ELSEVIER
PII: S0140-7007(96)00021-7
Int J. ReJ?ig. Vol. 19, No. 4, pp. 223-230, 1996
Copyright @ 1996 Elsevier Science Ltd and IIR
Printed in Great Britain. All rights reserved
0140-7007/96/$15.00 + 00
Sensible heat and friction characteristics of plate fin-and-tube heat
exchangers having plane fins
Chi-Chuan Wang and Yu-Juei Chang
E n e r g y a n d R e s o u r c e s L a b o r a t o r i e s , I n d u s t r i a l T e c h n o l o g y R e s e a r c h Institute,
Hsinchu, Taiwan, ROC
Yi-Chung Hsieh and Yur-Tsai Lin
D e p a r t m e n t o f M e c h a n i c a l Engineering, Y u a n - Z e Institute o f T e c h n o l o g y ,
Taiwan, ROC
Received 10 October 1995; revised 14 March 1996
In the present study, 15 samples of plate fin heat exchangers with different geometrical parameters, including
the number of tube rows, fin spacing and fin thickness are tested and compared in an induced flow open wind
tunnel. Results are presented in the form of friction factor and Colburn j-factor against Reynolds number
based on the tube collar diameter in the range of 300 to 7500. Comparisons with the existing plate fin
correlation are also reported. It is found that the fin spacing does not affect the heat-transfer coefficient. The
number of tube rows has negligible effect on the friction factor, and the fin thickness does not affect the heattransfer or friction characteristics.
(Keywords: heat transfer; pressure loss; battery; tube; fin; air; measurement; Reynolds)
Copyright ~) 1996 Elsevier Science Ltd and IIR
Transfert de chaleur sensible et caract6ristiques de frottement pour
6changeurs de chaleur plaque-ailettes, pourvus d'ailettes planes
Dans /'article, les auteurs essaient et comparent, dans un tunnel aOrodynamique ouvert it ~coulement./brcO.
quinze Ochantillons d'Ochangeurs de chaleur it plaque-ailettes, en en modifiant les parambtres g~omOtriques, h
savoir: le nombre de rang~es de tubes, l'espacement des ailettes et leur ~paisseur. Ils pr~sentent les rOsultats sous
jorme du facteur de frottement et du facteur j de Co~burn, compar& au hombre de Reynolds" fondd sur de
diambtre circulaire du tube, dans la plage de 300 h 7500. Ils rapportent Ogalement des comparaisons avecla
correlation existante des plaques-ailettes, lls d~duisent que l'espacement des ailettes n 'a aucune incidence sur le
coefficient de transfert de chaleur. Le nombre de rang~es de tubes a un effet ndgligeable sur le facteur de
j?ottement, et l'(paisseur des ailettes n'effecte ni le transfert de chaleur ni les caract~ristiques de frottement.
(Mot cl+s: Transfert de chaleur; perte de pression: batterie; tube; ailette: air: mesure: Reynolds)
Copyright (~! 1996 Elsevier Science Ltd and IIR
The plate fin-and-tube heat exchangers, consisting of
mechanically or hydraulically expanded round tubes in a
block of parallel continuous fins, are widely used in
industry and particularly in the heating, air-conditioning
and refrigeration industries. The complex airflow pattern
across the fin-and-tube surface makes the theoretical
prediction of heat-transfer coefficients very difficult, and
therefore most publications are related to experimental
works. The most systematic study was carried out by
Rich 1'2, who investigated a total of 14 coils, in which the
fin spacing was varied from H I D e = 0.084 to 0.64. He
concluded that the heat-transfer coefficient was essentially independent of the fin spacing. He further
concluded that the pressure drop per row is independent
of the number of tube rows.
McQuiston 3 stated that the j-factor could be correlated by applying a correction 'finning factor', defined as
Ao/Ato , to the Reynolds number. A strong dependence of
heat-transfer coefficients on the finning factor was
observed. McQuiston 3 showed an ( A o / A t o ) - 015 dependence in his plate-fin data. Kayansayan 4 indicated that
the j-factor is proportional t o (Ao/Ato) -0362. Based on
the previously published data, Gray and Webb 5 proposed a correlation for the existing experimental data.
The RMS error of the resulting correlation is 7.3% for
heat-transfer coefficients and 7.8% for friction factors.
Numerous studies have been devoted to plate fin-andtube heat exchangers. However, most of the previously
published data are for large tube diameter (e.g.
Do = 12.7 and 15.8mm). Kayansayan 4 presented six
experimental data sets for a 9.52-mm-tube. However, the
heat exchangers he tested were all four-row coils. Kays
and London 6 have published few data for tube diameter
of the order 10 mm. To date, there is no systematic study
223
224
C.-C. Wang et al.
