effective efficiency for the straight one is the maximum when its effective thermal length based on profile area is greater than 1.4. Furthermore, the exponential straight fin is found to have effective volumetric heat dissipation that can be 440% and 580% above the parabolic and triangular straight fins, respectively. In contrast, the exponential pin fin is found to possess effective volumetric heat dissipation that can be 120% and 132% above the parabolic and triangular pin fins, respectively. Finally, new high performance fins are mathematically generated that can have effective volumetric heat dissipation of 24% and 12% above those of exponential pin and straight fins, respectively.

An Analytical and a Numerical Method for Nonlinear Convection-Radiation Problems in Porous Fins

“…Nowadays, high-performance heat transfer components are related to the need to achieve high heat transfer rates with low cost and, above all, limited space and weight. Heat transfer on extended surfaces is, currently, one of the main focuses of high-performance heat transfer studies, accounting for the most varied parameters and respective behavior in the thermal mapping [1][2][3].…”

Generalized Correlations for Heat Transfer through High Performance Fins

“…The objective of the present work is to find out a generalized correlation that can be used to estimate the fin efficiency of any kind of high performance fins. This task is vital in order to avoid seeking for the exact fin efficiency equation among the large number of researches devoted to this topic in the literature [12][13][14][15][16][17][18][19]. To achieve the latter objective, the common characteristics that most high performance fins share need to be identified and analyzed.…”