FURTHER ASSESSMENT OF POOL AND FLOW BOILING HEAT TRANSFER
WITH BINARY MIXTURES
S atish G. Kandlikar
(Visiting Professor, Kyushu University)
Rochester Institute of Technology, Rochester, NY 14623, USA
[email protected]
Shurong Tian, Jian Yu and Shigeru Koyama
Institute of Advanced Material Study, Kyushu University,
Kasuga-kohen, Kasuga, 816-8580, JAPAN
ABSTRACT
The introduction of species conservation equation within the concentration boundary layer along with the 1-D
approximation for the heat transfer and mass transfer around a growing bubble was proposed as a mechanism to explain
the mass diffusion effects in binary mixtures by Kandlikar [1,2]. This model was able to predict the pool boiling data for
mixtures of several chemical compounds including benzene, methanol, and ethylene glycol. The model was extended to
flow boiling by incorporating the mass diffusion effects in the nucleate boiling component of flow boiling correlations.
The theoretical model is further evaluated here for refrigerant mixtures, which are currently being considered as potential
replacements in refrigeration and air-conditioning systems. Experimental data from different sources are used and the
distinction between regions defined on the basis of suppression is studied.
1. INTRODUCTION
As a result of the phas e-out of CFC and HCFC refrigerants
in heat pump, refrigeration and air-conditioning systems, the
binary and ternary refrigerant mixtures have received attention
as potential alternatives. A number of researchers have carried
out experiments with different mixtures to obtain their pool
boiling and flow boiling heat transfer characteristics. The
experimental results showed that the heat transfer coefficient
for the mixture is lower than the mass-fraction or molefraction averaged value of respective pure components, and
depends on composition and the specific mixture constituents.
This decrease is a result of the mass diffusion resistance in
both liquid and vapor phases, and the changes in the mixture
properties. These effects are very difficult to predict in
practice due to complex mechanisms involved during the
boiling process.
Kandlikar [1] developed a theoretical analysis to estimate
the mixture effects on heat transfer. A pseudo -single
component heat transfer coefficient was introduced to account
for the mixture property effects. The liquid composition and
the interface temperature of a growing bubble are predicted
analytically and their effect on the heat transfer is estimated.
He applied this model in both pool boiling and flow boiling
cases [1,2], and obtained good agreement with experimental
data for several mixtures.
In this study, additional experimental data for refrigerant
mixtures from different sources are compared with the
Kandlikar [1,2] correlation.
2. HEAT TRANSFER MODEL
2.1. Pool boiling model
A brief summary of the Kandlikar model [1] is presented
here. The pool boiling heat transfer coefficient for a binary
mixture α B,P B is expressed in terms of the pseudo -single
component heat transfer coefficient as:
α PB.B = α PB.B.PSC FD
(1)
where FD is the diffusion-induced suppression factor that can
be obtained by comparing the mass transfer rates with and
without the diffusion resistance.
For the volatility parameters V1 >0.005



F D = 0.678 
  c p .L
1 + 
  ∆hLG



1

1/2
 k   ∆Ts  

 

 D12   g  



FD can be simplified as:



1
FD = 0.678 
1/ 2
  c
 k 
 1 +  P. L 

x 1,s − y 1,s

  ∆h LG  D12 
(




 dT  
)  
 dx1  
(2)
(3)
For 0< V 1 <0.005
(4)
FD = 1 − 64 .0V1
Subscript s refers to the interface conditions of a growing
bubble. Kandlikar [1] provided a theoretical method to predict
the interface concentration. Preliminary estimates can be
1
obtained by using the bulk phase concentrations. V1 is the
volatility parameter, obtained by using the slope of the bubble
point curve.
V1 =
c P. L
∆h LG
 k 


