International Journal of Refrigeration 30 (2007) 1153e1167
www.elsevier.com/locate/ijrefrig
Airside heat transfer and friction characteristics
for enhanced fin-and-tube heat exchanger with
hydrophilic coating under wet conditions
Xiaokui Maa, Guoliang Dinga,*, Yuanming Zhanga, Kaijian Wangb
b
a
Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, 1954 Huashan Road, Shanghai 200030, China
Fujitsu General Institute of Air-Conditioning Technology Limited, 1116 Suenaga, Takatsu-Ku, Kawasaki 213-8502, Japan
Received 8 November 2006; received in revised form 21 January 2007; accepted 1 March 2007
Available online 12 March 2007
Abstract
The airside heat transfer and friction characteristics of 14 enhanced fin-and-tube heat exchangers with hydrophilic coating
under wet conditions are experimented. The effects of number of tube rows, fin pitch and inlet relative humidity on airside performance are analyzed. The test results show that the influences of the fin pitch and the number of tube rows on the friction
characteristic under wet conditions are similar to that under dry surface owing to the existence of the hydrophilic coating.
The Colburn j factors decrease as the fin pitch and the number of tube rows increase. For wavy fin, the Colburn j factors increase
with the increase of the inlet relative humidity, but for interrupted fin, the Colburn j factors are relatively insensitive to the
change of the inlet relative humidity. The friction characteristic is independent of the inlet relative humidity. Based on the
test results, heat transfer and friction correlations, in terms of the Colburn j factor and Fanning f factor, are proposed to describe
the airside performance of the enhanced fin geometry with hydrophilic coating under wet conditions. For wavy fin, the correlation of the Colburn j factor gives a mean deviation of 7.6%, while the correlation of Fanning f factor shows a mean deviation of
9.1%. For interrupted fin, the correlation of the Colburn j factor gives a mean deviation of 9.7%, while the correlation of Fanning
f factor shows a mean deviation of 7.3%.
Ó 2007 Elsevier Ltd and IIR. All rights reserved.
Keywords: Heat exchanger; Cooler; Humid air; Finned tube; Enhanced surface; Heat transfer; Coefficient; Friction; Coating
Transfert de chaleur côté air et caractéristiques de frottement
d’un échangeur à tubes ailetés muni d’un enrobage
hydrophile sous des conditions mouillées
Mots clés : Échangeur de chaleur ; Refroidisseur d’air ; Air humide ; Tube aileté ; Surface augmentée ; Transfert de chaleur ; Coefficient ;
Frottement ; Revêtement
* Corresponding author. Tel.: þ86 21 62932110; fax: þ86 21 62932601.
E-mail address: glding@sjtu.edu.cn (G. Ding).
0140-7007/$35.00 Ó 2007 Elsevier Ltd and IIR. All rights reserved.
doi:10.1016/j.ijrefrig.2007.03.001
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1154
Nomenclature
a
A1
A2
Afr
Amin
A0
b
Cp
Dc
f
Fp
Fs
Gc
hm
hs
i
ifg
I0
I1
j
k
K0
K1
Le
m
m*
Mfb
M*
N
Pl
Pr
Pt
coefficient defined by Eq. (14)
outside surface area of tubes (m2)
surface area of fin (m2)
frontal area (m2)
minimum free-flow area (m2)
total airside surface area (m2)
coefficient defined by Eq. (14)
specific heat (J kg1 K1)
fin collar outside diameter (mm)
friction factor
fin pitch (mm)
fin spacing (mm)
mass flux of the air based on the minimum flow
area (kg m2 s1)
mass transfer coefficient (kg m2 s1)
sensible heat transfer coefficient (W m2 K1)
enthalpy (J kg1)
saturated water vapor enthalpy (J kg1)
modified Bessel function solution of the first
kind, order 0
modified Bessel function solution of the first
kind, order 1
the Colburn factor
thermal conductivity (W m1 K1)
modified Bessel function solution of the second
kind, order 0
modified Bessel function solution of the second
kind, order 1
Lewis number
mass flow rate (kg s1)
coefficient defined by Eq. (22)
coefficient defined by Eq. (10)
coefficient defined by Eq. (9)
number of longitudinal tube rows
longitudinal tube pitch (mm)
Prandtl number
transverse tube pitch (mm)
1. Introduction
Enhanced fins including wavy fin and interrupted fin
are widely used to improve the performance of fin-andtube heat exchangers. The wavy fin enhances heat transfer
by lengthening the air flow channel and causing better
mixing of air flow. The interrupted fin, including louver
fin and slit fin, enhances heat transfer by renewing the
boundary layer and reducing the thickness of the boundary
layer. In practical application of fin-and-tube heat exchangers, condensation phenomena will occur on the fin
surface when the surface temperature is below the dew
point temperature of incoming air. The presence of condensate water makes the heat/mass transfer process more
DP
Q
Qs
Ql
r
ReDc
RH
T
Ta*
V
W
pressure drop of airside (Pa)
average heat transfer rate (W)
sensible heat transfer rate (W)
latent heat transfer rate (W)
fin radius (m)
Reynolds number based on tube collar diameter
relative humidity
temperature ( C)
coefficient defined by Eq. (11)
velocity (m s1)
humidity ratio of moist air (kg kg1)
Greek symbols
b
coefficient defined by Eq. (12)
d