Nomenclature
Area (m 2)
Total surface area (m 2)
External tube surface area (m 2)
Heat capacity rate (W K -1)
Specific heat at constant pressure
(Jkg -1K -l)
D~
Fin collar outside diameter (m)
Inside tube diameter (m)
Di
Tube outside diameter (m)
Do
Friction factor
f
G~
Mass flux of the air based on the
minimum flow area (kg m 2 s)
H
Fin spacing (m)
h
Heat-transfer coefficient
( W m -2 K -l)
j = N u / R e P r 1/3
the Colburn factor
Thermal conductivity
k
(Wm -1 K -1)
Abrupt contraction pressure-loss
Kc
coefficient
Abrupt expansion pressure-loss
ICe
coefficient
Depth of the heat exchanger in
L
airflow direction (m)
Number of tube row
N
Mass flow rate (kgs -1)
rn
N T U = U A / Cmin Number of transfer unit
Nusselt number
Nu = hDc/k
AP
Pressure drop (Pa)
Fin pitch (m)
rp
Longitudinal tube pitch (m)
Pl
Prandtl number
Pr
Transverse tube pitch (m)
l?.t
Q
Heat-transfer rate (W)
A
Ao
Ato
C
¢p
Qmax = Cmin(Twater,in-Tair,in)
The maximum possible heat
transfer rate (W)
rc
Tube outside radius, including
collar thickness (m)
Re = p V D / #
Reynolds number
to the air side performance of the plane fin heat
exchangers having a nominal tube diameter of
9.52 mm. As is well-known, coils having a tube diameter
of 9.52mm are very popular in recent HVAC&R
applications. As a result, the objective of the present
study is to provide more experimental data on plate finand-tube heat exchangers having a 9.52-mm tube
diameter. In addition, the effect of fin spacing, the
number of tube rows and fin thickness on the heattransfer and friction characteristics are also investigated.
Experimental apparatus
Experiments were conducted in a forced draft wind
tunnel as described in Figure 1. The airflow was driven by
a 5.6 kW centrifugal fan with an inverter. To avoid and
minimize the effect of flow maldistribution, an air
straightener-equalizer and a mixer were provided. The
inlet and the exit temperature across the sample coil were
Req
r
T
t
U
Equivalent radius for ciruclar fin (m)
Tube inside radius (m)
Temperature (°C)
Fin thickness (m)
Overall heat-transfer coefficient
(Wm -2 K -l)
/
X L = V(Pt/2)2 + p2t/2
geometric parameter (m)
geometric parameter (m)
XM = Pt/2
Greek letters
6
e = Qave/Qmax
q
q0
#
Thickness of the tube wall (m)
Heat exchanger effectiveness
Finn efficiency
Surface effectiveness
Dynamic viscosity of fluid
(kgm -1 s-1)
Density (kg m -3)
Contraction ratio of crosssectional area
Subscripts
1
2
air
ave
b
i
in
f
m
min
max
o
out
water
w
air side inlet
air side outlet
air side
average value
base surface
tube side
inlet
fin surface
mean value
minimum value
maximum value
total surface
outlet
water side
wall of the tube
measured by two T-type thermocouple meshes. The inlet
measuring mesh consisted of 8 thermocouples, while the
outlet mesh contained 16 thermocouples. The sensor
locations inside the rectangular duct were established by
following ASHRAE 7 recommendations• The thermocouple data were individually recorded and then
averaged. During the isothermal test, the variance of
these thermocouples were within +0.2°C. All the
thermocouples were pre-calibrated by a high-resolution
(0.01°C) quartz thermometer. The calibrated uncertainties of the thermocouples, as depicted in Table 1, were
within +0.1°C. The pressure drop of the test coil was
detected by a precision differential pressure transducer,
reading to 0.1 Pa. The airflow measuring station, a
multiple nozzle code test, was designed on the basis of
the ASHRAE 41.2 standard s. The geometric parameters
of the tested coils are illustrated in Table 2. The working
medium on the tube side was hot water. The inlet
temperature was controlled by a thermostat reservoir
Characteristics of heat exchangers
®@
©
I;i
® ®G 9 ,&_? ®
i-
___>
lh)l
q
Water
;,
I
i',',
w,
w,
i',',
<
I ]r ----j
.
Rt~N('I 'v ()ll
rvoiv ~
.
.
.
.
n~,]1,~ ~
I
l
I
I
........
.
.
.
.
.
.
"=---'l
....
I)rld
'"
I Rccordcr
k
.