D 
 12 
1/ 2
dT
(y − x )
dx1 1 1
( ) (D )
~
x2
The pure component correlation [4] was able to represent
the dependence of α on quality x , mass flux G , and heat
flux q . The flow boiling for pure fluids is as follows:
(5)
D12 is the diffusion coefficient of component 1 in mixture of
1 and 2, and is given by:
D12 = D12 0
2.2 Flow boiling model
~
0 x1
21
(6)
αTP. NBD
αTP = larger of 
αTP.CBD
The subscripts NBD and CBD in Eq. (15) refer to the
nucleate boiling dominant and the convective boiling
dominant regions, for which the respective values of α TP are
given by:
α TP. NBD = 0 .6683Co −0.2 (1 − x ) α LO
0
0
where D12
are diffusion coefficients of components 1
and D 21
and 2 present in infinitely low concentration of liquid mixture.
D12 0 = 1.1782 × 10 −16
(φ M 2 )1 / 2 T
(7)
µ L.2υ m,1
the molar specific volume of component 1.
α PB.B.PSC , the pseudo-single phase coefficient for the
mixture, is based on the actual mixture properties obtained
from REFPROP [3].
 ρG .m 


 ρG .avg 


0 .297




 σm

 σ avg

−0 .674
 ∆hLG .m

 ∆hLG.avg





−0 .317
 λL.m

 λL.avg





(16)
+ 1058 .0 Bo 0.7 (1 − x )0 .8 FFlα LO
and
α TP.CBD = 1.136 Co −0.9 (1 − x ) α LO




FFl in Eq s. (16) and (17) is a fluid-surface parameter related to
the nucleation characteristics. Table 1 lists its value for several
refrigerants. T he single-phase heat transfer coefficient α LO is
obtained from the Petukhov [5], and Gnielinski [6]
correlations. The correlation of Petukhov [5] is for
0.5≤ Pr L ≤2000 and 104≤ Re LO ≤5×106 ; as:
[
(
)
= Re LO PrL ( f 2 ) 1 .07 +12 .7 Pr 2 3 − 1 ( f 2 )0. 5
0.284
Nu LO = α LO D λ L
[
(
)
= Re LO PrL ( f 2 ) 1.0 + 12.7 Pr 2 3 − 1 ( f 2 )0.5
]
(19)
The friction factor in Eqs. (18) and (19) is given by
f = [1 .58 ln (Re LO ) − 3.28]
(9)
−2
(20)
Table 1: Fluid-surface parameter F FL for refrigerants in
copper or brass tubes
The individual property variations with composition are as
following average equations.
Fluid
FFL
Fluid
FFL
Tsat.m.avg = x1Tsat.1 + x2Tsat. 2
(10)
Water
1.00
R-113
1.30
ρG .m. avg = x1 ρG1 + x2 ρG 2
(11)
R-11
R-12
1.30
1.50
R-114
R-124
1.24
1.90
R13B1
1.31
R-134a
1.63
R-22
2.20
R32
1.20
R-152a
1.10
R125
1.10
∆ hLG. m.avg = x1∆ hLG.1 + x 2∆ hLG. 2
(18)
The correlation of Gnielinski [6] for 0.5< Pr L <2000 and
2300< Re LO <5×104 ; as:
−1 



]
(8)
is found to be predict ed directly from α1 and α 2 for pure
fluids .



(17)
+ 667 .2 Bo 0.7 (1 − x )0.8 FFlα LO
Nu LO = α LO D λ L
0. 371
α PB. B.avg is the average mixture heat transfer coefficient, and

x
x
α PB.B .avg = 0.5 ( x1α 1 + x 2 α 2 ) +  1 + 2

α1 α 2

0 .8
0 .8
M is the molecular weight and φ is the association factor for
the solvent (2.26 for water, 1.9 for methanol, 1.5 for ethanol,
1.9 for ethylene glycol, and 1.0 for unassociated solvents
including benzene, enther, heptane, and refrigerants); υ m,1 is
 T
α PB.B .PSC = α PB.B .avg  sat.m
 Tsat.avg