fin thickness (mm)
hf,wet
wet fin efficiency
ho
overall surface effectiveness
x
boundary line between dry region and wet
region
ri
inlet air density (kg m3)
rm
mean air density (kg m3)
ro
outlet air density (kg m3)
s
contraction ratio of the fin array
Subscripts
a
air
d
dew point
dry
dry bulb temperature
f
fin
fb
fin base
ft
fin tip
i
inner
in
inlet
o
outer
out
outlet
s
saturated
w
water
complicated. In recent years, airside performance research
of enhanced fin-and-tube heat exchangers in wet conditions was performed gradually. Mirth and Ramadhyani
[1,2] presented test results for five smooth wavy fin patterns. Their results showed that the Nusselt numbers are
very sensitive to the change of inlet air dew point temperature, and the Nusselt numbers decrease with the increase
of inlet air dew point temperature. Wang et al. [3e5] analyzed the effects of the number of tube rows, the fin pitch
and tube size etc. on airside performance for herringbone
wavy fin patterns in wet conditions, and developed the airside heat transfer and friction correlations. For slit fin,
only Wang et al. [6] presented test results for three slit
fin-and-tube heat exchangers under wet conditions. The
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
Until now, there is no research on the enhanced finand-tube heat exchangers with hydrophilic coating under
wet conditions. As a consequence, the objective of the present study is to study the effects of the fin pitch, the number of
tube rows and the inlet relative humidity on the airside heat
transfer and friction characteristics for the enhanced fin with
hydrophilic coating under wet conditions with experimental
method, and develop heat transfer and friction correlations,
in terms of the Colburn j factor and Fanning f factor, based
on the test results.
effects of the number of tube rows, the fin pitch and the
inlet relative humidity on airside performance were reported, and the heat transfer and friction correlation
were developed. For louver fin, Wang et al. [7] and Kim
et al. [8e10] did experimental research relating to airside
performance under wet conditions. The test results indicated that the effect of the number of tube rows and the
fin pitch on the heat transfer performance is comparatively
small, while the friction factors increase significantly with
the fin pitch for fully wet conditions. The effect of the inlet relative humidity on the sensible heat transfer performance is negligible, and there is detectable effect of the
inlet humidity on the friction factors. The above researches are focused on the fully wet conditions. In practice, partially wet conditions will happen if the fin tip
temperature is higher than the dew point temperature
whereas the fin base temperature is lower than the dew
point temperature. There are a number of papers addressing the heat transfer performance of the heat exchangers
under partially wet surface conditions [11e14], but most of
them are academic research, relative experimental research
is limited.
The above-mentioned researches are focused on the enhanced fin without hydrophilic coating. The condensate
water may adhere as droplets on the fin surfaces without
hydrophilic coating, and this phenomenon will cause bridging between the fins and increasing air pressure drop. Furthermore, the condensate water may corrode aluminum fins, and
produce corrosion problems. A solution to solve this problem
is to add hydrophilic coating on the aluminum fins. The hydrophilic coating can effectively improve the condensate
drainage and decrease airside pressure drop [15,16]. The airside performance is different between fin-and-tube heat exchangers with hydrophilic coating and fin-and-tube heat
exchangers without hydrophilic coating [17,18], and the hydrophilic coating has been applied on the fin surface widely,
so it is necessary to study the airside performance of enhanced fin with hydrophilic coating under wet conditions.
7
4
8
6
5
13
9
10
12
11
13
14
15
2. Experimental apparatus
The experimental apparatus is schematically illustrated
in Fig. 1, which includes an air flow loop, a water flow
loop, a data acquisition system and the test heat exchangers.
A closed type wind tunnel is used to conduct the air
flow through the heat exchanger. The air duct is made
of galvanized steel sheet and the test section has
a 210 mm 210 mm cross-section. A variable speed centrifugal fan (0.75 kW) is used to circulate the air, which passes
through nozzle chamber, air conditioner box, mixing device,
straightener, and test heat exchanger orderly. The air flow
rate measurement is detected by multiple nozzles based on
the ASHRAE 41.2 standard [19]. A differential pressure
transducer with 5.0 Pa precision is used to measure the
pressure difference across the nozzles. A pressure transducer
with 1.0 kPa precision and a dry bulb and wet bulb temperature transducer with 0.3 C precision are used to measure
the inlet air conditions of nozzles. The air conditioner box is
used to control the temperature and humidity of inlet air,
which are allowed 0.2 C and 3% fluctuation range.
