Modeling of fin-and-tube heat exchangers based on the volume averaging theory (VAT) requires proper closure of the VAT based governing equations. Closure can be obtained from reasonable lower scale solutions of a computational fluid dynamics (CFD) code, which means the tube row number chosen should be large enough, so that the closure can be evaluated for a representative elementary volume (REV) that is, not affected by the entrance or recirculation at the outlet of the fin gap. To determine the number of tube rows, three-dimensional numerical simulations for plate fin-and-tube heat exchangers were performed, with the Reynolds number varying from 500 to 6000 and the number of tube rows varying from 1 to 9. A clear perspective of the variations of both overall and local fiction factor and the Nusselt number as the tube row number increases are presented. These variation trends are explained from the view point of the field synergy principle (FSP). Our investigation shows that 4 + 1 + 1 tube rows is the minimum number to get reasonable lower scale solutions. A computational domain including 5 + 2 + 2 tube rows is recommended, so that the closure formulas for drag resistance coefficient and heat transfer coefficient could be evaluated for the sixth and seventh elementary volumes to close the VAT based model.

References

References
1.
Travkin
,
V.
, and
Catton
,
I.
, 1995, “
A Two-Temperature Model for Turbulent Flow and Heat Transfer in a Porous Layer
,”
J. Fluids Eng.
,
117
(
1
), pp.
181
188.
2.
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.
3.
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
, eds.,
Elsevier
,
San Diego, CA
, pp.
1
144
.
4.
Catton
,
I.
, 2006,
“Transport Phenomena in Heterogeneous Media Based on Volume Averaging Theory,”
Heat Mass Transfer
,
42
(
6
), pp.
537
551
.
5.
Horvat
,
A.
, and
Catton
,
I.
, 2003, “
Numerical Technique for Modeling Conjugate Heat Transfer in an Electronic Device Heat Sink
,”
Int. J. Heat Mass Transfer
,
46
(
12
), pp.
2155
2168.
6.
Horvat
,
A.
, and
Mavko
,
B.
, 2005, “
Hierarchic Modeling of Heat Transfer Processes in Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
48
(
2
), pp.
361
371.
7.
Whitaker
,
A.
, 1999,
The Method of Volume Averaging
,
Kluwer Academic Publishers
,
Boston
.
8.
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.
9.
McQuiston
,
F. C.
, 1978, “
Correlations of Heat Mass and Momentum Transport Coefficients for Plate-Fin-Tube Heat Transfer Surfaces With Staggered Tubes
,”
ASHRAE Trans.
84
, pp.
294
308.
10.
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.
11.
Gray
,
D. L.
, and
Webb
,
R. L.
, “
Heat Transfer and Friction Correlations for Plate Fin-and-Tube Heat Exchangers Having Plain Fins
,”
Proceedings Eighth International Heat Transfer Conference
, pp.
2745
2750
.
12.
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.
13.
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.
14.
Torikoshi
,
K.
,
Xi
,
G.
,
Nakazama
,
Y.
, and
Asano
,
H.
, 1994, “
Flow and Heat Transfer Performance of a Plate Fin-and-Tube Heat Exchanger
,”
ASME J. Heat Transfer
,
4
, pp.
411
416.
15.
Jang
,
J.-Y.
,
Wu
,
M.-C.
, and
Chang
,
W.-J.
, 1996, “
Numerical and Experimental Studies of Three Dimensional Plate-Fin and Tube Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
39
(
14
), pp.
3057
3066.
16.
Jang
,
J.-Y.
, and
Chen
,
L.-K.
, 1997, “
Numerical Analysis of Heat Transfer and Fluid Flow in a Three-Dimensional Wavy-Fin and Tube Heat Exchanger
,”
Int. J. Heat Mass Transfer
,
40
(
16
), pp.
3981
3990.
17.
Jang
,
J.-Y.
, and
Yang
,
J.-Y.
, 1998, “
Experimental and 3-D Numerical Analysis of the Thermal-Hydraulic Characteristics of Elliptic Finned-Tube Heat Exchangers
,”
Heat Transfer Eng.