(15)
(12)
σ m. avg = x1σ 1 + x2 σ 2
(13)
λL.m .avg = x1λL. 1 + x2 λL.2
(14)
Notes: 1) The values of FFL for R32 and R125 were
estimated from the data set of Yoshida et al. [7]; 2) FFL for
stainless steel tubes is 1 for any fluid.
2
The flow boiling correlation for binary mixtures is divided
into three regions, and the suppression factor for the nucleate
boiling term is applied as follows.
Region I: Near-azeotropic Region; V1 ≤0.03,
α TP. B. NBD
α TP .B = larger of 
α TP. B.CBD
(21)
αTP , B, NBD and α TP , B ,CBD are given by Eqs. (16) and (17)
respectively using mixtures properties.
Region II: Moderate diffusion-induced suppression region,
0.03< V1 ≤0.2, and Bo >10-4 ;
(1 − x ) α LO
0 .8
+ 667 .2Bo 0 .7 (1 − x ) FFl α LO
α TP , B = 1.136 Co
−0 .9
0.8
(22)
Region III: Severe diffusion-induced suppression Region, (a)
For 0.03<V1 ≤0.2 and Bo <10-4, and (b) V1 >0.2;
α TP .B = 1 .136Co −0. 9 (1 − x )0.8 α LO
+ 667 .2 Bo0.7 (1 − x )0.8 FFLα LO FD
(23)
The region covers the two ranges as indicated in (a) and (b)
above. FD is obtained from Eq. (3).
The severe diffusion-induced region is dominated by the
connective effects and the nucleate boiling dominant region
does not exist. The nucleate boiling contribution in this region
is further reduced due to the large difference in composition
between the two phases, and the resulting mass diffusion
resistance at the liquid-vapor interface of a growing bubble.
The fluid-surface parameter is obtained as the mass
fraction-averaged value given by the following equation:
FFL = x 1 F FL,1 + x 2 FFL,2
(24)
Table 2 Experimental data sets used to compare
with the Kandlikar model.
Source
Binary
System
Pressure
(MPa)
Heat Flux
(kW/m2 )
Inoue
and
Monde
[8]
R12/R113
R22/R113
R22/R11
R134a/R113
0.4
40~100
5.3kPa, respectively. The properties of the mixtures were
calculated from the Peng-Robinson equation of state, and
transport properties were calculated using reliable predictive
methods in the experimental data. The experiment data of Shin
et al. [10] is obtained with a stainless steel tube with inner
diameter of 7.7 mm and thickness of 0.9 mm and heated by
direct current. The effective heating length is 5.9 mm. The
estimated error for outer wall temperature measurement is 0.2
K and that for the saturation temperature measurement of the
refrigerant is ±0.5 K. The total estimated error in measuring
heat transfer coefficients is 7.3%. The saturation temperature
is calculated using a modified Carnahan-Starling-Desantis
equation of state. The Kattan et al. [11] experiment used plain
horizontal copper tubes with diameter of 12.00 mm and 10.92
mm. Hot water was used as the heating source. The heat
release curves were determined using REFPR OP [12]. The
experiment by Yoshida et al., obtained with a horizontal
smooth copper tube with diameter of 6.34 mm. The properties
of refrigerant mixture of R32/R134a and R32/R125 were
calculated from REFPROP [3]. The details of these
experiment conditions are shown in Table 3.
4. RESULTS
4.1 Pool Boiling
3. DETAILS OF EXPERIMENTAL DATA
3.1 Pool Boiling
The experimental data of Inoue and Monde [8] was
employed to compare with the Kandlikar model. Inoue and
Monde [8] reported pool boiling on a horizontal platinum wire
(d=0.30mm, L=88.0mm, heated by direct electric current) in
non-azeotropic binary mixtures of R12/R113, R22/R113,
R22/R11, R134a/R113 at a pressure of 0.4MPa and heat flux
from 40 to 100kW/m2 . The properties of each mixture were
calculated with BWR method. The details of the experimental
conditions are given in Table 2.