The test section is insulated with a 15 mm thick standard
sheet. A differential pressure transducer with 0.2 Pa precision is used to measure the pressure difference across the
heat exchangers. The dry bulb temperature and relative
humidity of the inlet and outlet air are measured by two temperature and humidity transducers with 0.1 C and 1.4%
2
1
16
1155
3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Volume flow meter
Pump
Thermostat
Air conditioner box
Mixer
Straightener
Temperature and humidify transducer
Fin-and-tube heat exchanger
Video camera
Pressure difference transducer
Pressure difference transducer
Pressure transducer
Straightener
Nozzle
Dry and wet bulb temperature meter
Variable speed centrifugal fan
Fig. 1. Schematic of experimental setup.
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1156
precision. Six K-type thermocouples with 0.1 C precision
welded on the tube surface are used to measure the fin base
temperature.
Water flow loop consist of a thermostat, a centrifugal
pump and a magnetic flow meter with 0.15 L/min precision. The purpose of this loop is to provide the cool capacity
of the test heat exchangers. After the water reaches the required temperature, it is pumped out from the thermostat,
delivered to the heat exchanger and then returned to the thermostat. The water temperature difference between inlet and
outlet of heat exchangers is measured by two K-type thermocouples with a calibrated accuracy of 0.1 C. All signals
are registered by a data acquisition system and finally averaged over the elapsed time.
Fourteen fin-and-tube heat exchangers for testing are
made of aluminum fin and copper tube. Detailed dimensions
of the heat exchangers and the enhanced fins are shown in
Figs. 2 and 3, respectively. Their detailed configurations are
tabulated in Table 1. Fin surface coatings including anticorrosive layer and hydrophilic coating are shown in Fig. 4.
The coating material is organic resin, the thickness of anticorrosive layer and hydrophilic coating is 1.1 mm and 0.8 mm,
and the water contact angle of hydrophilic coating surface is
10e20 initially. Coating process chart is shown in Fig. 5.
Condensation phenomena on the fin surface are recorded
by a video camera put at the outlet of air. Totally, 23 test conditions are listed in Table 2. The experimental rig’s repetition quality as well as the influence of the camera on the
airside pressure drop measurement was tested with the No.
1 heat exchanger in Table 1 under No. 5 and No. 10 test conditions in Table 2. Experimental rig’s repetition quality data
are listed in Table 3. The maximum repetition error of heat
transfer capacity is 2.1%, and the maximum repetition error
of airside pressure drop is 1.1%. Experimental rig’s repetition quality is fine. The influence of the camera on the airside
pressure drop measurement is shown in Table 4, the existence of the camera changes the pressure loss of air flow
through heat exchangers by less than 1.1%, and the influence
of the camera can be omitted in the following study. Experimental uncertainties are reported according to the analysis
method proposed by Moffat [20], and the maximum error
of the Colburn j factor and Fanning f factor are 10.2%
and 9.4%, respectively. The detailed analysis results are
tabulated in Table 5.
3. Data reduction
3.1. Airside sensible heat transfer coefficient hs
Under wet conditions, the heat transfer rate of test heat
exchangers Q includes sensible heat transfer rate Qs and
latent heat transfer rate Ql, namely,
h i
ð1Þ
Q ¼ Qs þ Ql ¼ ho A0 hs Ta Tfb þ hm ifg Wa Wfb
The ho in Eq. (1) is the overall surface efficiency, and is
related to the fin surface area, total surface area, and wet
fin efficiency:
ho ¼ A1 þ hf;wet A2 A0
ð2Þ
The heat transfer and mass transfer coefficients are correlated
by the ChiltoneColburn analogy [21], which is expressed as
hs
¼ Cp;a Le2=3
hm
ð3Þ
From Eqs. (1)e(3), the airside sensible heat transfer coefficient hs can be gotten,
hs ¼ A1 þ hf;wet A2
h
Q
i
ifg
Ta Tfb þ Cp;a Le
2=3 Wa Wfb
ð4Þ
3.2. Heat transfer rate Q
The total heat transfer capacity Q used in Eq. (4) is averaged from the airside and the waterside as follows:
Q ¼ ðQa þ Qw Þ=2
ð5Þ
where
Qa ¼ ma ðia;in ia;out Þ
ð6Þ
Water Inlet
Water Outlet
Base Temperature Measurement
Unit: mm
Fig. 2. Structure dimensions of the tested fin-and-tube heat exchangers.
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1157
(a)
1.393
16.3º
9.525
Air flow direction: From reader into the paper
(b)
A
Air flow
direction
A
DETAIL A-A
(c)
A
Air flow
direction
A
DETAIL A-A
Unit: mm
Fig. 3. Structure dimensions of the test enhanced fin patterns (a) wavy fin, (b) slit fin, and (c) louver fin.
Qw ¼ mw Cp;w ðTw;out Tw;in Þ
ð7Þ
In the experiments, only those data that satisfy the ASHRAE
standard [22] requirements (namely, the energy balance conditions, jQw Qj=Q 0:05) are considered in the final analysis.
