International Journal of Heat and Mass
Transfer 64 (2013) 591 -608

Flow boiling heat transfer of HFO1234yf and HFC32 refrigerant mixturesin a smooth horizontal tube: Part II. Prediction methodaMinxia Lia, Chaobin Dangb*, Eiji Hiharab
Key Laboratory of Medium-Low Temperature Energy Efficient Utilization, Ministry of Education, Departmentof Thermal Engineering, Tianjin University, Tianjin, Chinab
Institute of Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa-shi, Chiba, Japan

Abstract: A prediction model has been developed using the results of prior experimental
investigations into the flow boiling heat transfer of pure HFO1234yf, HFC32, and their refrigerant
mixtures at two mass fractions (80/20 and 50/50 by mass%) in a smooth horizontal tube having an
inner diameter of 2 mm. In the prior experiment, the saturation temperature was 15 °C, the mass fluxes
ranged from 100 to 400 kg/m2s, and the heat fluxes ranged from 6 to 24 kW/m2. In this paper, we
propose a new semi-empirical correlation for pure refrigerants based on the superposition of thecontributions from nucleate boiling and convection. We introduced two new factors in the correlationto account for the effects of the convection on two-phase flow and nucleate boiling. Comparisons
between the experimental results and the predictions of seven correlations showed that the proposedcorrelation had reasonable agreement with the magnitudes and trends of the variations in the measured
heat transfer coefficient of pure HFO1234yf, HFC32, and the 50/50 mass% mixture (with a mean
absolute error of approximately 20%) when the average properties of the mixtures were used.
However, this simple approach was found to overestimate the experimental results for the 80/20
mass% mixture. The inhomogeneity of the concentration in the mixture significantly affects its heattransfer with a high temperature glide; the predicted deviation was large when only the average
properties of the mixture are considered. After taking into consideration the effects of mass diffusionon the flow boiling heat transfer of refrigerant mixtures, we introduced suppression factors for the
mixture into both the existing and proposed correlations. Superior prediction accuracies were obtainedusing these modified correlations. When predicting the heat transfer coefficients of the refrigerant
mixtures of HFO1234yf and HFC32 (80/20 and 50/50 by mass%), the average deviation of the
proposed correlation with suppression factors was less than 20%.
Keywords: HFO1234yf; HFC32; Refrigerant mixture; Flow boiling heat transfer; Prediction model;
low GWP refrigerant

NOMENCLATURE
A
ac
Bo
cpl
C
d,D
Dm
F
Fr
G
h
k
m
mf
n
p
pcr
pr
*

correcting factor
thermal diffusion factor, m2/s
boiling number,/specific heat at constant pressure in liquid phase, J/kgK
correcting factor
inner diameter, mmass diffusion factor, m2/s
convective enhancement factor
Froude number,/mass flux, kg/m2s
boiling heat transfer coefficient, W/m2K
Boltzmann’s constantmass, molmass flow rate, kg/s
particle number density of fluidpressure, Pa
critical pressure, Pa
reduced pressure /Corresponding author. dangcb@k.u-tokyo.ac.jp

Prandtl number, Pr/
heat flux, W/m2
diameter of bubble, mReynolds number, Re/
suppression factor
temperature, K
inner-wall temperature, K
fluid saturation temperature, K
Weber number,/vapor quality
mole fraction of volatile component in liquid phase
X, XttLockhart–Martinelli parameterymole fraction of volatile component in vapor phasez
coordinate along tube direction, mZ
compressibility factor
Δhv, hlv latent heat, J/kg
ΔT
superheat, K
ΔTI
ideal superheat, KΔTbp
temperature difference between dew point and bubble point, K
ΔTE
maximum rise in local bubble point temperature, K
Greek symbols

thermal conductivity, W/mKviscosity, Pasdensity, kg/m3

surface tension, N/m
idiameter of species i, mФ
two-phase flow multiplierγ
activity coefficientηpacking fraction
εvoid fraction
Subscriptsbbubbleb0liquid feed to a reboilerbivapor leaving a reboiler
bk
bulk
cal
calculated
CS
Carnahan–Starling equation of statecv
convective boilingexp
experimental
I, id
ideal
in
interfaceintliquid–vapor interfacekinkinetic
L, lliquid phasel0
all flow as liquid phasemmix, mixturenb
nucleate boilingPpressure
PY
Percus–Yevick virial equationT
temperaturetp
two-phasev
gas phase, vapor phasev0
all flow as vapor phase1
component 1

Pr
q
R
Re
S
T
Twall
Tsat
We
x

2
component 2
Superscripts
Ens
Enskog transport equation

1 INTRODUCTION
The refrigerants used in refrigeration systems typically have measurable environmental effects
including the ozone depletion potential (ODP) and global warming potential (GWP). Today, eitherhydrofluorocarbons (HFCs) with high GWP values or hydrochlorofluorocarbons (HCFCs) with small
ODP values are used in stationary air conditioners. Hence, it is crucial to replace these refrigerants
with low GWP variants. HFO1234yf, a newly developed refrigerant with a low GWP of 4, has been
proposed as a drop-in solution for current automotive air conditioners [1]. However, HFO1234yf has
smaller latent heat than HFC410A. When it is substituted directly into a stationary air conditioner, thecoefficient of performance (COP) of the system decreases significantly. The COP might be improvedby combining a highly efficient refrigerant, such as HFC32, with a low GWP refrigerant. Hence, arefrigerant mixture of HFO1234yf and HFC32 was considered, and experimental measurements wereconducted to clarify its flow boiling heat transfer characteristics. The results were reported in Part I of
this paper [2]. The experiments were performed at an evaporation temperature of 15 °C, refrigerant
mass flux within a range from 100 to 400 kg/m2s, and heat flux of 6–24 kW/m2. The heat transfer
coefficient of the HFO1234yf + HFC32 refrigerant mixture (80/20 by mass%) was 20%–50% lower
than that of pure HFC32 and 10%–30% lower than that of HFO1234yf. When the concentration of
HFC32 was increased to 50%, the heat transfer coefficient of the mixture became 10%–20% higher
than that of pure HFO1234yf but was still 20%–40% lower than that of HFC32.
In this paper, the experimental heat transfer coefficients determined in Part I are compared withthe predicted results obtained using some prediction models from the literature. Further, a newcorrelation is proposed to predict the heat transfer coefficients of pure HFC32, HFO1234yf, and two
HFO1234yf + HFC32 mixtures (80/20 and 50/50 by mass%). Because the mechanisms of flow boilingheat transfer in the pre-dryout region are different from those in the post-dryout region, the predictionof heat transfer coefficients described in this paper focuses mainly on the pre-dryout region.

2 SURVEY OF LITERATURE ON FLOW BOILING HEAT TRANSFER
For the flow boiling of pure refrigerants, the most widely accepted heat transfer model is that ofChen’s correlation [3], in which the heat transfer coefficient of a two-phase flow, htp, is a linear
superposition of the coefficients of nucleate boiling (hnb) and convective heat transfer (hcv).
(1)
htp   Shnb  Fhcv 
In Chen’s original correlation, hnb and hcv were calculated using the correlation proposed by Forster
and Zuber [4] and the Dittus–Boelter equation, respectively. Chen also defined a suppression factor S
as a function of the Reynolds number to account for the suppression of the nucleate boiling heattransfer by the effects of convection. The factor F, which is defined to account for the ratio of thetwo-phase Reynolds number to the liquid-phase Reynolds number, was introduced to revise hcv.
Subsequently, Chen and Tuzla [5] experimentally investigated the contributions of convection andboiling to saturated convective flow boiling. Their results indicate that, in comparison withsingle-phase flow, two-phase flow enhances the convection heat transfer and suppresses the nucleateboiling heat transfer. Many researchers have adopted the superposition formula proposed by Chen,
after modifications to the factors F and S in accordance with their own experimental results.
For example, the Gungor–Winterton correlation [6], given by Eq. (2), is a modification of theChen correlation:(2)
htp   Shnb  Ehcv 
where E is an enhancement factor for the convection defined by Gungor and Winterton. The nucleateboiling heat transfer coefficient is calculated from the pool boiling correlation of Cooper [7]. Further,
the convective heat transfer coefficient is based on the Dittus–Boelter correlation. Yoshida et al. [8]and Zhang et al. [9] both applied the Dittus–Boelter convective heat transfer correlation and thenucleate boiling correlation of Stephan and Abdelsalam [10] using their own proposed S factors.
In addition to models applying linear superposition, a model comprising a general power law has
also been proposed and widely used :nhtp   hnb
 hcvn 