3.2 Flow Boiling
The experimental data of Zhang et al. [9], Shin et al. [10],
Kattan et al. [11], and Yoshida et al. [7] were employed to
compare with the Kandlikar correlation. For the Zhang et al.’s
data, which is obtained from four horizontal smooth stainless
steel tubes with i.d. of 6.0 mm, o.d. of 7.0 mm and length of
1000 mm. The total length of the evaporator was 4000mm.
The evaporator tubes were heated by applying d.c. voltage
across the tube. The measurement accuracy of thermocouples,
refrigerant flow rate and pressure gauge were 0.1K, 0.25% and
Figures 1 (a), (b), (c) and (d) show a comparison of the
experimental data of Inoue and Monde [8] for the mixture of
R12/R113, R134a/R113, R22/R11, R22/R113 with the
Kandlikar model and empirical correlations of Fujita et al. [13]
and Inoue and Monde [8]. The empirical correlation of Inoue
and Monde [8] looks very well over the entire range for all of
the heat flux and the mixture. The empirical correlation of
Fujita et al. [13] is also good especially for the mixture
R22/R11. For the Kandlikar model, it is reasonably well
especially for the low concentration of each mixture, but
overpredicts in the rest of the range. One of the main reasons
for this result is believed to be due to the differences in
saturation temperatures as calculated from different
calculation method for thermophysical properties.
The
differences are quite significant, shown in Table 4, and are
believed to cause large errors in heat transfer coefficient. It is
recommended that the same programs be used for data
reduction and prediction methods.
4.2 Flow Boiling
Pure Refrigerant . Figures 2 (a) and (b) show a comparison
between the data set obtained by Shin et al. [8] for pure R22
using an electrically heated stainless steel test section and
3
Table 3 Details of flow boiling data sets used for comparison with the Kandlikar correlation.
Source
(year)
Refrigerant Pressure Temperature Tube I.D.
System
kPa
K
mm
R32
Zhang et al. R125
293.15
6.0
[9]
R134a
R32/R134a
R22
R32
R134a
Shin et al R290
289.15
7.7
[10]
R600a
R32/R134a
R290/R600a
R32/R125
Kattan et al.
R502
619
12
[11]
Yoshida et R32/R12
550
6.34
al. [7]
R32/R134a
940
Mass
Fraction
Quality
Heat Flux
(kW/m2)
Mass Flux
(kg/m2s)
0.3
0~1
10~20
150~400
0~1
0~1
10~30
40~100
0~1
8~10
102-318
0~1
10~30
100-500
0~1
Heat Transfer Coefficient a (W/m 2 K )
10000
8000
Kandlikar [1]
q=100kW/m 2
Inoue & Monde [8]
q=70kW/m 2
Kandlikar [1]
[1]
Kandlikar
Inoue &
& Monde
Monde [8]
[8]
Inoue
q=100kW/m 22
q=100kW/m
q=70kW/m22
q=70kW/m
Fujita et al. [13]
q=40kW/m 2
Fujita et
et al.
al. [13]
[13]
Fujita
q=40kW/m22
q=40kW/m
q=100kW/m 2
q=100kW/m 2
6000
R12/R113
q=70kW/m 2
q=70kW/m 2
R134a/R113
q=40kW/m 2
q=40kW/m 2
4000
2000
(b)
(a)
0
Heat Transfer Coefficient a
(W/m 2 K )
12000
10000
Kandlikar [1]
q=100kW/m 2
Kandlikar [1]
q=100kW/m 2
Inoue & Monde [8]
q=70kW/m 2
Inoue & Monde [8]
q=70kW/m 2
Fujita et al. [13]
q=40kW/m 2
Fujita et al. [13]
q=40kW/m 2
8000
q=100kW/m 2
6000
R22/R11
q=100kW/m 2
q=70kW/m 2
q=70kW/m 2
q=40kW/m 2
q=40kW/m 2
R22/R113
4000
2000
(c)
(d)
0
0
0.2
0.4
0.6
0.8
Mass Fraction x
1
0
0.2
0.4
0.6
0.8
1
Mass Fraction x
Fig.1: The Kandlikar correlation compared with the experimental data of Inoue and Monde [8].
Kandlikar correlation. In this case the FFl =1.0 applies for
stainless steel tubes. The agreement between the Kandlikar
correlation and the data is good, with the mean absolute error
seen from Table 5 as only 5.5 percent for the entire data set.
Figure 3 shows a comparison of the same experimental data of