J
Q
@
L I
I;;
i:p
I
l ')'-~
0 ,~ 0
l i-
f
.j
iII
,,,,,
225
•
•
~(Oml)U t
L 7 .....
• . . . . . . .
|
~-J
"--
III
Ill
,
tj
f I
@
III
©
9 code
1 inlel
honey cone straight(met
:~ d c v c h q ) i n g
seclion
4 'I'/C i n l e t , l c m t ) e r a t . u r e
ill(,aHIll'illg
st al.ion
,-) t)l,(~,..;slli,(~ t a l ) ( i n h H
)
6 lest unit
7 pressul'c lap(outlet)
[+ T / C o u l l e t t e m p e r a t u r e
tll(+aSlll'illg s l a t i o n
t e s t e r for lllf!a~lll'OlllUll[
flow l ' a l e
selling means
nozzle pr(rssurc Iap(inlel)
nozzle pressure
tap(outlel)
m u l t i t ) l e llozzl(~s p l a l e
s e l l i n g nteans
variable exhausl
fan system
discharge
waler putnp
of
10
11
12
13
14
15
16
17
aiF
Figure 1 Schematic of experimental set-up
Figure 1 Scheme de l'installation exp&imentale
Table 1
Summary of estimated uncertainties
Tableau 1 Dimensionsg~om~triques de plusieurs ~chantillons d'&hangeurs de chaleur h plaque-ailettes
Primary measurements
Derived quantities
Parameter
Uncertainty
Parameter
'}/air
?ilwate r
0.3 1%
0.5 %
0.5%
0.05"C
0. I C
0.05~C
Reoc
Rei
Ap
Twater
Tair
T
f
qwater
qair
j
Uncertainty (%)
ReDs = 600
Uncertainty 1%)
+1.0
+0.73
+17.7
:t:2.95
4-3.5
+9.4
±0.47
+0.73
+1.3
+0.89
± 1.6
-]=3.9
ReDs = 7000
Table 2 Geometric dimensions of the sample plate fin-and-tube heat exchangers
Tableau 2 R#sum#des erreurs estim&s
No.
Fin thickness (ram)
Fin pitch (mm)
Dc (mm)
Pt (mm)
& (ram)
Row No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.2
0.2
0.2
0.2
0.2
0.2
1.82
2.24
3.20
2.03
2.23
3.00
1.85
2.21
3.16
1.77
3.21
1.77
3.17
1.74
3.16
10.23
10.23
10.23
10.23
10.23
10.23
10.23
10.23
10.23
10.23
10.23
10.23
10.23
10.23
10.23
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
25.4
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
2
2
2
4
4
4
6
6
6
2
2
4
4
6
6
Notes: tube wall thickness after expansion: 0.336 mm; the test samples are all staggered layout
having an adjustable heat capacity up to 80 kW. Both the
inlet and outlet temperatures were measured by two precalibrated RTDs (Pt-100 f~) which have an accuracy of
0.1°C. The water volumetric flowrate was detected by a
magnetic flow meter with 0.0021s -z resolution. All the
data signals were collected and converted by a data
acquisition system (a hybrid recorder). The data
acquisition system then transmitted the converted signals
through a GPIB interface to the host computer for
further operation. During the experiments, the water
inlet temperature was held constant at 60.0 + 0.1 °C. The
air frontal velocities ranged from 0.3 to 6 . 2 m s -1.
C.-C. Wang et al.
226
Generally, the energy balance between air side and tube
side was within 2%. In all cases, the water side resistance
(evaluated as 1/hiAi) was less than 12% of the overall
resistance in all cases, and the wall resistance (evaluated
as 6w/kwAw) was negligible. The dominant thermal
resistance was always on the air side. Uncertainties in
the reported experimental values of the Colburnj-factor
and friction factor f were estimated by the method
suggested by Moffat 9. The maximum uncertainties are
tabulated in Table 1. The highest uncertainties were
associated with the lowest Reynolds number.
Analysis
In the analysis, to provide the heat transfer characteristics of the tested coils, the e-NTU method is used to
determine the UA term of the heat exchanger. The UA
product was calculated using the e-NTU method for the
unmixed-unmixed cross-flow configuration. Correspondingly, the appropriate e-NTU relationship l° is
= 1 - e x p [ N T U ° 2 2 / C * { e x p ( - C * N T U °78) - 1}]
(1)
Cmin
Cmax
~b/airCp,air
r/'twaterCp,water
-
0ave
Qmax
.