1n(3)

where the exponent n is an empirical constant. Kutateladze [11] suggested using n = 2, whereas
Steiner and Taborek [12] proposed power law models using n = 3.
In contrast to the superposition model that simultaneously considers the contributions of nucleateboiling, convective heat transfer, and their interactions, Shah [13] proposed the use of the maximum of
the two values. In the Shah correlation, a dimensionless parameter N is introduced as a threshold. For
different N values, various correlations are proposed to calculate the values of the nucleate boiling andconvective coefficients. Subsequently, the higher value is chosen as the heat transfer coefficient of thetwo-phase fluid, as expressed in Eq. (4):(4)
htp  max  hnb , hcv Kandlikar [14] proposed a correlation similar to that of Shah in which hnb and hcb were revised on thebasis of the single-phase convection correlation of Gnielinski [15]. In this correlation, similar to that of
Shah [13], the convection number (Co), boiling number (Bo), and Froude number (Fr) are used torepresent the convection and nucleate boiling parts.
Although there have been numerous studies of flow boiling prediction models for different
refrigerants at different tube scales, it is very difficult to obtain a universal prediction model that canbe applied to all the refrigerants because the flow boiling heat transfer characteristics are related toboth the thermophysical properties of the refrigerant and the flow pattern. Saitoh et al. [16] measured
the flow boiling heat transfer characteristics of HFO1234yf in a horizontal tube with inner diameter(ID) 2 mm and used a proposed Chen-type correlation by Saitoh et al. [17] that can be applied to
low-pressure refrigerants like R134a. However, this correlation is not applicable to HFC32. Shin et al.
[18] investigated the flow boiling heat transfer coefficient of several pure refrigerants and mixtures
including pure HFC32 and HFC134a in a horizontal tube with ID 7.7 mm. They used a correlation
proposed by Gungor and Winterton [19] to predict the heat transfer coefficient of these fluids. The
average deviations of their prediction are 18.3% for HFC32 and 47.5% for HFC134a.
It is more difficult to predict the heat transfer coefficient of a refrigerant mixture than that of apure refrigerant. For non-azeotropic refrigerant mixtures, which are the most commonly encountered,
the saturation temperature increases during the evaporation process while decreases during thecondensation process because each component has a different boiling point. The difference in thesaturation temperature between the start and end points of the evaporation or condensation process at aconstant pressure is called the temperature glide. Figure 1 shows an example of the temperature glides
of HFO1234yf + HFC32 and R134a + HFC32 against the HFC32 mass fraction under the pressure atwhich the saturation temperature is 15 °C at a vapor quality of 0.5. Based on the measurement ofKamiaka et al. [20], the maximum temperature glides of HFO1234yf + HFC32 and R134a + HFC32
are 7.7 °C at a 22% mass fraction of HFC32 and approximately 6.1 °C at a 32% mass fraction of
HFC32, respectively.
Previous analyses of the boiling heat transfers of non-azeotropic refrigerant mixtures have shownthat the mass diffusion resistance of the mixture, which is the result of different boiling points, has asignificant influence on the heat transfer. Figure 2 shows a schematic drawing of the mass diffusion
when a bubble is generated in a binary mixture. A diffusion layer forms around the bubble because thecomponents in the mixture have different boiling points, and the temperature and fraction of the
mixture in the diffusion layer are different from those of the liquid bulk and saturation vapor. Scriven[21] developed the first analytical model for the bubble growth based on the energy balance and massbalance in a binary mixture. According to Scriven’s model, the rate of bubble growth in a binary
mixture is delayed due to the mass diffusion resistance. Van Stralen [22] proposed a model for aspherical bubble growing inside a binary liquid mixture which assumes that the composition gradientin the liquid surrounding the bubble retards the bubble growth. Van Wijk et al. [23] concluded that theeffective superheat of a bubble growing in a binary mixture is less than that of a pure fluid with thesame properties, because the saturation temperature at the bubble interface increases due to theaccumulation of less-volatile components around the bubble.
For non-azeotropic mixtures, the typical approach for constructing predictive models is to modify
the heat transfer correlation of pure fluids by considering the mass diffusion resistance. The massdiffusion resistance influences bubble growth related to the superheating of the liquid. Stephan and| of theKorner [24] noted that the maximum temperature difference occurs at the maximum |mixture, whereandare the mole fraction of volatile components in the vapor and liquid phase,respectively. They defined a real wall superheat ΔT that is the sum of the ideal superheat ΔTI and theexcess superheat ΔTE, as expressed in Eq. (5). Factor A is a function of the type of mixture and isdetermined by Eq. (6). Note that the recommended A0 value for acetone and ethanol is 0.75, whereasthat of ethanol and benzene is 1.18. A value of 1.53 for A0 is suggested if the composition of the
mixture is unknown.
(5) T   TI   T E  x1  T1  x 2  T2  A | y  x |  TI

A  A0  0.88  0.12  p 101325  

(6)

where ∆ is the difference between the wall temperature and the saturation temperature ofcomponent i (i = 1, 2) .
For predicting variations in the wall superheat based on the composition, Calus andLeonidopoulos [25] suggested an analytical expression
1/ 2
 a c   c pl   dT   T   x1  T1  x 2  T2  1   y  x  
 



 D m    hv   d x  

(7)

where Dm is the mass diffusion coefficient, ac is the thermal diffusion factor, cpl is the specific heat at a/is the slope of the bubble
constant pressure in the liquid phase, Δhv is the latent heat, andpoint line.
Thome and Shock [26] postulated that the maximum rise in the local bubble temperature is equal
to the temperature difference between the dew point and bubble point with the liquid feed composition.
The heat transfer coefficient for the pool boiling of the mixture, h, is expressed as follows:h  TI TIhI  T TI   Tbp(8)

where hI is the ideal heat transfer coefficient defined as hI  1   x1 h1    x 2 h2   .
The Chen correlation [3] is one of the most commonly adopted models for predicting the flow
boiling heat transfer coefficients of pure refrigerants, and it also has been suggested as the basic
method for mixtures if suitable corrections are applied. Based on this approach, Bennet and Chen [27]proposed the following correlation for mixtures and compared its predictions with the available data
for ethylene glycol and water:(9)htp  hml Fmix  hmnb S mix
They postulated that the heat transfer coefficient during nucleate boiling is related to the effective
liquid superheat expressed by the Scriven equation [21]. Therefore, the suppression factor is expressedby the following equation:
0.5
 Tmix dT   c pl   a c  
S mix  S
 S 1   y  x  

 

 TI
 dx    hv   D m  


1

(10)

Jung et al. [28] studied azeotropic CFC12 + HFC152a refrigerant mixtures and compared theresults with the data obtained for non-azeotropic HCFC22 + CFC114 mixtures. They proposedcorrelations based on the Chen correlation [3] and considered the mixture effects using only the phaseequilibrium data. The mean deviations for the pure and mixed refrigerants were 7.2% and 9.6%,
respectively. Zhang et al. [9] studied the flow boiling heat transfer coefficients of ternary mixtures(HFC32 + HFC125 + HFC134a) and modified the Yoshida et al. [8] correlation by adding correction
factors to represent both nucleate boiling and forced convection. Mishra et al. [29] correlated theirexperimental data for R12 + R22 and reported coefficients for two different compositions as well as
the revised factors for those mixtures. Bivens and Yokozeki [30] suggested a modification of both theJung correlation [28] and the Wattelet correlation [31] to account for the mass transfer resistances of
HFC32 + CFC12, HFC32 + HFC125, and HFC32 + HFC125 + HFC134a.