3.3. Wet fin efficiency hf,wet
For fin-and-tube heat exchanger, the wet fin efficiency
hf,wet is normally calculated by the equivalent circular area
method. McQuiston and Parker [23] extended the analysis
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1158
Table 1
Geometric dimension of the enhanced fin-and-tube heat exchangers
No. Fp (mm) d (mm) Dc (mm) Pt (mm) Pl (mm) N Interrupted
type
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1.2
1.5
1.7
1.4
1.8
1.5
1.4
1.2
1.5
1.7
1.5
1.4
1.8
1.4
0.105
0.105
0.105
0.105
0.105
0.105
0.105
0.105
0.105
0.105
0.105
0.105
0.105
0.105
7.21
7.21
7.21
9.74
9.74
7.21
9.74
7.21
7.21
7.21
7.21
9.74
9.74
9.74
21.0
21.0
21.0
25.4
25.4
21.0
25.4
21.0
21.0
21.0
21.0
25.4
25.4
25.4
19.05
19.05
19.05
19.05
19.05
19.05
19.05
13.3
13.3
13.3
13.3
19.05
19.05
19.05
2
2
2
2
2
3
3
2
2
2
3
2
2
3
Wavy fin
Wavy fin
Wavy fin
Wavy fin
Wavy fin
Wavy fin
Wavy fin
Slit fin
Slit fin
Slit fin
Slit fin
Louver fin
Louver fin
Louver fin
to circular fins using the approximation proposed by
Schmidt [24]. The wet fin efficiency is given as
tanhðMm ri qÞ
Mm ri q
ð8Þ
2hs
Cifg
1þ
kf df
Cp
ð9Þ
hf;wet ¼
where
Mm2 ¼
q¼
ro
ro
1 1 þ 0:35 ln
ri
ri
ð10Þ
Wa Wfb
Ta Tfb
ð11Þ
Following the approximation (Eq. (11)) proposed by
McQuiston [25], Hong and Webb [26] derived the analytical
formulation of wet surface for circular fins as
hf;wet ¼
where
2hs
ð1 þ abÞ
kf df
ð14Þ
2hs
ð1 þ bCÞ
kf df
ð15Þ
M 2 ¼
2
¼
Mfb
Ta þ bWa bb
1 þ ab
ifg
b ¼ 2=3
Le Cp;a
Ta ¼
2ri
ro2 ri2
Mm
K1 ðMm ro ÞI1 ðMm ri Þ I1 ðMm ro ÞK1 ðMm ri Þ
K1 ðMm ro ÞI0 ðMm ri Þ þ K0 ðMm ri ÞI1 ðMm ro Þ
ð12Þ
ð16Þ
ð17Þ
In the calculation, coefficients a, b and the fin tip temperature Tft need to be iterated. Tft can be calculated by
Eq. (18). If the fin is totally wet (Tft Ta,d), the values of
a and b can be readily determined with Eqs. (19) and (20).
If the fin is partially wet (Tfb Ta,d Tft), the values of
a and b can be determined according to Tfb and Ta,d.
Tf ¼ Ta þ Tfb Ta
K1 ðM ro ÞI0 ðM rÞ þ I1 ðM ro ÞK0 ðM rÞ
ð18Þ
K0 ðM ri ÞI1 ðM ro Þ þ K1 ðM ro ÞI0 ðM ri Þ
Ws;f ¼ aTf þ b
and the constant C in Eq. (9) is given by
C¼
In fact, the parameter C defined by Eq. (11) is not constant, it varies over the fin surface. So Liang et al. [27] developed the wet fin efficiency analytical model as follows:
2ri M Ta Tfb
hf;wet ¼ 2 2
Mfb ro ri2 Ta Tfb
K1 ðM ro ÞI1 ðM ri Þ I1 ðM ro ÞK1 ðM ri Þ
ð13Þ
K1 ðM ro ÞI0 ðM ri Þ þ K0 ðM ri ÞI1 ðM ro Þ
ð19Þ
Ws;f ¼ 3:7444 þ 0:3078Tf þ 0:0046Tf2 þ 0:0004Tf3
103 ; 0 Tf 30 C
ð20Þ
Liang et al. [27] concluded that the above wet fin efficiency
analysis model is suitable for fully wet conditions, but for
partially wet conditions, the above model will bring bigger
error. So we use Liang et al. analytical model [27] to calculate wet fin efficiency for fully wet conditions, and the wet
fin efficiency analytical model for partially wet conditions
is developed in this paper. It should be noted that Liang
et al. [27] did not consider the absolute value for actual
Hydrophilic layer
Anti-corrosive layer
Fin
Anti-corrosive layer
Hydrophilic layer
Fig. 4. Coating structure of fin surface.
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1159
Fig. 5. Coating process of fin surface.
heat transfer rate of fin, a minus value will be gotten if we
use Eq. (13) to calculate the wet fin efficiency, a modified
Equation of Eq. (13) will be used in the final calculation.
The modified equation is given as
2ri M Tfb Ta
hf;h;fullywet ¼ 2 2
Mfb ro ri2 Ta Tfb
K1 ðM ro ÞI1 ðM ri Þ I1 ðM ro ÞK1 ðM ri Þ
ð21Þ
K1 ðM ro ÞI0 ðM ri Þ þ K0 ðM ri ÞI1 ðM ro Þ
There are two conditions under wet conditions. One is fully
wet condition; the other is partially wet condition. First, the
Table 2
The test conditions of experiment
wet fin efficiency is calculated according to the method of
fully wet conditions, but when the fin tip temperature is
larger than the dew point temperature, the partially wet conditions happen, then the wet fin efficiency is calculated
according to the method of partially wet conditions.