Shin et al. for five refrigerants, R22, R32, R134a, R290 and
4
Heat Transfer Coefficient a ( W / m2K )
10000
Shin et al. [10]
R22
8000
Shin et al.( [10]
R22
(a)
G=742 k g/m 2s
Te =12 oC
6000
q=25kW/m 2
T e=12?
q kW/m
30
25
18
10
4000
2000
(b)
2
Kandlikar [4]
G kg/m 2s
424
583
742
Kandlikar [4]
0
0
0.2
0.4
0.6
0.8
Quality
1
0
0.2
0.4
0.6
0.8
1
Quality
Fig. 2: The Kandlikar correlation compared with the experimental data of Shin et al. [10]
with different heat flux and different mass flux, respectively.
Table 4 Saturation temperatures of Refrigerant Mixtures
calculated from the different program at 400 kPa.
Binary
Mixture
R12/R113
R22/R113
R22/R11
Mass
Fraction
0.1
0.5
0.1
0.5
0.1
0.5
0.1
0.5
T s From
REFPROP[3]
339.06K
296.66K
315.30K
276.55K
308.91K
276.46K
315.27K
287.75K
T s From Inoue
& Monde [8]
347.00K
301.68K
332.25K
282.01K
321.65K
282.61K
342.19K
298.05K
mean error for each data is seen from Table 5 to be 5.5, 2.5,
5.4, 15.7 and 24.2 percent respectively. Figure 4 shows the
data of Zhang et al. [9] for pure refrigerant s R32, R134a and
R125, which were obtained in smooth, electrically heated ,
horizontal stainless steel tubes with an i.d. of 6.0 mm (for
stainless steel tubes, F Fl is 1.0). The Kandlikar correlation
predicts the experimental data very well for these sets as well.
The mean error for each data is 6.8, 11.4 and 26.3 percent
respectively. For R125, the mean error is rather large , and a reevaluation of the F FL is suggested.
Binary Mixture. Region I: Near -Azeotropic region. In this
region, the compositions of the two phases are nearly equal.
The data of Shin et al. [10], Yoshida et al. [7] and Kattan et al.
[11] for azeotropic mixtures of R32/R134a with a mass
fraction of 0.75 of R32, R32/R125
with a mass fraction of 0.50, and
Table 5 Parameter ranges of data sources and comparison with correlation.
R502 which is an azeotrope of
R22/R115 with a mass fraction of
Refrig.
Mean Abs.
0.448 of R22 respectively, are used.
Data Source
Bo
V1
Region
System
Deviation, %
The volatility parameter is very small
in this region. F or the data sets
R22
7.0-36.8
5.51
considered, it ranges between
R32
17.4-23.9
2.49
0.00058 and 0.017. Figure 5 shows a
R134a
27.2-37.4
5.41
comparison between the Kandlikar
R290
19.8
15.72
Shin et al.
correlation and the experimental data
R600a
20.6
24.24
[10]
by Yoshida et al. [7] with the mixture
R32/R125
23.8
I
17.03
of R32/R125 which obtained from
R32/R134a
17.19
0.017
I
16.33
electrically heated horizontal smooth
R32/R134a
18.46-20.77 0.044-0.072
II
20.17
copper tube for which FFL=1.15. As
R290/R600 19.89-20.12 0.055-0.108
III
13.83
seen from Figure 5, the Kandlikar
a
R32
14.2
6.83
correlation is able to predict the
Zhang et al.
R134a
21.9
11.37
experimental
data
very
well
[9]
R125
34.6
26.32
especially for the lower mass flux and
R32/R134a
16.3
0.065
II
0.64
heat flux. For higher mass flux and
Kattan et al.
R502
19.5
I
19.97
heat flux at high quality the error
[11]
increases, but the mean absolute error
Yoshida et al. R32/R125
44.46
0.00054
I
9.64
from Table 5 is seen to be only 9.64
[7]
R32/R134a
37.27
0.072
II
7.53
percent . Figure 6 shows experimental
R134a/
R113
R600a. For each data, the Kandlikar correlation is able to
represent them quite well and the trends in heat transfer
coefficient versus quality are also accurately represented. The
data of Shin et al. [10] with
R32/R125
(50/50
wt%)
R32/R134a (75/25 wt%) mixtures comparing with
Kandlikar correlation. For the mixture of R32/R134a,
agreement between the Kandlikar correlation and
