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

Mladen Bošnjaković, Simon Muhič, Ante Čikić and Marija Živić
Additional contact information
Mladen Bošnjaković: Technical Department, College of Slavonski Brod, Dr. M. Budaka 1, 35000 Slavonski Brod, Croatia
Simon Muhič: Faculty of Mechanical Engineering, University of Novo mesto, Na Loko 2, 8000 Novo mesto, Slovenia
Ante Čikić: Department of Mechanical Engineering, University North, 104. brigade 3, 42000 Varaždin, Croatia
Marija Živić: Mechanical Engineering Faculty in Slavonski Brod, Josip Juraj Strossmayer University of Osijek, Trg Ivane Brlić Mažuranić 2, 35000 Slavonski Brod, Croatia

Energies, 2019, vol. 12, issue 9, 1-18

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.

Keywords: efficiency of annular fin; analytical and numerical method; computational fluid dynamics; fin base temperature (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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