For partially wet conditions, the fin base temperature is
lower but the fin tip temperature is higher than the dew point
of air. On the fin surface there is a place, r ¼ x, where the surface temperature equals the dew point of the air. The fin is
then separated into two regions: a wet region (ri r < x)
and a dry region (x r < ro).
For dry region
d2 Tf 1 d2 Tf
þ
þ m2 Ta Tf ¼ 0; x r ro
dr2 r dr 2
1
ð22Þ
No.
Ta,in ( C)
RHin (%)
V (m s )
Tw,in ( C)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
20
20
20
27
27
27
27
27
27
27
27
27
35
35
35
35
35
27
27
27
27
27
27
50
50
50
50
60
70
80
50
50
50
50
50
50
50
50
50
50
60
70
80
60
70
80
0.5
1.0
2.0
1.0
1.0
1.0
1.0
0.5
1.0
2.0
3.0
4.0
0.5
1.0
2.0
3.0
4.0
1.0
1.0
1.0
1.0
1.0
1.0
6
6
6
6
6
6
6
12
12
12
12
12
12
12
12
12
12
12
12
12
18
18
18
The boundary conditions for fin temperature are as
follows:
8
>
< Tf r¼x ¼ Tdew
vTf
ð23Þ
>
¼0
: vr
r¼ro
Then,
Tf ¼ Ta þ ðTdew Ta Þ
K1 ðm ro ÞI0 ðm rÞ þ I1 ðm ro ÞK0 ðm rÞ
K0 ðm xÞI1 ðm ro Þ þ K1 ðm ro ÞI0 ðm xÞ
ð24Þ
For wet region
d2 Tf 1 dTf
þ M 2 Ta Tf ¼ 0; ri r x
þ
dr2 r dr
ð25Þ
The boundary conditions for fin temperature are:
(
Tf r¼ri ¼ Tfb
Tf r¼x ¼ Tdew
ð26Þ
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1160
Table 3
The experimental rig’s repetition quality experiment
No. 5
First
Second
Third
Table 5
Summary of estimated uncertainties
No. 10
Parameter Uncertainty
Heat transfer
capacity (W)
Pressure
drop (Pa)
Heat transfer
capacity (W)
Pressure
drop (Pa)
1709
1731
1722
17.7
17.9
17.7
1380
1363
1351
48.2
48.6
48.5
Using the boundary conditions (26), the analytical solution
of Eq. (25) can be expressed as
I0 ðM rÞK0 ðM xÞ I0 ðM xÞK0 ðM rÞ
Tf ¼ Ta þ
I0 ðM ri ÞK0 ðM xÞ I0 ðM xÞK0 ðM ri Þ
Tfb Ta
I0 ðM ri ÞK0 ðM rÞ I0 ðM rÞK0 ðM ri Þ þ
Tdew Ta
I0 ðM ri ÞK0 ðM xÞ I0 ðM xÞK0 ðM ri Þ
0.9
1.5
1.8
2.5
ma
mw
Qa
Qw
I1 ðM ri ÞK0 ðM xÞ þ I0 ðM xÞK1 ðM ri Þ
I0 ðM ri ÞK0 ðM xÞ I0 ðM xÞK0 ðM ri Þ
Tfb Ta
I0 ðM ri ÞK1 ðM ri Þ þ I1 ðM ri ÞK0 ðM ri Þ
M
I0 ðM ri ÞK0 ðM xÞ I0 ðM xÞK0 ðM ri Þ
Tdew Ta
ð28Þ
r¼ri
The fin efficiency is defined as the ratio of the actual fin heat
transfer rate over the maximum possible heat transfer rate if
the entire fin were at the base temperature. Hence,
6.0
0.1
6.9
3.7
8.4
4.0
10.2
9.4
2
Mfb
ro2
The parameter x in Eq. (30) can be determined from the
continuity of heat flow at the point separating the dry and
wet surfaces.
dTf
dr
¼
r¼x
dTf
dr
ð31Þ
r¼xþ
The fin surface temperature distribution at dry region and
wet region in Eq. (31) can be seen as follows.