3

EXPERIMENTAL PROCEDURE

The test facility has been described in detail in Part I of this paper [2]. A pump cycle was used tomeasure the heat transfer coefficients of both the pure refrigerants and the refrigerant mixtures. The
test section was a stainless steel tube with an inner diameter of 2 mm and wall thickness of 0.5 mm.
The heat input for evaporation was provided by the Joule effect, and it can be assumed that the heat
flux is constant along the tube length. The purity of the refrigerant HFO1234yf was 99.7% and that of
HFC32 was 99.9%. HFO1234yf and HFC32 were mixed at the desired mass fraction in advance andcharged into the system as liquid. The concentration of the mixture in the test tube was calculated on
the basis of the fluid parameters measured at the inlet and outlet of the pre-heater using thePeng–Robinson-type equation of state proposed by Kamiaka et al. [20] and was confirmed using a gas
chromatograph. The saturation temperature of the mixture at the vapor quality of 0.5 was set as 15 °C
during the experiments. The local heat transfer coefficient hexp in the test tube was defined as

hexp 

q
Twall  Tsat(11)

where Twall is the temperature of the inner wall and Tsat is the saturation temperature of the mixture orpure refrigerant, as deduced from the measured local refrigerant pressure.
The experimental conditions are summarized in Table 1. The data for pure HFO1234yf weretaken from the measurements of Saitoh et al. [16]. The saturation vapor pressure of the mixture wasvery important for the saturation temperature, which is directly related to the temperature difference(T) in Eq. (11). The vapor–liquid equilibrium properties of the mixtures were acquired
using the Peng–Robinson-type state equation recommended by Kamiaka et al. [20]. The bubble anddew temperatures predicted by this new state equation agreed with the experimental results with ahigher accuracy than in the case of REFPROP 8.0 [32], as shown in Fig. 2. The other properties of the
HFO1234yf and HFC32 mixtures were obtained from the revised REFPROP 8.0 using the changed
Peng–Robinson-type state equation. The properties of the pure refrigerants were calculated using
REFPROP 8.0.

4 PREDICTION MODELS OF PRE-DRYOUT HEAT TRANSFER
Using the measurements in Part I [2], the variation in the heat transfer coefficients of the mixturesfrom the overall composition at similar vapor qualities was determined and is presented in Fig. 3. The
variation between the heat transfer coefficient and the HFC32 concentration is not linear. Shin et al.
[18] claimed that this is because of nonlinear variations in the thermophysical properties of a mixture,such as the viscosity, thermal conductivity, surface tension, density of the liquid and vapor phases, andother properties, with respect to the overall composition and mass transfer resistance at thevapor–liquid interface of a non-azeotropic mixture.
In this study, a prediction model for two pure refrigerants—HFO1234yf and HFC32—isdeveloped, as well as a correlation for the prediction of the refrigeration mixture.

4.1

Boiling Heat Transfer Coefficient vs. Lockhart–Martinelli Parameter

Typically, the flow boiling heat transfer in a tube is calculated as a superposition of the nucleateboiling heat transfer and the forced convective evaporation. At the region dominated by the forced
1⁄X∝,
convective evaporation, the flow boiling data can be correlated by the relation
where hl is the heat transfer coefficient for the liquid flow alone and X is the Lockhart–Martinelliparameter. The magnitude of the forced convective evaporation can thus be represented by gradient nof the linear regression applied to the experimental data. Figure 5 shows logarithmic plots of themeasured heat transfer coefficients against 1⁄X for HFC32, HFO1234yf, and HFO1234yf + HFC32(80/20 and 50/50 by mass%) in the pre-dryout region. Clearly, most of the data can be fitted to the⁄ ∝ 1⁄X
relation, where the exponent n lies between 0.55 and 0.75. It can also be seen in⁄ are similar for pure refrigerants or mixtures when the sets of theFig. 5 that the values ofmass flux and heat flux have the same proportional relationship. For example in the cases of a massflux of 400 kg/m2s and a heat flux of 12 kW/m2 and a mass flux of 200 kg/m2s and heat flux of 6
kW/m2. The Bo, as shown in Eq. (12), can depict the relative importance of nucleate boiling against
convective heat transfer in flow boiling heat transfer, and the interaction between them. At a high Bo,
nucleate boiling absolutely dominates the heat transfer, as in a case with a mass flux of 200 kg/m2s andheat flux of 24 kW/m2. Although it has the same Reynolds number as the case with a mass flux of 200⁄ value of the former is much higher than that of thekg/m2s and heat flux of 6 kW/m2, thelatter.

q
hlv G
4.2 Prediction of Heat Transfer Coefficient of Pure HFO1234yf and HFC32
4.2.1 Existing correlations for pure fluids
Bo 

(12)

Several correlations have been proposed to predict the heat transfer coefficients of pure
HFO1234yf and HFC32. The details of the correlations compared in this study are summarized in the
Appendix. Most of the correlations have adopted the form of Chen’s correlation, which includes twoparts: a nucleate boiling term and convective heat transfer term. The Dittus–Boelter correlation,
Eq. (A.3), generally has been accepted to calculate the convective heat transfer of a fluid. The
Stephan–Abdelsalam correlation [10], as expressed in Eq. (A.8), is used to calculate the nucleateboiling heat transfer coefficient. Based on the Dittus–Boelter correlation (Eq. (A.3)) and theStephan–Abdelsalam correlation (Eq. (A.8)), Yoshida et al. [8], Zhang et al. [9], and Saitoh et al. [17]predicted two-phase fluid evaporation heat transfer coefficients by introducing a new suppression
factor S and an enhancement factor F. Yoshida et al. suggested that the expression of S should include
not only the effect of local two-phase Reynolds number but also of the boiling number. Saitoh et al.
[16] used their correlation to predict the heat transfer coefficient of HFO1234yf and obtained highprediction accuracies. In their correlation, a Weber number was introduced into factor F to represent
the effects of small tube diameters on the heat transfer performance, as shown in Eq. (A.13). Gungor
and Winterton [19] developed a simplified correlation of the Chen form, as expressed in Eq. (A.18).
Except for the correlation of Gungor and Winterton, all the correlations use the functionnF  f  1 X tt   as the F factor. Shah’s correlation [13] is also a popular correlation to predict theheat transfer coefficients of refrigerants.
Figures 6 (a) and (b) show comparisons of the experimental results and the results predicted forpure HFO1234yf using the six abovementioned correlations. The experimental data for pure
HFO1234yf are best fitted by the correlations proposed by Saitoh et al., Shah, and Chen. Some of thedata predicted by the correlation of Yoshida et al. exceed the deviation limit of 20% but are still within
25%. The correlations of Zhang et al. [9] and Gunger and Winterton [19] slightly overestimate theexperimental results for pure HFO1234yf but the deviations are less than 35% on average. Figures 6 (c)and (d) show the comparison for pure HFC32. From the correlations of Yoshida et al. [8], Chen [3],Zhang et al. [9], and Gungor and Winterton [19], 80% of the experimental points are captured withdeviations in the range of ±20%. The tendencies of the results by Saitoh et al. and Shah are similar andthe deviations of most of the prediction data are greater than 20%. Figures 6 (b) and (d) show that theresults evaluated with the correlations of Gunger and Winterton [19] change slightly under different
conditions. Hence, the prediction tendency is different from that of the experimental data.