the
and
the
the
the
5
10000
Heat Transfer Coefficient a (W/m 2 K)
Heat Transfer Coefficient a (W/m 2 K)
12000
Shin et al. [10]
G=424kg/m 2 s
q=30kW/m 2
10000
T e=12 ?
8000
6000
Kandlikar [4]
R22
4000
R32
R134a
2000
R290
R600a
0.2
0.4
Quality
0.6
0.8
4000
2000
0
10000
8000
k W / m2
100
100
200
200
300
200
500
300
Yoshita et al. [7]
R32/R125(50/50) wt%)
[2]
6000
4000
2000
0
0
0.2
0.4
0.6
0.8
1
Quality
Heat Transfer Coefficient a (W/m 2 K)
4000
G k g / m2 s K a n d l i k a r [ 2 ]
318
3000
200
2500
102
2000
1500
Kattan et al. [11]
1000
R502
Psat=619kPa
500
q = 8 ~ 1 0 k W / m2
0
0
0.2
0.4
0.6
0.4
0.6
0.8
1
14000
Shin et al. [10]
12000
G = 5 8 3 k g / m2 s
Ts=12 ?
10000
q = 3 0 k W / m2
8000
6000
4000
Kandlikar [2]
R32/R125(50/50wt%)
2000
R32/R134a(75/25wt%)
0
0
0.2
0.4
0.6
0.8
1
Quality
Fig. 5: The Kandlikar correlation compared with the
experimental data of Yoshida et al. [7].
3500
0.2
Quality
Heat Transfer Coefficient a (W/m 2 K)
Heat Transfer Coefficient a (W/m 2 K)
k g / m2 s
12000
Kandlikar
0
Fig. 4: The Kandlikar correlation compared with the
experimental data of Zhang et al. [9].
14000
q
R134a
R125
Ts=20 ?
1
Fig. 3: The Kandlikar correlation compared with the
experimental data of Shin et al. [10].
G
R32
6000
0
0
Kandlikar [4]
Zhang et al. [9]
q=10kW/m2
G=250kg/m2s
8000
0.8
1
Quality
Fig. 7: Comparison of the Kandlikar correlation with the
experimental data of Kattan et al. [11].
experimental data is good. For the mixture of R32/R125 at
intermediate qualities, the Kandlikar model can correlate the
experimental data very good, but it is not in good agreement at
Fig. 6: The Kandlikar correlation compared with the
experimental data of Shin et al. [10].
the lower quality. In this region, the nucleate boiling term is
important and the uncertainties in estimating F FL have
significant impact on predictive ability. The correlation is
valid up to a quality of approximately 0.8, beyond which the
local dryout characteristics affect the heat transfer. Figure 7
shows a comparison of the Kandlikar correlation with the
experimental data of Kattan et al. [11], which used water
heated horizontal copper tube as the test section, with
FFL=1.59 for the mixture. From Kattan et al. paper, the heat
flux for each data point is not reported and an average value of
heat flux for entire data is employed in calculations using the
Kandlikar correlation. From Fig. 7, the Kandlikar correlation
is able to predict the data with a mean absolute error of 19.97
percent.
Region II: Moderate Diffusion-Induced Suppression
Region. Here the nucleate boiling dominant region (NBD) is
not present, and the heat transfer is mainly in the CBD region.
However, the diffusion -induced suppression is moderate, and
does not affect the nucleate boiling term in the expression of
heat transfer coefficient in the CBD region. The volatility
parameter is in the range of 0.03<V1<0.2 with Bo>1E-4. The
data of Yoshida et al. [7], Zhang et al. [9] and Shin et al. [10]
were employed to compare with the Kandlikar correlation in
this region. Figure 8 shows the experimental data of Yoshida
6
4000
G
14000
q
kg/m2 s k W / m2
12000
10000
100
10
300
20
500
30
Heat Transfer Coefficient a (W/m 2 K)
Heat Transfer Coefficient a (W/m 2 K)
16000
Kandlikar
Yosita et al. [7]
[2]
R32/R134a
(30/70, wt%)
8000
6000
4000
2000
0
0
0.2
0.4
0.6
0.8
3000
R32/R134a(30/70wt%)
2000
Kandlikar [2]
Zhang et al. [9]
1000
q=10 kW/m 2
G=250 kg/m 2 s
Ts=20 ?
0
1
0
0.2
Quality
Shin et al. [10]
G=583kg/m 2 s
T s =12?
6000
q=30kW/m 2
5000
4000
3000
R32/R134a(wt%)