,
19
(
4
), pp.
55
67.
18.
Guo
,
Z. Y.
,
Li
,
D. Y.
, and
Wang
,
B. X.
, 1998, “
A Novel Concept for Convective Heat Transfer Enhancement
,”
Int. J. Heat Mass Transfer
,
41
(
14
), pp.
2221
2225.
19.
Ma
,
L.-D.
,
Li
,
Z.-Y.
, and
Tao
,
W.-Q.
, 2007, “
Experimental Verification of the Field Synergy Principle
,”
Int. Commun. Heat Mass Transfer
,
34
(
3
), pp.
269
276.
20.
Tao
,
W. Q.
,
He
,
Y. L.
,
Wang
,
Q. W.
,
Qu
,
Z. G.
, and
Song
,
F. Q.
, 2002, “
A Unified Analysis on Enhancing Single Phase Convective Heat Transfer With Field Synergy Principle
,”
Int. J. Heat Mass Transfer
,
45
(
24
), pp.
4871
4879.
21.
Guo
,
Z. Y.
,
Tao
,
W. Q.
, and
Shah
,
R. K.
, 2005, “
The Field Synergy (Coordination) Principle and Its Applications in Enhancing Single Phase Convective Heat Transfer
,”
Int. J. Heat Mass Transfer
,
48
(
9
), pp.
1797
1807.
22.
He
,
Y. L.
,
Tao
,
W. Q.
,
Song
,
F. Q.
, and
Zhang
,
W.
, 2005, “
Three-dimensional Numerical Study of Heat Transfer Characteristics of Plain Plate Fin-and-Tube Heat Exchangers From View Point of Field Synergy Principle
,”
Int. J. Heat Fluid Flow
,
26
(
3
), pp.
459
473.
23.
Tao
,
W. Q.
, 2001,
Numerical Heat Transfer
,
Xi’an Jiaotong University Press
,
Xi’an
.
24.
Incropera
,
F. P.
,
DeWitt
,
D. P.
, and
Ber
,
T. L.
, 2006,
Fundamentals of Heat and Mass Transfer
,
Wiley
,
New York
.
25.
Cheng
,
Y. P.
,
Qu
,
Z. G.
,
Tao
,
W. Q.
, and
He
,
Y. L.
, 2004, “
Numerical Design of Efficient Slotted Fin Surface Based on the Field Synergy Principle
,”
Numer. Heat Transfer
, Part A,
45
(
6
), pp.
517
538.
26.
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.
27.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere Publishing Corp.
,
Washington, DC
.
28.
Kupprn
,
T.
, 2000,
Heat Exchanger Design Handbook
,
Marcel Dekker, Inc.
,
New York
.
29.
Bejan
,
A.
, and
Kraus
,
A.
, 2003,
Heat Transfer Handbook
Wiley
,
New York
.
30.
Schmidt
,
T. E.
, 1949, “
Heat Transfer Calculations for Extended Surfaces
,”
Refrig. Eng.
,
57
, pp.
351
357.
31.
Tao
,
W.-Q.
,
Guo
,
Z.-Y.
, and
Wang
,
B.-X.
, 2002, “
Field Synergy Principle for Enhancing Convective Heat Transfer—Its Extension and Numerical Verifications
,”
Int. J. Heat Mass Transfer
,
45
(
18
), pp.
3849
3856.
32.
Kays
,
W. M.
, and
Crawford
,
M. E.
, 1980,
Convective Heat and Mass Transfer
,
McGraw-Hill Book Company
,
New York
.
33.
Wang
,
C.-C.
,
Chang
,
Y.-J.
,
Hsieh
,
Y.-C.
, and
Lin
,
Y.-T.
, 1996, “
Sensible Heat and Friction Characteristics of Plate Fin-and-Tube Heat Exchangers Having Plane Fins
,”
Int. J. Refrigeration
,
19
(
4
), pp.
223
230.
34.
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.
You do not currently have access to this content.