4.2.2 Model proposed for pure refrigerants
Based on the measured pre-dryout heat transfer coefficients for both pure refrigerants andrefrigerant mixtures, a new correlation is proposed following Chen’s correlation, as shown in Eq. (13).
The nucleate boiling heat transfer form is the correlation proposed by Cooper [7] because it can
predict the heat transfer coefficient of refrigerants with high accuracy. The forced convective heattransfer correlation, Eq. (15), is calculated using the Dittus–Boelter equation. In factor F, we applied
the similar correlation proposed by Saitoh et al. [17], in which a Weber number is introduced toconsider the effect of the surface tension on flow patterns at different tube diameters. Saitoh et al. [17]introduced the Weber number based on experimental data with an inner tube diameter from 0.51 to
10.92 mm; compared to that of gravity and inertia force, the effect of surface tension on a two-phaseflow becomes more significant as the tube diameter decreases. However, the correlation proposed by
Yoshida et al. [8] was based on experimental data with an inner tube diameter from 4.8 mm to 16.9mm, in which the effect of surface tension on flow pattern is negligible. Because this paper discusses
the flow boiling heat transfer characteristics at a relatively small tube diameter of 2 mm, it isreasonable to introduce the Weber number into our proposed factor F. The exponent n in factor F is
⁄ at ataken as 0.88, i.e., the same as the value recommended by Yoshida et al. [8]. In Fig. 5, thehigh vapor quality (large 1/Xtt) under various conditions can be unified. This means that when the1⁄Xconvective heat transfer dominates the whole heat transfer, the∝. The maximum
exponent n in Fig. 5 is 0.72, which is close to the value of 0.88 proposed by Yoshida et al. [8] but far
less than the value of 1.05 proposed by Saitoh et al. [17]. The exponent n is therefore set to be 0.88 tobe consistent with Yoshida’s correlation because Yoshida’s correlation was proposed under a wider
range of experimental conditions and using different refrigerants.
The Bo number is introduced into the function of S, similar to that of Yoshida et al. [8], because
experimental results indicate that some regulations of the heat transfer coefficient under various
conditions are related to the Bo number. In Yoshida’s correlation, both Retp and Xtt are used to reflect
the effect of the acceleration of the vapor on the boiling. However, Retp = RelF1.25, which also includes
Xtt. To simplify the correlation, the Xtt is not used explicitly, but only the Retp is applied in S to express
the influence of convective heat transfer on nucleate boiling by selected proper constants based on our
experimental results. These constants, therefore, are different from those in the factor S proposed by
Yoshida et al.
(13)
htp  Shnb  FhCV

hnb  55 p r0.12   log p r  0.55M 0.5 q 0.67

  G 1  x  d 
hcv  0.023 l 

d 
l

F  1.0  1.8  0.3  1 X tt 

0.88

0.8

Pr 0.4(15)

1  We 

(16)

 0.4
v

1

S
0.5  0.5

(14)

 Re tp  10 3 

0.3

(17)

 Bo  10 

3 0.23Figure 7 shows a comparison of the prediction results obtained by the proposed correlation withthe experimental results for different refrigerants, under different mass flux and heat flux conditions.
Figure 7 (a) shows the comparison results for HFO1234yf with different heat fluxes while a constantmass flux is maintained. As the heat flux increases, the predicted results also increase in a manner
similar to the measured results. When the heat flux is 24 kW/m2, the proposed model slightly
overestimates the experimental results at high vapor qualities. Figure 7 (b) shows the results for
HFO1234yf at different mass fluxes while a constant heat flux is maintained. The heat transfer
coefficient increases monotonically with the vapor quality when the mass flux becomes large. This
result obeys the rule that the heat transfer is basically dominated by nucleate boiling at low vapor
qualities and by forced convection at high vapor qualities or large mass fluxes. The correlation
represents the trend in the heat transfer coefficients quite well but slightly overestimates the values byapproximately 10% on average.
Comparisons of the measured results and predicted results based on the proposed correlation for
HFC32 at identical mass and heat fluxes are shown in Fig. 7 (c) and Fig. 7 (d), respectively. Similar tothe case of HFO1234yf, the results estimated for HFC32 almost follow the variations in the trend forthe experimental data. From these two figures, the correlation slightly underestimates the measured
heat transfer coefficients when the mass flux is 200 kg/m2s and the heat flux is 24 kW/m2, but
underestimates by a higher magnitude of 22% on average, when the mass flux is 100 kg/m2s and theheat flux is 12 kW/m2.
Figure 8 shows direct comparisons of the predicted and measured results for pure HFO1234yf
and pure HFC32. The deviation limit of the proposed correlation for these pure refrigerants is less than
±20% for 85% of the data.

4.2.3 Accuracy of proposed correlation
To compare the accuracies of the prediction methods with the data in the experimental database,the deviation is defined by the relative mean absolute error as follows:

RMAE 1 n hexp,i  hcal ,i hn i 1
exp, i(18)

From the comparisons in Tables 2 and 3, the best fitting correlations for pure HFC32 and pure
HFO1234yf are those proposed in this study. Moreover, acceptable prediction results are obtained by
the correlations of Yoshida et al. [8] and Chen [3]. Although the correlations of Zhang et al. [9] andGunger and Winterton [19] can accurately predict the heat transfer coefficient of HFC32, they show
errors in the trend for the heat transfer coefficient of HFO1234yf. The predicted results of thecorrelation proposed by Saitoh et al. [17] are in good agreement with the results obtained for pure
HFO1234yf but exhibit the worst fit with those for pure HFC32.

4.3 Prediction Model for Refrigerant Mixtures
4.3.1 Existing correlations for mixtures of HFO1234yf and HFC32
In this study, we first presumed that the mass diffusion resistance is negligible; therefore thecorrelation proposed for pure refrigerant can be applied to the prediction of refrigerant mixture as longas the average properties of the mixture are properly employed. The correlations proposed by Yoshida
et al. [8], Chen [3], Zhang et al. [9], Shah [13], and the present study for pure refrigerants were
employed to predict the heat transfer coefficients of the HFO1234yf + HFC32 (80/20 and 50/50 by
mass%) mixture using the average properties of the mixtures.
In addition, we verified the applicability of three models proposed for different refrigerant
mixtures to the HFO1234yf + HFC32 refrigerant mixtures. Mishra et al. [29] developed a correlation
based on their data for R12 + R22, as expressed in Eq. (A.21). In this correlation, the factors C, m, andn are constants based on the mass fraction of R12. Sami et al. [33] developed a correlation expressedin Eq. (A.22) for mixtures in enhanced tubes. Bivens and Yokozeki [30] considered the effects of themass transfer resistance on the heat transfer of the HFC32 + HFC125 and HFC32 + HFC125 +HFC134a mixtures and suggested modifications to the Jung correlation [28] and the Wattelet
correlation [31].
Figure 9 shows the measured results and the results estimated by the seven correlations for the
HFO1234yf + HFC32 (80/20 and 50/50 by mass%) mixtures. Figures 9 (a) and (b) show that thecorrelations of Mishra et al. [29] and Sami et al. [33] both underestimate the measured heat transfer
coefficients of HFO1234yf + HFC32 (80/20 and 50/50 by mass%). The correlation of Bivens andYokozeki [30] also overestimates the results for HFO1234yf + HFC32 (80/20 by mass%). However,most of the results predicted for HFO1234yf + HFC32 (50/50 by mass%) are within the deviation limitof ±20%.
Figure 9 (c) shows that most of the results predicted by the correlations of Yoshida et al. [8], Chen[3], Zhang et al. [9], and the present study exceed the deviation limit of ±20%. This means that themeasured heat transfer coefficients of the mixtures are lower than those calculated using thecorrelations for pure refrigerants. However, the four correlations are in good agreement with the heattransfer coefficient of HFO1234yf + HFC32 (50/50 by mass%), as shown in Fig. 9 (d). The
temperature glide of the HFO1234yf + HFC32 (50/50 by mass%) mixture is about 4.5 oC at the test
saturation pressure of 1.06 MPa. Because of the large temperature glide of the HFO1234yf + HFC32(80/20 by mass%) mixture—about 7.4 oC at a test saturation pressure of 0.77 MPa—and the existenceof mass diffusion resistance, the evaporative heat transfer of the mixture was drastically suppressed.
Hence, the predicted results are not sufficient when only the average properties of the mixture areconsidered. According to the analysis of Scriven [21] and Van Stralen et al. [22], the gradient of theconcentration in a binary mixture will lead to the suppression of the boiling heat transfer. Although the
influence of mass diffusion is considered in the correlations of Mishra et al. [29], Sam et al. [33], andBivens and Yokozeki [30], these three correlations for the mixtures cannot produce a good fit to theheat transfer coefficients of the HFO1234yf + HFC32 (80/20 by mass%) mixture, as shown in Table 4.
A detailed comparison of the results of the seven correlations listed in Tables 4 and 5 indicates thatthe correlations of Yoshida et al. [8], Chen [3], Zhang et al. [9], and the present study must be
improved to obtain reasonable predictions for refrigerant mixtures with a relatively large temperature
glide. Further, new suppression factors must be introduced into the correlations to reflect the
suppressions caused by the concentration distribution.