2000
Kandlikar [2]
50/50
1000
25/75
0
0
0.2
0.4
0.8
1
0.6
Fig. 9: Comparison of the Kandlikar correlation with the
experimental data of Z hang et al. [9].
Heat Transfer Coefficient a (W/m 2 K)
Heat Tranfer Coefficient a (W/m 2 K)
9000
7000
0.6
Quality
Fig. 8: Comparison of the Kandlikar correlation with
the experimental data of Yoshida et al. [7].
8000
0.4
0.8
10000
Shin et al. [10]
G = 4 2 4 k g / m2 s
8000
q = 3 0 k W / m2
T =12?
e
6000
4000
R290/R600a(wt%)
2000
50/50
20/75
0
0
et al. [7] with R32/R134a at three different conditions. For this
case F Fl is 1.501 as calculated from Eq. (24). As seen from Fig.
8, the Kandlikar correlation does an excellent job in predicting
the heat transfer coefficient for q=10 and 20 kW/m 2, and
represents the trend well for q=30 kW/m 2 within ten percent
deviation. The absolute mean error is seen from Table 5 to be
only 7.53 percent for the entire data set.
Figure 9 shows the data of Zhang et al. [9] using the
stainless steel tube with the same mixture of R32/R134a, for
which F Fl=1.0 applies. As seen from the figure, the Kandlikar
correlation works very well. The mean absolute error is only
0.64 percent in the entire data set. The experimental data of
Shin et al. [10] from the stainless steel tube heated by directly
current are shown in Fig. 10. The mean absolute error
compared with the Kandlikar correlation is 20.17 percent as
seen from Table 5.
Region III: Severe Diffusion-Induced Suppression. In this
region, the nucleate boiling mechanism is strongly affected by
the mass diffusion effects, and the nucleate boiling component
in the CBD region is suppressed considerably. The
experimental data of Shin et al. [10] with R290/R600a fall in
this region. A comparison with the Kandlikar correlation is
shown in Fig. 11. As seen from this figure, the Kandlikar
correlation represents this data set well and the trends in α
0.2
0.4
0.6
0.8
Quality
Quality
Fig. 10: Comparison of the Kandlikar correlation with the
experimental data of Shin et al. [10] .
Kandlikar [2]
75/25
Fig. 11: Comparison of the Kandlikar correlation with
the experimental data of Shin et al. [10] .
versus x are also accurately represented. The mean absolute
error is only 13.8 percent for the entire data set.
5. CONCLUSIONS
In this study, the Kandlikar model is tested with pool boiling
and flow boiling data presented in literature. Based on the
comparison, the following conclusions are drawn:
a) Pool Boiling
Comparing with the experimental data of the Inoue and
Monde [8], the Kandlikar correlation can predict them
reasonably well. However, the accuracy in estimating the
saturation temperature is critical. It is suggested that the same
property prediction program should be used in predicting the
heat transfer as that used in reducing t he experimental data.
b) Flow Boiling
The Kandlikar correlation is compared with the experimental
data for six pure refrigerants and for four binary mixture s
reported in the literature. For these data sets, the Kandlikar
correlation can predict them well with an average absolute
mean deviation of l2.8 percent.
7
NOMENCLATURE
Bo : boiling number, q /(G∆h LG )
Co : convection number, ( ρG / ρ L )0 .5 ((1 − x ) / x )0.8
c p : specific heat, J/kg K
D : diameter, m
D12 : diffusion coefficient of component 1 in mixture
of 1 and 2, m 2/s
f : friction factor
FFL : fluid-surface parameter
FD :diffusion factor, given by Eq. (2)
G : mass flux, kg/m2s
g : (x 1 − x 2 ) ( y1, s − x 1,s )
∆ hLG : latent heat of vaporization, J/kg
Jao : modified Jakob number,
−1
1/2