1
-- - -
1
rlohoA o
+
¢5w
~
+ -
1
hiA i
(5)
(6)
where
f = (l.581n(ReD~) - 3.28) -2
(7)
where Re i = p VDi/iz. The finned surface effectiveness,
~0, is defined as the ratio of the actual heat transfer to the
heat-transfer rate occurring when both fin and base are
at the same base temperature. This term may be written
in terms of the fin efficiency ~, fin surface area Af and
total surface area A0 as
r/0 = 1 - A f ( 1 -~7)
A0
(8)
where A0 = Af + A b and Af, A b are the areas of the fin
and base, respectively. In the present investigation, the
estimation of fin efficiency, ~7, is calculated using the
Schmidt 12 approximation for the staggered plate-fin
geometry. The fin efficiency is expressed as
-
tanh(mr0)
mrO
Req = 1.27 XM
r
r
XL --0.3
(12)
With Equations (9)-(12), an iterative process is needed
to obtain the air side heat-transfer coefficient h0 and the
surface effectiveness r/0. The heat-transfer characteristics
of the heat exchanger are presented in the following nondimensional groups:
Nu = hoDc/k
(13)
ReDo = pVmaxDc/#
(14)
j = Nu/(ReocPfl/3)
AcPm [2R1AP
The tube-side heat-transfer coefficient, hi, is evaluated
from the Gnielinski ll semi-empirical correlation:
(k)
( R e i - lOOO)Pr(fi/2)
hi = ~ i 1 + 1 2 . 7 x / - ~ ( P r 2/3 - 1)
(11)
(15)
f -Ao
where the total heat transfer rate, Qave, is the arithmetic
average of the air side and the water side heat-transfer
rates. The overall heat-transfer resistance is evaluated
from the following relationship:
UA
~=(~9-)[l+0.351n(Req/r)]
(4)
rr/waterCp,water(Tin,water- Tin,air)
N T U =- UA/Crnin
(10)
(3)
(2)
Oave
-
2~°
m--v
All the fluid properties are evaluated at the average
values of the inlet and outlet temperatures.
The core friction of the heat exchanger is calculated
from the pressure drop equation described by Kays and
London 6, which includes the entrance and exit pressure
loss coefficients Kc and Ke. The relation for the nondimensional friction f a c t o r f in terms of pressure drop is:
where
c * _= - - -
where
(9)
Pl [ Gc2
2(P_21 _ )
(Kc -[- 1 -- 0 "2) --
\P2
1
/16/
where A 0 and Ac stand for the total heat-transfer area
and the flow cross-sectional area, respectively, and 0- is
the ratio of the minimum flow area to frontal area.
Results and discussion
The experimentally determined values of the Colburn jfactor and friction f a c t o r f for the 15 test samples plotted
against Reynolds number (ReDo) are displayed in Figure
2. The characteristic dimension of the Reynolds number,
ReDc, is the tube outside diameter including collar
thickness. As expected, the friction factor decreases
with the increase of Reynolds number for all test
samples. The j-factors, for samples 7 and 14, show a
maximum for the Reynolds number is less than 2000.
The experimental data of Rich 2 also reveals this kind of
phenomenon. A private discussion between Webb and
Rich 5 had attributed this unexpected phenomenon to the
experimental error at low airflow rates. Gray and Webb 5
therefore, had neglected the experimental data for
ReL < 5000 (corresponds to ReDo = 2750) in correlating
the data of Rich 12
' . Since the present experiments were
carried out carefully with the standard nozzles operated
following the ASHRAE standard 8 recommendation
(nozzle velocities are between 15 and 70ms-l). The
energy balance between air side and tube side is less than
3% throughout the experiments, and good experimental
repeatabilities are achieved at low velocities. Consequently, the maximum of the Coburn j-factors for
samples 7 and 14 may not be due to experimental
Characteristics of heat exchangers
227
0
10
0
10
q~)-#1
"--~"-:#2
-A-:N3
"~-:#4
-~-:#5
"O-:#6
-~-:#7
~:#8
4~:#9
-'~P'-#10
,
-'~:#11
--B--:#I2
-C--:#13
-{-]-:#14
--.~--#15
~ , i,,,
I
E
,
, , ~ ,i
I
i
I
-¢¢-:#10, H = 1 . 5 7 mm, R o w = 2
--t9--:#12, H = 1 . 5 7 mm, R o w = 4
-[]-:#14. H = 1 , 5 4 mm, R o w = 6
f
f
-1
10
-1
10
-2
10
9
10"
I
I
I IIIII
I
I
I
10
4
10
ReDc
Figure 2
j a n d f f o r the tested s a m p l e s
Figure 2
j e t f pour les ~chantillons essayks
mm
I
I
I I I I
3
10
t=0.2
uncertainty. Note that samples 7 and 14 are of six-row
configuration and smallest fin spacing. The possible
explanation for this unusual phenomenon are twofold.