4.3.2 Characteristics of flow boiling heat transfer in mixtures
In a manner similar to that of pure fluids, the flow boiling heat transfer of a mixture also occurs
owing to the interaction of nucleate boiling and convective heat transfer. Figure 2 clearly shows thatmass diffusion exists and affects the heat transfer coefficients of mixtures during the nucleate boilingprocess. Mass diffusion also exists during the convective heat transfer process, as shown in Fig. 10. In
convection heat transfer, the main flow pattern is annular flow and the convective evaporation process
occurs at the liquid–vapor interface. Because the components in the liquid mixture have different
evaporation rates, it is considerably easier for a volatile component to escape from the interface. A
composition gradient layer forms near the interface, and the volatile component in the liquid bulk has
to pass through the diffusion layer before arrives at the interface, thereby affecting the heat transfer
coefficient of the fluid. Therefore, for a mixture, the heat transfer coefficients are affected not only by
the interaction between the nucleate boiling and convective heat transfer, but also by the mass transfer
resistance inside the diffusion layer.
In addition, the test results of Li et al. [2] indicate that the mass diffusion resistance is also related
to the Bo number. Comparing the heat transfer coefficient of a mixture to that of a pure refrigerant
against the vapor quality at high and low Bo values shows that, at a high Bo, the heat transfer of the
mixture deteriorates across the entire pre-dryout region, whereas at a low Bo, the deviation of the heattransfer coefficient of the mixture increases with an increase in vapor quality.
At a high Bo, nucleate boiling dominates the entire heat transfer, with a high heat flux causing
violent boiling. Because of the high density of bubbles on the surface, the boundary layers of two
bubbles may overlap each other, as shown in Fig. 11 (a). It is more difficult for the volatile component
to reach the interface, and a larger compositional inhomogeneity forms in the interface around the
bubble. Compared to the influence of heat flux on the form of the mass diffusion layer, thedisturbances in the fluid caused by the mass flux are too weak to decrease the mass diffusion
resistance effectively.
When Bo is low, at a high vapor quality, the convective heat transfer dominates the entire heattransfer. Because of the acceleration of the vapor phase, the velocity of the liquid phase increases, andnucleate boiling is suppressed completely. Subsequently, evaporation occurs violently at the interfaceof the liquid and vapor phases, not at the surface of the bubble. According to the same principle ofevaporation, the volatile component evaporates first through the interface, and a concentration gradientlayer forms near the interface, as shown in Fig. 11 (b). The volatile component in the bulk has to passthrough this layer to complement the content of the volatile component attributable to theconcentration gradient. Although a large mass flux can help eliminate the concentration gradient, themass diffusion still affects the convective heat transfer owing to the strong compositional
inhomogeneity during the intense evaporation process.
At moderate Bo values, both the nucleate boiling and convective heat transfer contributes to theflow boiling heat transfer, a concentration gradient layer exists at not only the surface of the bubble,
but also at the liquid and vapor phase interface, as shown in Fig. 11 (c). Because the bubble density islow, it is easy to complement the volatile component from the bulk to the interface, and thecompositional inhomogeneity is decreased in comparison to that at a high Bo. The component gradientnear the evaporation interface is low because the evaporation process is less vigorous. Moreover, abubble transitioning from the liquid phase to the vapor phase can cause agitation, which decreases theeffect of the mass diffusion.
These results imply that at a high Bo, the heat transfer deteriorates mainly because of the masstransfer resistance for the nucleate boiling, whereas at a low Bo, the effect of the mass transfer
resistance on the convective heat transfer is more remarkable than that on the nucleate boiling.

4.3.3

Model proposed for mixtures of HFO1234yf and HFC32

As noted in section 4.3.2, the mass diffusion resistance influences the nucleate boiling andconvective heat transfer by different degrees under various conditions. Therefore, revising factors are
introduced into the prediction correlation of pure refrigerants to predict the heat transfer coefficient of
the mixture. Two suppression factors—Fmix and Smix—are introduced into Chen’s correlation (Eq. 13)
to reflect the influence of the mass diffusion resistance on both the convective heat transfer andnucleate boiling, as shown in Eqs. (19–21).
(19)
htp  Fmix Fhcv  S mix Shnb



Fmix  exp  0.027 Tm ,sat  Tb 

0.5
 Tm 
 dT   c pl   a c   1   y  x  
S mix  dx    hv   D m   Tid 




(20)
1

(21)

In forced convective boiling, the evaporating process mainly occurs at the vapor–liquid interface,
as shown in Fig. 10. The mole fraction difference,, which relates to the difference between theinterface temperature and saturation temperature, is a very important driving force to influence the| or 1|| to correct themass diffusion. Many previous studies have applied either |heat transfer coefficient of a mixture. For example, Sami et al. [33] used the correlations of.
.
∑|| . , and Shin et al. [34] used h/hI = (1 - CF)F,
where
1
0.155 /|
| . Because it is not easy to obtain
where F is Chen’s two-phase correction factor andthe interface temperature, in this study, we used the temperature difference between the bulk
temperature and bubble point temperature of the fluid to correct the forced heat transfer coefficient.
The Fmix formula is similar to the equation of Palen and Small [35], but the definition of thetemperature difference is not the same. In Palen and Small’s correlation of Eq. (22),(22)
h hI  exp   0.027 Tbi  Tb 0  
is the temperature difference between the vapor leaving a reboiler and the liquid
the term
feed to it. As the vapor quality incrementally increases, the convective heat transfer intensifies
gradually; thus, the mass diffusion resistance near the vapor–liquid interface of convective heattransfer significantly rises with the concentration gradient, which is similar to the situation shown in
Fig. 11 (b). The temperature of the fluid deviates from the previous saturation temperature because ofthis concentration gradient. In the proposed Fmix of Eq. (20), the difference of the saturation
temperature of the mixture (Tsatm) and the bubble point temperature of the mixture (Tb) is applied; thisvalue increases gradually in the evaporation process to cause a decrease in Fmix to suppress theconvective heat transfer.
Smix is given by the formula of Scriven [21], who investigated the influence of mass transfer on
the growth of a spherical bubble in a binary mixture. The equation by Scriven describes the differenceof bubble growth in the nucleate boiling of pure materials and binary mixtures, as shown in Eq. (23).
0.5 dT   c pl   a c  
R  R pure 1   y  x  

 

 dx    hv   D m  


1

(23)

The growth of a bubble is related to the superheat of the fluid. The superheat required to grow a
bubble in a binary mixture is different from that in a pure fluid. Bennet and Chen [27] suggested thatthe deterioration of the heat transfer coefficient during nucleate boiling in a mixture is due to thegreater superheat required for a mixture than for a fluid without mass diffusion resistance. They
proposed a suppression factor Smix of the ratio of the effective liquid superheat to the ideal superheat;
this factor is equal to that of the Scriven equation, as shown in Eq. (21). For this equation, it is difficult; hence, the hard sphere model for the diffusion
to obtain the mass diffusion coefficient
coefficients of the components in a binary solution proposed by Kenneth et al. [36] is used, as shownin Eqs. (24)–(26).

