How Big Is an Error in the Analytical Calculation of Annular Fin Efficiency?

Mladen Bošnjaković,Marija Živić,Ante Čikić,Simon Muhič

doi:10.3390/en12091787

Mladen Bošnjaković, Marija Živić + Show 2 more

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https://doi.org/10.3390/en12091787

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Abstract

An important role in the dimensioning of heat exchange surfaces with an annular fin is the fin efficiency. The fin efficiency is usually calculated using analytical expressions developed in the last century. However, these expressions are derived with certain assumptions and simplifications that involve a certain error in the calculation. The purpose of this paper is to determine the size of the error due to the assumptions and simplifications made when performing the analytical expression and to present what has the greatest impact on the amount of error, and give a recommendation on how to reduce that error. In order to determine the error, but also to gain a more detailed insight into the physics of heat exchange processes on the fin surface, computational fluid dynamics was applied to the original definition of fin efficiency. This means that a numerical simulation was performed for the actual fin material and for the ideal fin material with infinite thermal conductivity for the selected fin geometry and Re numbers from 2000 to 18,000. The results show that fin efficiency determined by numerical simulations is greater by up to 12.3% than the efficiency calculated analytically. The greatest impact on the amount of error is the assumption of the same temperature of the fin base surface and the outer tube surface and the assumption of equal heat transfer coefficient on the entire fin surface area. Using a newly recommended expression for the equivalent length of the fin tip, it would be possible to calculate the fin efficiency more precisely and thus the average heat transfer coefficient on the fin surface area, which leads to a more accurate dimensioning of the heat exchanger.

Highlights

Gas-liquid type heat exchangers are very widespread in industry
The results show that fin efficiency determined by numerical simulations is greater by up to 12.3% than the efficiency calculated analytically
Stainless steel was selected as the fin material because it has lower thermal conductivity than other applied materials, the error is more pronounced

Summary

Introduction

Gas-liquid type heat exchangers are very widespread in industry. In order to increase the heat transfer, i.e., the reduction of the heat exchanger dimension, finned surfaces of different shapes have been developed. Designing a heat exchanger with such finned surfaces is done on the basis of analytical solutions developed at the beginning of the 20th century. The first to analyse heat transfer on extended surfaces were Harper and Brown [1] in 1922. They introduced the concept of fin efficiency and provided analytical solutions for the two-dimensional model for a longitudinal and annular fin of uniform thickness. They proposed the use of an adiabatic fin tip model with corrected fin height for the fin tip heat loss, which increases the fin height by half of the fin thickness

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