Firstly, as illustrated by Rich l, the standing vortices
form behind a cylinder in cross-flow at low Reynolds
number and the eddies breaks away from the cylinder
and move downstream at higher Reynolds number. The
size of the standing vortices is likely to increase with the
number of tube rows, and eventually a detectable decay
of the heat-transfer coefficient is found. Secondly, the
flow visualization experiments conducted by Chen and
Ren ~3 indicate that the smaller fin spacing is responsible
for reducing the vortex. As a result, the airflow pass
through the heat exchanger is somewhat like channel
flow and the exponent dependence in the Reynolds
number is changed. Note that for channel flow, the
Reynolds number dependence is Re -°z, whereas for pure
tube bank flow, the Reynolds number dependence is
Re -°'4. Combining these two effects, the 'maximum
phenomenon' is expected to form at low air velocities
especially for heat exchangers with larger number of tube
rows and smaller fin spacing. Similar results were also
shown in the automotive multilouver fin surface as
reported by Davenport TM and Achaichia and Cowel115.
Webb and Trauger r6 found that some of the air streams
bypass the louvers at low Reynolds number and act as
'duct flow' between the fin channels so that a lower jfactor will be obtained. Achaichia and Cowel115 identified the flow pattern as 'fin directed flow' for the low
Reynolds number region and 'louver directed flow' for
high Reynolds number region.
Figure 3 illustrates the effect of the number of tube
rows on the heat-transfer and friction characteristics.
The number of tube rows are 2, 4 and 6, respectively. The
fin spacing is approximately 1.57 mm. As can be seen, the
Colburn j-factors decrease with the increase of the
I
i I III]
I I I i
3
10
10
4
10
ReD c
F i g u r e 3 Effect o f the n u m b e r o f t u b e r o w o n the h e a t - t r a n s f e r a n d
friction characteristics
F i g u r e 3 Effet du nombre de rangOes de tubes sur le transfert de chaleur
et lefrottement
number of tube rows for Reynolds number less than
2000. However, the effect of the number of tube rows
diminishes as Reynolds number increases over 2000.
This phenomenon is very similar to the plate fin data as
shown by Rich 2 and Senshimo and Fujii 17. Figure 5
shows also that there is no detectable variation of the
heat-transfer coefficients with increasing row number for
Reo~ > 2000. This is due to the downstream turbulence
eddies shed from the tubes that cause good mixing in the
downstream fin region. As they Reynolds number
decreases, the downstream turbulence tends to diminish
and the vortices behind the tube cylinder are expected to
form. As a result, the number of tube rows shows a
significant effect on the heat-transfer characteristics for
ReD~ < 2000. Figure 3 also indicates that the friction
factors are independent of the number of tube rows.
Again, this phenomenon is very similar to other plate finand-tube heat exchangers as shown by Rich 2, the louver
fin geometry for Chang et al. 18, the wavy fin configuration of Wang et al. 19 and the convex-louver fin geometry
of Wang et al. 2°.
Figure 4 illustrates the effect of the fin thickness on the
thermal-hydraulic characteristics of the plate fin-andtube heat exchangers. The effect of fin thickness on the
thermal-hydraulic characteristics of the plate fin-andtube heat exchanger have not been investigated before.
Gray and Webb 5 argued that the fin thickness should not
affect the thermal-hydraulic characteristics of the plate
fin-and-tube heat exchangers. They explained that the fin
thickness affects only the airflow velocity in the heat
exchanger, which is accounted for by the Reynolds
number. In addition, the friction correlation excludes the
entrance and exit losses. As a result, it is likely that the fin
C.- C. Wang et a l.
228
0
0
10
i
r
p
i
i
i
~J
10
r
I
"0-:#9, H=3.03 mm, Row= 6, t=0.13 mm
-0-:#4. H= 1.90 mm
--A--:#15, H=2.96 mm. Row= 6, t=0.2 mm
t1-:#5, H=210 mm
-&-:#3. H=3.07 ram, Row
-Q-:#6, H=2.87 mm
2, t=0.13 mm
R o w = 4, t = 0 . 1 3 m m
--$-:#11, H=3.01 ram, Row= 2, t=0.2 mm
f
f
10-1
10
10 .2
10
-2
I
i
i
I I IIII
I
I
I
I I II
I
3
10
4
10
I
10
10
Figure 4 Effectof fin thickness on the heat-transfer and friction
characteristics
Figure4 Effet de l'~paisseur des ailettes sur le transfert de chaleur et le
Figure 5
istics
frottement
froltement
thickness may not effect the thermal-hydraulic characteristics of the plate fin-and-tube heat exchanger.
