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Journal of Heat Transfer | Volume 133 | Issue 11 | Research Paper
Research Papers: Heat Exchangers

Obtaining Closure for Fin-and-Tube Heat Exchanger Modeling Based on Volume Averaging Theory (VAT)

[+] Author and Article Information
Feng Zhou

School of Energy and Environment, Southeast University, 2 Si Pai Lou, Nanjing 210096, China;  Department of Mechanical and Aerospace Engineering, University of California, 48-121 Engineering IV, 420 Westwood Plaza, Los Angeles, CA 90095zhoufeng@ucla.edu

Nicholas E. Hansen, David J. Geb, Ivan Catton

 Department of Mechanical and Aerospace Engineering, University of California, 48-121 Engineering IV, 420 Westwood Plaza, Los Angeles, CA 90095hansenen@gmail.com

J. Heat Transfer 133(11), 111802 (Sep 20, 2011) (8 pages) doi:10.1115/1.4004393 History: Received January 09, 2011; Revised June 02, 2011; Accepted June 06, 2011; Published September 20, 2011; Online September 20, 2011
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Modeling a fin-and-tube heat exchanger as porous media based on volume averaging theory (VAT), specific geometry can be accounted for in such a way that the details of the original structure can be replaced by their averaged counterparts, and the VAT based governing equations can be solved for a wide range of heat exchanger designs. To complete the VAT based model, proper closure is needed, which is related to a local friction factor and a heat transfer coefficient of a representative elementary volume. The present paper describes an effort to model a fin-and-tube heat exchanger based on VAT and obtain closure for the model. Experiment data and correlations for the air side characteristics of fin-and-tube heat exchangers from the published literature were collected and rescaled using the “porous media” length scale suggested by VAT. The results were surprisingly good, collapsing all the data onto a single curve for friction factor and Nusselt number, respectively. It was shown that using the porous media length scale is very beneficial in collapsing complex data yielding simple heat transfer and friction factor correlations and that by proper scaling, closure is a function of the porous media, which further generalizes macroscale porous media equations. The current work is a step closer to our final goal, which is to develop a universal fast running computational tool for multiple-parameter optimization of heat exchangers.
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Figures

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+A schematic diagram of a fin-and-tube heat exchanger
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A schematic diagram of a fin-and-tube heat exchanger
Figure 1

A schematic diagram of a fin-and-tube heat exchanger

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+REV for a fin-and-tube heat exchanger
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REV for a fin-and-tube heat exchanger
Figure 2

REV for a fin-and-tube heat exchanger

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+Overlay plot of friction factor using Dc as the length scale
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Overlay plot of friction factor using Dc as the length scale
Figure 3

Overlay plot of friction factor using Dc as the length scale

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+Overlay plot of friction factor using Dh as the length scale
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Overlay plot of friction factor using Dh as the length scale
Figure 4

Overlay plot of friction factor using Dh as the length scale

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+Effect of tube row number on f and Nu according to Wang correlations [9]
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Effect of tube row number on f and Nu according to Wang correlations [9]
Figure 5

Effect of tube row number on f and Nu according to Wang correlations [9]

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+Overlay plot of Nu number using Dc as the length scale
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Overlay plot of Nu number using Dc as the length scale
Figure 6

Overlay plot of Nu number using Dc as the length scale

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+Overlay plot of Nu number using Dh as the length scale
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Overlay plot of Nu number using Dh as the length scale
Figure 7

Overlay plot of Nu number using Dh as the length scale

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+Comparison between rescaled correlations and experimental data by Tang [16]
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Comparison between rescaled correlations and experimental data by Tang [16]
Figure 8

Comparison between rescaled correlations and experimental data by Tang [16]

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