D m  D kin 1    ln  1 /  ln x1 T ,P  m Ens
D kin  D kin
AC   , 1 , 1 , x1 
 m 2  2 m  m  m C   , 1 , 1 , x1   x1C   , 1 , 1 ,1   x 2 C   , 1 , 1 , 0 
 m 2  2

 m 2  2 
 m 2  2 

(24)
(25)
(26)

where Dm is the mass diffusion coefficient, and Dkin is the kinetic diffusion coefficient defined byis the Enskog transport equation for the kinetic mutual diffusion coefficient,
Kenneth et al. [36].
which is only valid for the fluid of a smooth hard sphere. Factors A and C are introduced to correct theneglected part in Enskog theory. A detailed explanation for the corrected factor is given in the
Appendix.
The activity coefficient ( ) and fugacity of the mixture are required in the calculation. Hence,
they are evaluated using REFPROP Ver. 8.0. The fugacity is the effective pressure of a real gas. The
predicted mass diffusion coefficient of HFO1234yf + HFC32 is approximately 2 × 10–5 cm2/s during
the evaporation process, as shown in Fig. 12.
The suppression factors for the mixture, Smix and Fmix, are introduced into the correlations for purerefrigerants, i.e., the correlations of Yoshida et al. [8], Chen [3], Zhang et al. [9], and the present
study.
Figure 13 shows the comparison of experimental results with the predicted values for the
HFO1234yf + HFC32 (80/20 and 50/50 by mass%) mixtures using the proposed model with the
suppression factors for the mixtures. Figure 13 (a) shows that the measured heat transfer coefficient of
the HFO1234yf + HFC32 (80/20 by mass%) mixture increases monotonically with the vapor quality ata mass flux of 200 kg/m2s and heat flux ranging from 6 to 24 kW/m2. The correlation predicts both thetrend and magnitude (10% difference) of the heat transfer coefficient. Figure 13 (b) shows the results
for the HFO1234yf + HFC32 (80/20 by mass%) mixture at a heat flux of 12 kW/m2, with the massflux ranging from 100 to 400 kg/m2s. The correlation overestimates the heat transfer coefficient athigh and low mass fluxes by approximately 20%. Figures 13 (c) and (d) compare the measurementswith the predictions for the HFO1234yf + HFC32 (50/50 by mass%) mixture. Figure 13 (c) shows theresults when the heat flux is varied from 6 to 24 kW/m2 while the mass flux is maintained at 200
kg/m2s. The entire trend for the measured heat transfer coefficient versus vapor quality becomesmoderate as the heat flux increases. The correlation captures this trend when the heat flux changes.
Figure 13 (d) shows the results when the mass flux varies from 100 to 400 kg/m2s while the heat flux
is maintained at 12 kW/m2. The moderate increase of heat transfer coefficient against vapor quality ata mass flux of 100 kg/m2s turns to a steep increase at a mass flux of 400 kg/m2s. The correlation
accurately predicts the trends with the changes in the mass flux, and the absolute values of the heattransfer coefficients are captured by the correlation with an average deviation of less than 10%.
Tables 6 and 7 list the relative mean deviations of the results predicted for HFO1234yf + HFC32(80/20 and 50/50 by mass%) using the suppression factors in these four correlations for purerefrigerants. When the Fmix and Smix factors were introduced for the mixture, the prediction accuraciesof the four correlations improved. The correlation proposed in this study outperforms the others for theheat transfer coefficient predictions for the mixture, but slightly overestimates the values under someconditions, such as the case with a mass flux of 100 kg/m2s and heat flux of 12 kW/m2, with anaverage deviation less than 20%. The results predicted using the correlations of Yoshida et al. [8] andChen [3] are also acceptable after the introduction of suppression factions.
5

PREDICTION OF PRESSURE DROP
The pressure drop of flow boiling includes two parts in a horizontal tube: the friction pressure
drop and momentum pressure drop. The pressure drop caused by the acceleration of vapor is
calculated by using Eq. (38) as recommended by Thome [37]. ε is the void fraction, which is
calculated by Eq. (39) [38]. The friction pressure drops for the pure refrigerants HFO1234yf and
HFC32 and the HFO + HFC32 mixtures with two concentrations were predicted using five separated
flow models: the models of Grönnerud [39], Lockhart–Matinelli [40], Müller-Steinhagen and Heck[41], and Friedel [42], which were developed for macrochannels, and the Hwang and Kim correlation[43] that was developed for microchannels. The mean absolute errors of these models are shown in
Table 8. The model proposed by Müller-Steinhagen and Heck outperformed the other models. Figure
14 shows comparisons of the experimental results and the predicted total pressure drop obtained using
the momentum pressure drop model (Eq. 38) and the friction pressure drop model of
Müller-Steinhagen and Heck [41]. This method captured 80%–90% of the experimental results for
HFO1234yf and the two mixtures within a deviation of ±30%. Among the results for HFC32 predictedby the Müller-Steinhagen and Heck correlation exhibited the best agreement with the experimental
data within a deviation limit of ±30%. The Lockhart–Matinelli correlation also accurately predicted
the data for HFO1234yf and the mixtures, but in the case of HFC32, the deviation was over ±30%.
The correlation of Hwang and Kim for microchannels overestimated the results compared to theexperimental data.

 (1  x)2x2 x 2   (1  x)2
pmom  mf2 





 
 l (1   ) v  out  l (1   ) v in (38) x (1  x)  1.18(1  x)  g ( l  v )
x 
  (1  0.12(1  x))  

v 
l 
mf2 l0.5
 v

0.25

6





1

(39)

CONCLUSIONS

Predictions were performed based on experiments on the flow boiling heat transfer of pure
HFO1234yf, HFC32, and the HFO1234yf + HFC32 (80/20 and 50/50 by mass%) refrigerant mixture
in a 2 mm smooth tube. The results are summarized as follows:(1) Several existing correlations were applied to predict the heat transfer coefficients of pure
HFO1234yf, HFC32, and HFO1234yf + HFC32 (80/20 and 50/50 by mass%). The correlations of
Yoshida et al. and Chen predicted the heat transfer coefficient of HFO1234yf and HFO1234yf +HFC32 (50/50 by mass%) with acceptable accuracy. However, these two correlations
underestimated the heat transfer coefficients of HFC32 under some conditions.
(2) A new semi-empirical correlation based upon the superposition of the contributions from nucleateboiling and convection was in very good agreement with the magnitudes and trends of the heattransfer coefficients of pure HFO1234yf, HFC32, and HFO1234yf + HFC32 (50/50 by mass%)with a relative mean absolute error of approximately 20%. The average properties of the mixture
were used in the calculation.
(3) The existing correlations and the proposed correlation overestimated the heat transfer coefficientof HFO1234yf + HFC32 (80/20 by mass%) with a large temperature glide of 7.4 oC at the test
saturation pressure because of the effects of mass diffusion resistance.
(4) Suppression factors were proposed for the mixture and introduced into both the existingcorrelations and the newly proposed correlation. The prediction accuracies of these correlations
were improved for the HFO1234yf + HFC32 (80/20 and 50/50 by mass %) mixture. The absolutevalues of the heat transfer coefficients obtained by the proposed correlation have an average
deviation of less than 20%.
(5) The correlation proposed by Müller-Steinhagen and Heck [41] can predict the pressure drops ofthe mixtures and pure HFO1234yf and HFC32. In the case of the predicted results for the
HFO1234yf + HFC32 mixtures, 80%–90% are in good agreement with the measured pressure
drops within a deviation of ±30%.