However, the heat transfer correlation for the
individually finned and tube heat exchanger as proposed
by Briggs and Young 21 is
(17)
TM
As seen, the fin thickness shows a slight effect on the
transfer coefficients. Rabas et al. 22 developed more
accurate j and f correlations for low fin height and
small fin spacings. The correlation also indicates that the
j are related to the fin thickness, and is given by
1.12
j=O.292Ren(~o)
.
(L.
(---He)°26\ H /
I
i
I I I r i
3
10
4
10
ReDc
ReDc
j=O.134Re-°'319(H)°2(H)
I I I I II]
2
0.67 ( d e
.~ 0.47 ( @ )
0.77
\Doj
(18)
where n = -0.415 + 0.0346 de/s.
The effect of fin thickness on the thermal-hydraulic
characteristics is generally small for individual fin
geometry. For the present continuous fin-and-tube
configuration, as depicted in Figure 4, the effect of fin
thickness on both the friction factor and the Coburn jfactor are negligible. The correlation form of Equation
(17) was used for the present data. It was found that the
exponent dependence of fin thickness is smaller than that
of Equation (17).
Figure 5 depicts the effect of fin spacing on the heattransfer and friction factors. Rich l concluded that the
heat-transfer coefficients are essentially independent of
fin spacing. In the analysis by Elmahdy and Biggs23, the
heat-transfer coefficient increased with fin spacing. On
Effect of fin spacing
on heat-transfer
and friction character-
Figure 5 Effet du pas des ailettes sur le transfert de chaleur et le
the contrary, the experimental results of McQuiston and
Tree 24 showed a decrease in heat-transfer coefficient with
decreasing fin spacing. Using an oil-lampblack visualization technique, Chen and Ren 13 studied the airflow
pattern for a two-row plate fin-and-tube heat exchanger.
They concluded that the vortices behind the tube do not
effect the heat-transfer coefficient for ReDo < 7000 when
H / D c < 0.33, and the fin spacing does not affect the
heat-transfer coefficient for H / D c > 0.33. The present
three samples are of four-row configuration and their
corresponding H / D c values are 0.186, 0.205 and 0.281,
respectively. Since the Reynolds number of most of the
experimental data are less than 7000, it is seen that the
heat-transfer coefficient is nearly independent of the fin
spacing. The data here are consistent with the data of
Rich 1 and the criteria proposed by Chen and Ren 13 .
Figure 6 compares the ability_ of the correlations by
McQuiston 3, Gray and Webb 5 and Kayansayan4 to
predict the j and f data for two-, four- and six-row
configurations. The McQuiston 3 correlation considerably overpredicts the friction factors and yields an
unacceptable overprediction of the j-factors for Reynolds number less than 1000. Good agreements of jfactors with the Gray and Webb 5 correlation are
generally reported, and the deviations between the
predictions of the Gray and Webb 5 correlation and the
present experimental data are generally within
+ 2 0 / - 8%. The deviation between the prediction of
the Gray and Webb 5 correlation and the present data
increases with decrease in Reynolds number. This is
probably due to the data bank of the Gray and Webb 5
correlation usually having a Reynolds number higher
than 2500. The predictions of the friction factors of the
plate fin data by the Gray and Webb 5 correlation are
Characteristics of heat exchangers
0
10
--.