TW − TL, sat  ∆hLG  κ  dT


=
+ 
(x1 − y1 )
ρV / ρL  c p , L  D12  dx1



M : molecular weight, kg/kmol
Nu : Nusselt number
P : pressure, Pa
Pr : Prandtl number
2
q : heat flux, W/m
Re : Reynolds number
T : temperature, K
∆ Tbp : boiling point range, difference between the dew point
and bubble point temperatures, K
∆Tid : wall superheat for ideal mixture as defined by earlier
investigators, K
∆Ts = Ts − Tsat , K
∆T1 , ∆T2 : wall superheats for components 1 and 2
in pool boiling, K
V1 : volatility parameter, defined by Eq. (5)
v: molar specific volume, m3 /kg-mol
x : quality
x1 , x2 : mass fraction of components 1 and 2 in liquid phase
~
x1 , ~
x2 : mole fraction of components 1 and 2 in liquid phase
y1 , y 2 : mass fraction of components 1 and 2 in vapor phase
~
y1 , ~
y 2 : mole fraction of components 1 and 2 in vapor phase
Greek symbols:
α : heat transfer coefficient, W/m 2K
η : viscosity, kg/m s
κ : thermal diffusivity, m2 /s
λ : thermal conductivity, W/m K
φ : association factor, defined in Eq. (7)
3
υ m,1 : molar specific volume of component 1, m /mol
id: ideal
L: liquid
LO: all liquid
m: mixture
NBD: nucleate boiling dominant
PB: pool boiling
PSC: pseudo-single component
s: liquid-vapor interface of a bubble
sat: saturation
TP: two-phase
REFERENCES
1. S.G. Kandlikar, Boiling Heat Transfer with Binary
Mixtures: Part I – A Theoretical Model for Pool Boiling,
ASME Journal of Heat Transfer, Vol. 120, pp. 380-387,
May 1998.
2. S.G. Kandlikar, Boiling Heat Transfer with Binary
Mixtures: Part II – Flow Boiling in Plain Tubes, ASME
Journal of Heat Transfer, Vol. 120 pp. 388-394, May 1998.
3. NIST, REFPROP, Ver.4.0, National Institute for Science
and Technology, Washington, DC, 1995.
4. S.G. Kandlikar, A General Correlation for Two-phase
Flow Boiling Heat Transfer Coefficient Inside Horizontal
and Vertical Tubes, J. Heat Transfer, Vol.102, pp.219-228,
1990.
5. B.S. Petukhov, Heat Transfer and Friction in Turbulent
Flow with Variable Physical Properties, Advances in Heat
Transfer, J.P. Hartnett and T.F. Irvine, Jr., eds., Vol.6,
Academic Press, New York, pp.503-564, 1970.
6. V.Gnielinski, New Equations for Heat and Mass Transfer
in Turbulent Pipe and Channel Flow, Int. Chem. Eng.,
Vol.1, No.2, pp.41-46, 1976.
7. Yoshida et al., Personal communications, 19 94.
8. T. Inoue, and M. Monde, Nucleate Pool Boiling Heat
Transfer in Binary Mixtures, Warme und stoffubertragung,
Vol.29, pp.171-180, 1994.
9. L. Zhang, E. Hihara, T. Saito, and J.T. Oh, Boiling Heat
Transfer of a Ternary Refrigerant Mixture Inside a
Horizontal Smooth tube, Int. J. Heat Mass Transfer, Vol.
40. No. 9. Pp. 2009-2017, 1997.
10. J.Y. Shin, M.S. Kim, and S.T. Ro, Experimental Study on
Forced Convective Boiling Heat Transfer of Pure
Refrigerants and Refrigerant Mixture in a Horizontal Tube,
Int. J. Refrig. Vol. 20, No. 4, pp. 267-275, 1997.
11. N. Kattan, J.R. Thome and D. Favrat, Flow Boiling in
Horizontal Tubes: Part 2-New Heat Transfer Data for Five
Refrigerants, Transactions of the ASME. 148, Vol. 120,
February, 1998.
12. NIST, REFPROP, Ver.3.04a, National Institute for
Science and Technology, Washington, DC, 1992.
13. Y. Fujita and M. Tsutsui, Heat Transfer in Nucleate Pool
Boiling of Binary Mixtures, Int. J. Heat Mass Transfer,
Vol. 37, pp.291-302, 1994.
3
ρ : density, kg/m
σ : surface tension, N/m
Subscripts
avg: average
B: binary
CBD: convective boiling dominant
D: mass diffusion
G: vapor
8