ACKNOWLEDGMENTS
This study was sponsored by the “Development of Non-fluorinated Energy-Saving
Refrigeration and Air Conditioning Systems” project of the New Energy and Industrial
Technology Development Organization of Japan. The first author is grateful for the financial
support received from the Japan Society for the Promotion of Science (JSPS) and NSFC No.
51176133 and 50976075.
APPENDIX(1) Correlations of Chen [3]:htp  Shn  Fhl(A.1)

 l0.79 c pl 0.5  l0.49 
0.4
0.75
hn  0.00122  0.6 0.29 0.24 0.24  t w  tsat  pl    psat  t w   pl (A.2)
  l hlv  v 
0.4
hl  0.023Re0.8
 d
(A.3)
l Prl
Rel  G 1  x  d / l

(A.4)

S

1   2.56 10

1
6

(A.5)

 Re F 

1.25 1.17lF  1.0, X tt  10

(A.6)

F  2.0  0.213  1 / X tt 

0.736

, X tt  10

(A.7)

0.533

(A.8)

(2) Correlations of Yoshida et al. [8]:  qd 
hn  207 l  b 
db  lTl 

0.745

 v   l 2
d b  0.51  g  l   v  
F  1  2 1 X tt 

0.5
S  1 1  0.9  Retp 104 


0.581

Prl

0.5

(A.9)

0.88

(A.10)

 Bo 10   X 
0.5

4(A.11)

tt

Bo  q Ghlv
(3) Correlations of Saitoh et al. [17]:F  1  1 X tt 

1.05

(A.12)

1  We 
0.4(A.13)v

1.4
S  1 1  0.4  Retp 104  
Re tp  Re l F 1.25

(A.15)F  1  2 1 X tt 

(A.16)(A.14)(4) Correlations of Zhang et al. [9]:

S

0.88

1
0.5

 q 10000   1 
1  0.4(Re tp  0.0001) /   G  hlv   X tt 

(A.17)

0.5

0.5(5) Correlations of Gungor and Winterton [32]:htp  Ehl
E  1  3000 Bo

0.86(A.18)

 x 
 1.12 1 x 0.75

 l  v 

0.41(A.19)

If the tube is horizontal and the Froude number Fr1 is smaller than 0.05, E should be multiplied by thefactorE 2  Frl 

0.1 2 Frl (A.20)(6) Correlation of Mishra et al. [29]:htp ,m  C1 Bo 0.15 X tt0.23(7)(A.21)

Correlations of Sami et al. [33]:  Gd 
htp,m  0.015 l d  l 

0.62

Al 0.3100(A.22)A  1  0.79  y1  x1  y 2  x 2 

0 .8 2(A.23)(8) Correlations of Bivens and Yokozeki [30]:hcv  F  hl  R

2.5

htp  hnb  hcv(A.24)



2.5 1/ 2.5(A.25)

htp,m  htp / 1  htp  Tint  q (A.26)



Tint  0.175tbp 1  exp  q /1.3 /104 /  l / hv F  (0.29  1/ X tt )0.85
R  2.15 when Frl  0.25

(A.27)(A.28)(A.29)

when Frl  0.25

(A.30)

N  0.38Frl0.3Co Frl  0.04

(A.31)N  Co Frl  0.04

(A.32)

R  2.83  F

0.25
rl

(9) Correlation of Shah [13]:hnb hl  230 Bo

0.5

N  1.0, Bo  0.0003(A.33)

hnb hl  1  46 Bo

0.5

N  1.0, Bo  0.0003(A.34)

hnb hl  FBo

0.5

hnb hl  FBo

0.5

 0.1

)

1.0  N  0.1(A.35)

 0.15)N  0.1(A.36)

exp(2.74 N
exp(2.74 N

hcv hl  1.8 N

0.8(A.37)

htp  max  hcv , hnb (10) Grönnerud correlation [39]:(A.38)

pf  plgd(A.39)

gd  1   dp   l / v
1
 
0.25

 dz Fr   l / v 


(A.40)

 dp 
1.8
10 0.5   f Fr  x  4( x  x f Fr )
 dz Fr
f Fr  1.0, Fr  1.0(A.41)(A.42)2
1 
f Fr  Frl0.3  0.00 55  ln
 , Fr  1.0
 Frl G2
Frl gd l2(A.43)(A.44)(11) Correlation of Lockhart–Matinelli [40]: dp 
 dp        l2
 dz f dz lGl2
 dp 
2
f


l


D l
 dz l(A.45)(A.46)

Gv2
 dp 


2
f
v


D v
 dz  v
l2  1  C / X  1/ X 2
 dp / dz l
X2  dp / dz v(A.47)(A.48)(A.49)

 fl =0.079Re-0.25, Rel >2000l, Rel <2000 fl =16/Rel-0.25
 f v =0.079Rev , Rev >2000
, Rev <2000
 f v =16/Rev(12) Müller-Steinhagen and Heck correlation [41]: dp 
1/ 3
3
   C (1  x)  Bxdz
 Fr
C  A  2( B  A) x
 dp A 
 dz l0

 dp B 
 dz v0(A.50)(A.51)(A.52)(A.53)(A.54)(A.55)(13) Friedel correlation [42]:pf  pLf2(A.56)

pf  4 f l ( L / d )G (1/ 2 l )2

(A.57)

0.25
l0(A.58)

f  0.079 Re
Rel0  Gd l
3.24FH  E  0.045 0.035
FrH WeLf
E  (1  x)2  x2 l v
v fl(A.59)(A.60)(A.61)F  x 0.78 (1  x)0.224
 H  l  v 
(14) Correlation of Hwang and Kim [43]:0.91 v   l 

0.19

 v 
1 

l 


(A.62)
0.7

 dp 
 dp        l2
 dz f dz l2
l  1  C X  1 X 2

X2  dp / dz l dp / dz v

C  0.227 Re0.452
X 0.32 Bo 0.41
l0

(A.63)(A.64)(A.65)(A.66)(A.67)(15) The calculation of parameters in Eqs. (25) and (26) m 
 m   m 
C  , 1 , 1 , x1   x1C  , 1 , 1 ,1  x2C  , 1 , 1 , 0  m2  2
 m2  2 
 m2  2 (A.68)

 m m 
2C  , 1 , 1 , 0   0.84  7.69   0.463  32.3   0.463  0.299ln  1 
 m2  2 
 m2 
2

  m    
  m  0.165 ln  1    0.200  1   1  0.78  ln  1     0.463
  m2    2    m2       m      
 0.336 ln  1    1   1  5.33   0.463  1   1
  2    m2     2  (A.69)

 m   m  C  , 1 , 1 ,1  C  , 2 , 1 ,1
 m2  2 
 m1  2 (A.70)The quantity C is introduced to compensate for the neglect by the Enskog theory of thecorrelation motions in hard sphere fluids. For instance, the collisions of particles in hard sphere fluids
are different from those in actual fluids. ηi is the packing fraction of the i-th component, ηi =/6,and η = η1 + η2. Modification factor A is due to the coupling of translational and rotational degrees of
freedom, which is within 0–1 and is equal to 0.55 according to the analysis of Kenneth et al. [36].

g12  12   g PY  12   Z CS  1 /  Z PY  1 (A.71)

322
 1 
g PY 12   1    1    1   2 2 1  / 1   1   2   A.72)


2
 2 
3
(A.73)
Zcs  1     2  3 Y1  Y2   Y3 3  / 1  
ZPY,v  1     2  3 Y1  Y2   3Y3 3  / 1   

3(A.74)The quality of gis to reflect that the local density near a particular sphere is greaterthan the average density, which is related to the compressibility factor and is calculated by the) inPercus–Yevick pair correlation function between unlike particles in a hard sphere fluid (gEq. (A.72). The Carnaban–Starling compressibility factor for a binary mixture (Zcs) and the
Percus–Yevick compressibility factor (ZPYv) are calculated by Eqs. (A.73) and (A.74). The quantities
Yi are calculated by Eqs. (A.75–A.78).