•-, 10
10
i
i
i i E i ii I
--A-:#15, H = 2 . 9 6 mrn, R o w = 6
..... :McQuistion Correlation for #15
- - -:Gra y & Webb (1986) Correlation for #15
-C--:#13, H = 2 . 9 7 ram, R o w = 4
- - :McQuiston Correlation for #13
i - - : G r a y & Webb Correlation for #13
-e'4r-:#11, H = 3 . 0 1 mm, R o w = 2
[
:McQuiston Correlation for #11
/ "- - :Gray & Webb Correlation tor #11
-l
229
1
-B--:#12, H = 1 . 5 7 ram
..... :Gray & Webb (1986) Correlation for Sample#12
:McQuistion Correlation for #12
:Kayansayan Correlation for #12
-C---:#13, H = 2 . 9 7 rnm
- - :Gray & W e b b (1986) Correlation for Sample# 13
- - :McQuistion Correlation for # 13
- - - : K a y a n s a y a n Correlation for #13
- ~ - : K a y a n s a y a n 07, H = 2 . 2 0
-M-- :Kayansayan #8, H = 3.20
--6--:Kayansayan #9, H = 2 . 5 0
f
~'~
.~" -.~..,~
-2
10
10-~
t=0.2
mm
i
I
/
\Kayansayan Correlation for #15,#13,#11
I
i I i IlL
I
i
i
i i I I
3
10
Row=4,
i
4
10
ReDc
10
t=0.20
10
mm
I Iiiiii
~
~
3
111
t
4
10
10
i t Jt
5
10
ReDc
Figure 6 Comparisonofj andf betweentypicaltest sampleswith the
McQuiston-, Gray and Webb5 and Kayansayan4 correlations
Figure 6 Comparaisonde j et f, de plusieurs dchantillons types avec la
corrOlation de McQuiston. Gray et Webb et Kayansayan
Figure 7 Comparison of j values between test samples with
Kayansayan4 and the present experimental data with identical tube
of row, Pt, PI and fin thickness
Figure 7 Comparaisondes valeurs de j, de plusieurs &:hantillons types,
avec la corrOlation de Kayansayan et les donnOesexp&imentales aetuelles
tubes, P, P~et 6paisseur des ailettes identiques
approximately + 3 0 / - 15% compared to the present
data. The deviations here may be attributed to the data
bank used for their correlation being generally for larger
tube diameters. In addition, the prediction of friction
factors by the Gray and Webb 5 correlation are generally
linear (in a logarithmic scale plot). However, as is
known, the friction factors are usually4 nonlinear in a
logarithmic scale plot. The Kayansayan correlation for
j-factors considerably underpredicts the experimental
data, especially in low Reynolds number regions.
Figure 7 comp4ares the present j-factor data with that
of Kayansayan for identical transverse pitch, longitudinal pitch, tube diameter, number of tube rows and
fin thickness. Although the present data show a
negligible effect of fin spacing, the Kayansayan 4 data
are quite scattered. The present data show 5-25% higher
heat-transfer coefficients than those of Kayansayan4.
The Kayansayan correlation typically predicts lower jfactors than those of others.
It is obvious from the curves shown in Figure 2 that no
single curve can be expected to describe the complex
behaviors for both j- and f-factors. In addition, the
maximum phenomenon for samples 7 and 14 make the
problem even more complicated. As a result, using a
multiple linear regression technique in a practical range
of experimental data (800 < ReD~ < 7500), the appropriate correlation form o f j a n d f for the present data are
/
(Fp-~ -0.212
, \-0.0449
N 0.0897\DccJ
j = 0.394ReD°392~c)~
/
~, \ - 0 . 1 0 4
f=l'Og9ReD°4181~c)"
(
(19)
)-0.197
N-°°935 DccFP
(20)
As shown in Figure 8, Equation (19) can describe 97%
of the experimental data within 10% and Equation (20)
can describe 88% of the experimental data within 10%.
The RMS error of the resulting correlation is 4.1% for
heat-transfer coefficients, and 6.5% for friction factors.
Conclusions
Experiments on the heat-transfer and pressure drop
characteristics of plate fin-and-tube heat exchangers
were carried out for Dc = 10.23mm. In the present
study, 15 samples of plate fin-and-tube heat exchangers
with different geometrical parameters, including row
number, fin thickness and fin spacing. On the basis of
previous discussions, the following conclusions are
made:
1. The maximum phenomena of Colburn j-factor at
low Reynolds numbers occur for plate fin-and-tube
heat exchanger at larger number of tube row and
smaller fin spacing.
2. The experimental data indicate that the number of
tube rows does not affect the friction factors. A
significant reduction of the heat-transfer coefficients
is found for Reynolds number less than 2000 for the
six-row coil, and the effect of the number of tube row
diminishes for 2000 < Reoc < 7500.
3. Fin thickness has negligible effect on both heattransfer and friction characteristics of plate fin-andtube heat exchangers.
4. Fin spacing has negligible affect on the heat-transfer
C.-C. Wang et al.
230
0.1
/
information
appreciated.
/
f r o m Prof.
Ralph
Webb
are very m u c h
(f)
0.08
References
0.06
1
2
0.04
/
0.02
0.02
0.04
0.06
Correlation ( f )
i
0.08
3
4
5
O. 1
6
7
8
0.03
. . . .
I
. . . .
I
. . . .
9
10
()
11
£/A o
q
12
13
14
~0.01
15
16
•
0
F
5
0
0.01
0.02
Correlation ( j )
J
i
17
0.03
Figure 8 Comparison of the experimental data and the present
correlations: (a) friction factor, f ; (b)j-factors
Figure 8 Comparaison des donn~es exp&imentales et des correlations
aetuelles. (a) facteur de frottement, f. et (b) facteurs j
18
19
20
characteristics of plate fin-and-tube heat exchangers
at t h e p r e s e n t test r a n g e .