For wet region
dTf
dr
qact
hf;partiallywet ¼
qmax
hs
DP
j
f
2ri M ri2 Ta Tfb
I1 ðM ri ÞK0 ðM xÞ þ I0 ðM xÞK1 ðM ri Þ
I0 ðM ri ÞK0 ðM xÞ I0 ðM xÞK0 ðM ri Þ
Tfb Ta
I0 ðM ri ÞK1 ðM ri Þ þ I1 ðM ri ÞK0 ðM ri Þ
I0 ðM ri ÞK0 ðM xÞ I0 ðM xÞK0 ðM ri Þ
ð30Þ
Tdew Ta
hf;h;partiallywet ¼
Then,
¼ M
1.8
2.5
3.9
5.0
Min. (%) Max. (%)
Substituting Eq. (27) into Eq. (29), the partially wet fin
efficiency can be obtained as
ð27Þ
dTf
dr
Parameter Uncertainty
Min. (%) Max. (%)
I1 ðM xÞK0 ðM xÞ þ I0 ðM xÞK1 ðM xÞ
I0 ðM ri ÞK0 ðM xÞ I0 ðM xÞK0 ðM ri Þ
Tfb Ta
I0 ðM ri ÞK1 ðM xÞ þ I1 ðM xÞK0 ðM ri Þ
M
I0 ðM ri ÞK0 ðM xÞ I0 ðM xÞK0 ðM ri Þ
Tdew Ta
ð32Þ
¼ M
r¼x
dTf
2pri df kf
dr r¼ri
¼ 2
2p ro ri2 hs Ta Tfb þ b Wa Ws;fb
ð29Þ
For dry region
Table 4
The influence experiment of camera on airside pressure drop
No. 5
First
Second
Third
dTf
dr
¼ ðTdew Ta Þm
r¼xþ
Without
camera
With
camera
Without
camera
With
camera
17.7
17.7
17.6
17.7
17.9
17.7
48.0
48.2
48.3
48.2
48.6
48.5
K1 ðm ro ÞI1 ðm xÞ I1 ðm ro ÞK1 ðm xÞ
K0 ðm xÞI1 ðm ro Þ þ K1 ðm ro ÞI0 ðm xÞ
No. 10
ð33Þ
where
m 2 ¼
2hs
kf df
ð34Þ
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
3.4. Colburn j factor and Fanning f factor
The heat transfer performance is correlated in terms of
the Colburn j factor, i.e.,
j¼
hs
Pr 2=3
Gc Cp;a
ð35Þ
The reduction of the Fanning f factor of the heat exchanger is
evaluated from the pressure drop equation proposed by Kays
and London [28],
ri
Amin rm 2DPri 2
f¼
1
þ
s
1
ð36Þ
A0 ri G2c
ro
where
Amin
Afr
ma
Gc ¼
Amin
s¼
ð37Þ
ð38Þ
4. Results and discussion
Fig. 6 shows the fin efficiency with air inlet relative humidity predicted by the present model, Liang et al. analytical model [27], McQuiston and Parker model [23] and
Hong and Webb model [26]. The calculation of dry fin
efficiency uses Elmahdy and Biggs model [29]. Fig. 6
shows that for a given inlet air dry bulb temperature and
fin base temperature, the fin may work in dry condition,
partially wet condition and fully wet condition depending
1161
on the air inlet relative humidity. For a partially wet fin,
the fin efficiency decreases rapidly with the increase in
air inlet relative humidity. For a fully wet fin, the effect
of the air inlet relative humidity on the fin efficiency is
small. Comparison of the various models shows that the results of McQuiston and Parker model [23] and Hong and
Webb model [26] are significantly different from those of
present model and Liang et al. analytical model [27]. The
wet fin efficiency predicted by McQuiston and Parker
model [23] and Hong and Webb model [26] decreases approximately linearly with the increase of air inlet relative
humidity. These two models fail to distinguish the difference between a partially wet condition and fully wet condition, thus giving a much higher fin efficiency for
a partially wet fin. In these two models, a constant value
of C is assumed based on the conditions at the fin base.
In fact, the parameter C is not constant; it varies over the
fin surface. At a high air relative humidity, this method
underpredicts the fin efficiency due to the use of an unreasonably big C value at this condition. Comparison also
shows that the fin efficiency calculated by Hong and
Webb model [26] is bigger over 10% than the fin efficiency
calculated by McQuiston and Parker model [23], Hong and
Webb [26] indicated that the empirical approximation of
Schmidt [24] used in McQuiston and Parker model [23]
will bring errors. Fig. 6 also shows that analytical model
of Liang et al. [27] is unsuitable for the calculation of
fin efficiency for partially wet condition. Liang et al.
[27] also arrived at similar conclusion by comparing the
analysis model with numerical model for partially wet
condition.
Fig. 6. Comparison of fin efficiencies for a typical case.
1162
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
Fig. 7. Effect of the number of tube rows on the airside performance: (a) wavy fin and (b) interrupted fin.
Fig. 7 shows the effect of the number of tube rows on the
airside heat transfer and friction characteristics of enhanced
fin. The ordinates are Colburn j factors and Fanning f factors,
and the abscissa is the Reynolds number based on collar
diameter. The inlet relative humidity is 50% and the inlet
water temperature is 12 C. As shown in Fig. 7, the Colburn
j factors decrease with the increase of the number of tube
rows. This phenomenon is especially pronounced in low
Reynolds number region. The trend is similar to the results
of plain fin and wavy fin by Wang et al. [3,30]. The possible
explanations of this phenomenon are summarized as
follows. The downstream turbulence is deteriorated by the
vortices formed behind the tube row, and the downstream
turbulence tends to diminish with the increase of the number
of tube rows. When the Reynolds number decreases, the vortices behind the tube become more pronounced [31]. Fig. 7
also indicates that the friction factors are insensitive to the
number of tube rows for wavy fin. Because the condensate
water can be drained by the hydrophilic coating in time,
this phenomenon is very similar to plain fin-and-tube heat
exchanger under dry conditions as shown by Rich [32].
