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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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Citing Articles

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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References

1
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2
Travkin, V. S., and Catton, I., 1995, “A Two-Temperature Model for Turbulent Flow and Heat Transfer in a Porous Layer,” ASME J. Fluids Eng., 117 (1), pp. 181–188.  [CrossRef]
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Travkin, V. S., and Catton, I., 1998, “Porous Media Transport Descriptions—Non-Local, Linear and Non-Linear Against Effective Thermal/Fluid Properties,” Adv. Colloid Interface Sci., 76-77 , pp. 389–443.  [CrossRef]
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Rich, D. G., 1975, “The Effect of the Number of Tubes Rows on Heat Transfer Performance of Smooth Plate Fin-and-Tube Heat Exchangers,” ASHRAE Trans., 81 , pp. 307–317.
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McQuiston, F. C., 1978, “Correlations of Heat Mass and Momentum Transport Coefficients for Plate-Fin-Tube Heat Transfer Surfaces With Staggered Tubes,” ASHRAE Trans., Part1 (84), pp. 294–308.
6
Rich, D. G., 1973, “The Effect of Fin Spacing on the Heat Transfer and Friction Performance of Multirow, Smooth Plate Fin-and-Tube Heat Exchangers,” ASHRAE Trans., 79 (2), pp. 135–145.
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Gray, D. L., and Webb, R. L., “Heat Transfer and Friction Correlations for Plate Fin-and-Tube Heat Exchangers Having Plain Fins,” "Proceedings of the Eighth International Heat Transfer Conference", pp. 2745–2750.
8
Kang, H. J., Li, W., Li, H. Z., Xin, R. C., and Tao, W. Q., 1994, “Experimental Study on Heat Transfer and Pressure Drop Characteristics of Four Types of Plate Fin-and-Tube Heat Exchanger Surfaces,” J. Therm. Sci., 3 (1), pp. 34–42.  [CrossRef]
9
Wang, C.-C., Chi, K.-Y., and Chang, C.-J., 2000, “Heat Transfer and Friction Characteristics of Plain Fin-and-Tube Heat Exchangers, Part II: Correlation,” Int. J. Heat Mass Transfer, 43 (15), pp. 2693–2700.  [CrossRef]
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Whitaker, S., 1999, "The Method of Volume Averaging", Kluwer Academic, Boston.
11
Travkin, V. S., and Catton, I., 2001, “Transport Phenomena in Heterogeneous Media Based on Volume Averaging Theory,” "Advances in Heat Transfer", G.G.Hari and A.H.Charles, ed., Elsevier, pp. 1–144.
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15
Zhou, F., Hansen, N., and Catton, I., 2010, “Determining the Computational Domain Length to Obtain Closure for VAT Based Modeling by 3D Numerical Simulation and Field Synergy Analysis,” ASME Paper No. IMECE 2010-37561.
16
Tang, L.-H., Min, Z., Xie, G.-N., and Wang, Q.-W., 2009, “Fin Pattern Effects on Air-Side Heat Transfer and Friction Characteristics of Fin-and-Tube Heat Exchangers With Large Number of Large-Diameter Tube Rows,” Heat Transfer Eng., 30 (3), pp. 171–180.  [CrossRef]
17
Tang, L. H., Zeng, M., and Wang, Q. W., 2009, “Experimental and Numerical Investigation on Air-Side Performance of Fin-and-Tube Heat Exchangers With Various Fin Patterns,” Exp. Therm. Fluid Sci., 33 (5), pp. 818–827.  [CrossRef]
18
Xie, G., Wang, Q., and Sunden, B., 2009, “Parametric Study and Multiple Correlations on Air-Side Heat Transfer and Friction Characteristics of Fin-and-Tube Heat Exchangers With Large Number of Large-Diameter Tube Rows,” Appl. Therm. Eng., 29 (1), pp. 1–16.  [CrossRef]
19
Wang, C.-C., and Chi, K.-Y., 2000, “Heat Transfer and Friction Characteristics of Plain Fin-and-Tube Heat Exchangers, Part I: New Experimental Data,” Int. J. Heat Mass Transfer, 43 (15), pp. 2681–2691.  [CrossRef]
20
Tang, L. H., Xie, G. N., Zeng, M., Wang, H. G., Yan, X. H., and Wang, Q. W., 2007, “Experimental Investigation on Heat Transfer and Flow Friction Characteristics in Three Types of Plate Fin-and-Tube Heat Exchangers,” J. Xi’an Jiaotong Univ., 41 , pp. 521–525 (in Chinese).
21
Techo, R., Tickner, R. R., and James, R. E., 1965, “An Accurate Equation for the Computation of the Friction Factor for Smooth Pipes for the Reynolds Number,” ASME J. Appl. Mech., 32 , p. 443.

Figures

Grahic Jump Location
+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

Grahic Jump Location
+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

Grahic Jump Location
+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

Grahic Jump Location
+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

Grahic Jump Location
+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]

Grahic Jump Location
+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

Grahic Jump Location
+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

Grahic Jump Location
+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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