Acknowledgements
T h e a u t h o r s w o u l d like to e x p r e s s t h e i r g r a t i t u d e for
the E n e r g y R & D
foundation
f u n d i n g f r o m the
E n e r g y C o m m i s s i o n o f the M i n i s t r y o f E c o n o m i c
Affairs, T a i w a n , w h i c h p r o v i d e d f i n a n c i a l s u p p o r t
f o r the p r e s e n t study. V a l u a b l e s u g g e s t i o n s a n d
21
22
23
24
Rich, D. G. The effect of fin spacing on the heat transfer and friction performance of multi-row, plate fin-and-tube heat exchangers ASHRAE Trans (1973) 79(2) 137 145
Rich, D. G. The effect of the number of tube rows on heat transfer performance of smooth plate fin-and-tube heat ASHRAE
Trans (1975) 81(1) 307-317
McQuiston, F. C. Correlation of heat, mass and momentum
transport coefficients for plate fin-and-tube heat transfer surfaces with staggered tubes A SHRAE Trans (1978) 84(1) 294 309
Kayansayan, N. Heat transfer characterization of flat plain fins
and round tube heat exchangers Exper Thermal Fluid Sci
(1993) 6 263 272
Gray, D. L., Webb, R. L. Heat transfer and friction correlations
for plate finned-tube heat exchangers having plain fins Proc 8th
Heat Transfer ConJ (1986) 2745 2750
Kays, W. M., London, A. L. Compact Heat Exchangers 3rd ed
McGraw-Hill (1984)
ASHRAE Handbook Fundamental S1 Edition (1993) Ch. 13. 14
15
ASHRAE ASHRAE Standard 41.2-1987 Standard Methods[or
Laborato O' Air-flow Measurement (1987)
Moffat, R. J. Describing the uncertainties in experimental results
Exp Thermal Fluid Sci (1988) 1 3 17
McQuiston, F. C., Parker, J. D. Heating, Ventillating. and Airconditioning 4th ed. John Wiley, New York (1994) Ch. 14, 57l
Gnielinski, V. New equation for heat and mass transfer in turbulent pipe and channel flow Int Chem Engng (1976) 16 359 368
Schmidt, Th. E. Heat transfer calculations for extended surfaces
Refrig Eng (1949) April 351 357
Chen, Z. Q., Ren, J. X. Effect of fin spacing on the heat transfer
and pressure drop of a two-row plate fin and tube heat exchanger Int J Refrig (1988) 11 456-360
Davenport, C. J. Correlation for heat transfer and flow friction
characteristics of louvered fin AIChE Syrup Set (1983) 79(25)
19-27
Achaiehia, A., CoweU, T. A. Heat transfer and pressure drop
characteristics of flat tube and louvered plate fin surfaces Exp
Thermal Fluid Sci (1988) 1 147 157
Webb, R. L., Trauger, P. Flow structure in the louvered fin heat
exchanger geometry Exp Thermal Fluid Sci (1991) 4 205 217
Seshimo, Y., Fujii, M. An experimental study of the performance
of plate fin and tube heat exchangers at low Reynolds number
3rd ASME/JSME Thermal Engineering Joint Con/( 1991 ) 4
449-454
Chang, W. R., Wang, C. C., Tsi, W. C., Shya, R. J. Air-side performance of louver fin heat exchanger 4th ASME..rJSME Thermal Engineering Joint Conf (1995) 4 467 472
Wang, C. C., Fu, W. L., Chang, C. T. Heat transfer and friction
characteristics of typical wavy fin-and-tube heat exchangers Exp
Thermal Fluid Sci (1996) accepted for publication
Wang, C. C., Chen, P. Y., Jang, J. Y. Heat transfer and friction
characteristics of convex-louver fin-and-tube heat exchangers
Exp Heat Tran~br (1996) accepted for publication
Briggs, D. E., Young, E. H. Convective heat transfer and pressure drop of air flowing across triangular pitch banks of finned
tubes Chem Eng Prog Syrup Ser (1963) 59(41) 1 10
Rabas, T. J,, Eekels, P. W., Sabatino, R. A. The effect of fin density on the heat transfer and pressure drop performance of low
finned tube banks Chem Eng Commun (1981) 10(1) 127 147
Elmahdy, P. E., Biggs, P. E. Finned tube heat exchangers:
correlation of dry surface data ASHRAE Trans (1979) 85(2)
262 273
McQuiston, F. C., Tree, D. R. Heat transfer and friction data for
two fin-tube surfaces J Heat Tran~ffbr (1971) 93 249 250