But for interrupted fin, the friction factors decrease slightly
Fig. 8. Effect of the fin pitch on the airside performance: (a) wavy fin and (b) interrupted fin.
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1163
Fig. 9. Effect of the inlet relative humidity on the airside performance: (a) wavy fin, (b) slit fin and (c) louver fin.
with the increase of the number of tube rows. Possible explanations of the effect of the number of tube rows on the friction characteristics are summarized as follows. The structure
of interrupted fin is different with wavy fin, and the interrupted fin is easier to catch the condensate water drop than wavy
fin. As pointed out by the flow visualization experiments
conducted by Yoshii et al. [33] who tested a scale-up model
under wet conditions, when the fin pitch is close to each
other, the droplets adhering to the fin surface may cause
the air flow twisting. As humid air flows across the wet coils,
the corresponding specific humidity decreases along the direction of the air flow, the local dew point temperatures also
decrease and the driving potential of mass transfer also decreases. The condensate water rate and twisted air flow
may decrease as the number of tube rows increase. As a result, the friction factors decrease with the increase of the
number of tube rows.
Fig. 8 depicts the effect of fin pitch on the airside performance of heat exchangers having a 2-row configuration.
The tested fin pitches are 1.2, 1.4, 1.5, 1.7 and 1.8 mm,
respectively. The Colburn j factors decrease with the
increase of the fin pitch. Partially wet conditions will
happen with the increase of Reynolds number, and thus
phenomenon becomes more pronounced under partially
1164
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
Fig. 10. Condensation photos of fin-and-tube heat exchanger
(Fp ¼ 1.5 mm, Ta,dry ¼ 27 C, Va,in ¼ 1.0 m/s).
wet conditions. For wavy fin, the Colburn j factors for
Fp ¼ 1.2 mm which is about 10e20% higher than that
for Fp ¼ 1.7 mm. The causes of this result are summarized
as follows. When the fin pitch decreases, the air flow inside the wavy flow channel can be mixed better, which
leads to the increase of the heat transfer coefficient. The
mixing effect is amplified with the increase of Reynolds
number. For interrupted fin, the results are quite different
from the corresponding test results of interrupted fin without hydrophilic coating as reported by Wang et al. [17,18],
who found that the heat transfer performance is relatively
insensitive to change of fin pitch. A possible explanation
for the effect of fin pitch without hydrophilic coating
may be related to the presence of condensate water. In
fully wet conditions, the effect of strip may be offset by
the presence of condensate water. But for the interrupted
fin with hydrophilic coating, the condensate water will exist on the fin surface in the form of water film, and can be
drained away easily. Therefore, the effect of strip on heat
transfer performance will appear again. The friction factors
show a crossover phenomenon as fin pitch changes like
dry surface.
Fig. 9 shows the effect of inlet relative humidity on the
airside performance with different fin pitches (Fp ¼ 1.2,
1.5, 1.7 mm for wavy and slit fin, and Fp ¼ 1.4, 1.8 mm
for louver fin). The air dry bulb temperature Ta,dry ¼ 27 C,
the inlet air flow velocity Va,in ¼ 1.0 ms1, and the corresponding number of tube rows is 2. As shown in Fig. 9,
for wavy fin, the Colburn j factors increase with the increase
of the inlet relative humidity, while the friction factors are
insensitive to the change of the inlet relative humidity. For
interrupted fin, the Colburn j factors and the friction factors
are relatively insensitive to the change of inlet relative
humidity. The cause of these results can be explained by
photographs taken in the experiments. These photographs
are shown in Fig. 10. For wavy fin, the hydrophilic coating
makes the condensate water exist on the fin surface in the
form of film. When the inlet humidity increases, the mass
flux of water film becomes bigger. The more flows of water
film enhance the airside heat transfer. But the structure of
interrupted fin is different from that of wavy fin. The strips
on the interrupted fin surface may block the flow of the water
film, so the heat transfer enhancement of water film flow is
reduced. The hydrophilic coating makes the condensate
water drain from the fin surface easily, and then there is no
water bridge to block the air flow channel, so the friction factors are independent of inlet relative humidity. Fig. 9 also
shows that airside heat transfer performance of 6 C inlet
water temperature is better than that of 12 C inlet water
temperature for wavy fin. The Coburn j factors for
RHin ¼ 80% are approximately 6e15% higher than those
at RHin ¼ 50% under 12 C inlet water temperature, and
the Coburn j factors for RHin ¼ 80% are approximately
14e32% higher than those at RHin ¼ 50% under 6 C inlet
water temperature. The possible reason is that lowering of
inlet water temperature will cause more condensate water
on the fin surface, and the heat transfer enhancement
owing to the flow of condensate water film becomes more
sensible.
5. Development of correlations
It is obvious from the previous discussions that the airside performances of the enhanced fin-and-tube heat
exchanger with hydrophilic coating are very complicated.
