Mathematical Extrapolating of Highly Efficient Fin Systems

A.-R. A. Khaled

doi:10.1155/2011/909410

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.

Highlights

Fins are widely used in industry, especially in heat exchanger and refrigeration industries 1–5
Harper and Brown 7 are considered the forerunner who began analyzing heat transfer inside fins mathematically. They found that one-dimensional analysis was sufficient for heat transfer inside fins. They recommended that tip heat loss can be accounted by using a corrected fin length which is equal to half of the fin thickness added to its length
They pointed out that the differential surface area of the element is equal to the differential fin length element divided by the cosine of the taper angle

Summary

Introduction

Fins are widely used in industry, especially in heat exchanger and refrigeration industries 1–5 They are extended surfaces used to enhance heat transfer between the solids and the adjoining fluids 6. Harper and Brown 7 are considered the forerunner who began analyzing heat transfer inside fins mathematically. They found that one-dimensional analysis was sufficient for heat transfer inside fins. They recommended that tip heat loss can be accounted by using a corrected fin length which is equal to half of the fin thickness added to its length. They pointed out that the differential surface area of the element is equal to the differential fin length element divided by the cosine of the taper angle

Methods

Findings

Discussion

Conclusion