A multiple linear regression technique in a practical range
of experimental data (350 < ReDc < 4500) was carried out,
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1165
Fig. 11. Comparison of the proposed correlations with experimental data for wavy fin (a) j and (b) f.
and the appropriate correlation forms of j and f are given as
follows:
For wavy fin:
j ¼ 0:0605Re0:4218
Dc
f¼
j ¼ 0:2408Re0:3597
Dc
0:4122 0:8276
Fs
Pt
RH0:9222 N 0:27
Dc
Pl
ð39Þ
f ¼ 1:1285Re0:4911
Dc
Fs
Dc
0:6842 0:5947
Pt
RH0:2887 N 0:0333
Pl
ð40Þ
For interrupted fin:
0:5581
5:5335ReDc
Fs
Dc
0:7543 1:951
Pt
RH0:0073 N 0:2895
Pl
Fs
Dc
ð41Þ
0:313 0:3379
Pt
0:0045 0:1844
RH
N
Pl
ð42Þ
Ranges of applicability for Eqs. (39) and (40) are as
follows: ReDc, 350e4500; Pt, 21.0e25.4 mm; Pl,
19.05 mm; Dc, 7.21e9.74 mm; Fp, 1.2e1.8 mm; and N, 2e3.
Range of applicability for Eqs. (41) and (42) are as
follows: ReDc, 350e4500; Pt, 21.0e25.4 mm; Pl,
13.3e19.05 mm; Dc, 7.21e9.74 mm; Fp, 1.2e1.8 mm; and
N, 2e3.
Fig. 12. Comparison of the proposed correlations with experimental data for interrupted fin (a) j and (b) f.
X. Ma et al. / International Journal of Refrigeration 30 (2007) 1153e1167
1166
Table 6
Comparison of the proposed correlation with experimental dataa,b
Deviation
Wavy fin
j (%)
Interrupted fin
f (%)
j (%)
f (%)
10%
15%
20%
25%
Mean deviation
a
b
75.3
61.7
58.7
71.3
88.3
79.2
81.8
88.8
94.2
89.6
89.5
96.5
97.4
96.1
96.5
99.3
7.6
9.1
9.7
7.3
X
1
M jCorrelation Dataj
100%.
Mean deviation ¼
1
M
Data
M: number of data points.
As shown in Fig. 11, for wavy fin, the proposed heat
transfer j factor correlation, Eq. (39), can describe 88.3%
of the test data within the deviation limit of 15%, while
the correlation of the friction f factor, Eq. (40), can correlate
79.2% of the test data within the deviation limit of 15%.
The proposed correlations of j and f have a mean deviation
of 7.6% and 9.1%, respectively. As shown in Fig. 12, for interrupted fin, the proposed heat transfer j factor correlation,
Eq. (41), can describe 81.8% of the test data within the
deviation limit of 15%, while the correlation of the friction
f factor, Eq. (42), can correlate 88.8% of the test data within
the deviation limit of 15%. The proposed correlations of j
and f have a mean deviation of 9.7% and 7.3%, respectively.
Detailed comparisons between the proposed correlations of j
and f and the experimental data are depicted in Table 6.
6. Conclusion
The airside performance of enhanced fin-and-tube heat
exchanger with hydrophilic coating under wet conditions
is presented and discussed in this study. A total of 14 fin-andtube heat exchangers having enhanced fin geometry were
tested and examined. The following conclusions are made:
C
C
C
C
The wet fin efficiency analytical model for partially
wet conditions is developed. For a partially wet fin,
the fin efficiency decreases rapidly with the increase
in air inlet relative humidity. For a fully wet fin, the effect of air inlet relative humidity on the fin efficiency is
small.
The Colburn j factors decrease with the increase of the
number of tube rows. This phenomenon is especially
pronounced in the low Reynolds number region. For
wavy fin, the effect of the number of tube rows on
the friction factor is insensitive, but for interrupted
fin, the friction factors decrease slightly with the
increase of the number of tube rows.
The Colburn j factors decrease with the increase of the
fin pitch. This phenomenon becomes more pronounced
under partially wet conditions, and the friction factor is
very sensitive to change in fin pitch. The friction
C
factors also show a crossover phenomenon as fin pitch
changes like dry surface.
For wavy fin, the Colburn j factors increase with the
increase of the inlet relative humidity, while for
interrupted fin, the Colburn j factors are relatively insensitive to the change of inlet relative humidity. The
friction factors are relatively independent of inlet relative humidity. For wavy fin, the Colburn j factors of
lower inlet water temperature are bigger.
The heat transfer and friction correlations were proposed to describe the present test results. For wavy
fin, the mean deviations of the proposed j and f factor
correlations are 7.6% and 9.1%, respectively. For interrupted fin, the mean deviations of the proposed j and f
factor correlations are 9.7% and 7.3%, respectively.
Acknowledgments
The authors are very grateful to Dr C.C. Wang of ITRI,
Taiwan for giving advice and documents on experimental
rig design and correlation development for this study.
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