Y1     1   2  /  1 2 

1/ 2

Y2     1 2 

1/ 2(A.75)

1 /  1   2 /  2  / (A.76)
3

Y3   1   x 11/3  2   x 21/ 3 


1/ 2
2
1/ 2
  1 2    1   2   1 2   x1 x 2  


2/3

2 /3

(A.77)(A.78)REFERENCES[1] M. Spatz, B. Minor, HFO1234yf low GWP refrigerant: A global sustainable solution for mobile air
conditioning, SAE Alternate Refrigerant Systems Symposium, Scottsdale, AZ, 2008.
[2] M.X. Li, C. Dang, E. Hihara, Flow boiling heat transfer of HFO1234yf and HFC32 refrigerant
mixtures in a smooth horizontal tube, Part I: Experimental investigation, International Journal of Heatand Mass Transfer 55 (2012) 3437-3446.
[3] J.C. Chen, Correlation for boiling heat transfer to saturated fluids in convective flow, Industry
Chemical Engineering Process Design and Development 5(3) (1966) 322-339.
[4] H.K. Forster, N. Zuber, Dynamics of vapour bubbles and boiling heat transfer, Chemical
Engineering Progress 1(4) (1955) 531-535.

[5] J.C. Chen, K. Tuzla, Contributions of convection and boiling to convective flow boiling, in:
J.C. Chen (Ed.), Convective Flow Boiling, Taylor & Francis, Washington, 1995, pp. 181-186.
[6] K.E. Gunger, R.H.S. Winterton, A general correlation for flow boiling in tubes and annuli,
International Journal of Heat and Mass Transfer 29(3) (1986) 351-358.
[7] M.G. Cooper, Heat flow rates in saturated nucleate pool boiling—a wide-ranging examination
using reduced properties, Advances in Heat Transfer 16 (1984) 157-239.
[8] S. Yoshida, H. Mori, H. Hong, T. Matsunaga, Prediction of heat transfer coefficient for refrigerants
flowing in horizontal evaporator tubes, Transcripts of the JAR 11(1) (1994) 67-78.
[9] L. Zhang, E. Hihara, T. Saito, J. Oh, Boiling heat transfer of a ternary refrigerant mixture insidehorizontal smooth tube, International Journal of Mass Transfer 40(9) (1997) 2009-2017.
[10] K. Stephan, M. Abdelsalam, Heat transfer correlation for natural convection boiling, International
Journal of Heat and Mass Transfer 23 (1980) 73-87.
[11] S.S. Kutateladze, Boiling heat transfer, International Journal of Heat and Mass Transfer 4 (1961)
3-45.
[12] D. Steiner, J. Taborek, Flow boiling heat transfer in vertical tubes correlated by an asymptotic
model, Heat Transfer Engineering 13(2) (1992) 43-69.
[13] M.M. Shah, A new correlation for heat transfer during boiling flow through pipes, ASHRAE
Transcripts 82(2) (1976) 66-86.
[14] S.G. Kandlikar, A general correlation for two-phase flow boiling heat transfer coefficients insidehorizontal and vertical tubes, Journal of Heat Transfer 112 (1990) 219-228.
[15] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow,
International Chemical Engineering 16 (1976) 359-368.
[16] S. Saitoh, C. Dang, Y. Nakamura, E. Hihara, Boiling heat transfer of HFO1234yf flowing insmooth small-diameter horizontal tube, International Journal of Refrigeration 34(8) (2011) 1846-1853.
[17] S. Saitoh, H. Daiguji, E. Hihara, Correlation for boiling heat transfer of R-134a in horizontal
tubes including effect of tube diameter, International Journal of Heat and Mass Transfer 50 (2007)
5215-5225.
[18] J.Y. Shin, M.S. Kim, S.T. Ro, Experimental study on forced convective boiling heat transfer ofpure refrigerants and refrigerant mixtures in a horizontal tube, International Journal of Refrigeration,
20(4) (1997) 267-275.
[19] K.E. Gungor, R.H.S. Winterton, Simplified general correlation for saturated flow boiling andcomparisons of correlations, Chemical Engineering Research and Design 65 (1987) 148-156.
[20] T. Kamiaka, C. Dang, E. Hihara, Vapor-liquid equilibrium measurements for binary mixtures ofR1234yf with R32, R125, and R134a, International Journal of Refrigeration 36(3) (2013) 965-971.
[21] L.E. Scriven, On the dynamics of phase growth, Chemical Engineering Science 10 (1959) 1-13.
[22] S.J.D. Van Stralen, M.S. Sohal, R. Cole, W.M. Sluyter, Bubble growth rates in pure and binary
systems: Combined effect of relaxation and evaporation microlayers, International Journal of Heat andMass Transfer 18 (1975) 453-467.
[23] W.R. Van Wijk, A.S. Vos, S.J.D. Stralen, Heat transfer to boiling binary liquid mixtures
Chemical Engineering Science 5 (1956) 68-80.
[24] K. Stephan, M. Körner, Berechnung des Wärmeübergangs verdampfender binärer
Flüssigkeitsgemische, Chemie Ingenieur Technik 41(7) (1969) 409-417 (in German).
[25] W.F. Calus, D. J. Leonidopulos, Pool boiling—Binary liquid mixtures, International Journal of
Heat and Mass Transfer 17 (1974) 249-256.
[26] J.R. Thome, R.A.W. Shock, Boiling of multicomponent liquid mixtures, Advances in Heat
Transfer 16 (1986) 60-157.
[27] D.L. Bennet, J.C. Chen, Forced convective boiling in vertical tubes for saturated pure components
and binary mixtures, AIChE Journal 26(3) (1980) 454-461.
[28] D.S. Jung, M. Mclinden, R. Radmeracher, D. Didion, A study of flow boiling heat transfer withrefrigerant mixtures, International Journal of Heat and Mass TransfeHFC32(9) (1989) 1751-1764.
[29] M.P. Mishra, H.K. Varma, C.P. Sharma, Heat transfer coefficients in forced convection
evaporation of refrigerant mixtures, Letters in Heat Mass Transfer 8 (1981) 127-136.
[30] D.B. Bivens, A. Yokozeki, Heat transfer coefficients and transport properties for alternativerefrigerants, in: Proceeding of International Refrigeration Conference at Purdue, West Lafayette, IN,
1994, pp. 229-304.

[31] J.P. Wattelet, J.C. Chato, A.L. Souza, B.R. Christofferson, Initial evaporative comparison of R-22
with alternative refrigerants R134a and HFC32/R125, Air Conditioning and Refrigeration Center
Report TR-39, University of Illinois, 1993.
[32] E.W. Lemmon, M.L. Hube, M.O. Mclinden, Physical and chemical properties division,
REFPROP 8.0, NIST Standard Reference Database 23, Version 8.0.
[33] S.M. Sami, J. Schnotale, J.G. Smale, Prediction of the heat transfer characteristics of
R22/R152a/R114 and R22/R152a/R124, ASHRAE Transactions 98(2) (1992) 51-58.
[34] J.Y. Shin, M.S. Kim, S.T. Ro, Correlation of evaporative heat transfer coefficients for refrigerant
mixtures, Proceedings of the International Refrigeration Conference at Purdue, West Lafayette, IN,
1996, pp. 151-156.
[35] J.W. Palen, W. Small, A new way to design kettle and internal reboilers, Hydrocarbon Processing
43(11) (1964) 199-208.
[36] J.C. Kenneth, H.C. Andersen, R. Pecora, Light scattering measurement and theoreticalinterpretation of mutual coefficients in binary liquid mixtures, Chemical Physics 11 (1975) 451-473.
[37] J.R. Thome, Engineering data book III, Wolverine Tube, Inc. 2004, p.13-4[38] D. Steiner, VDI-Wärmeatlas (VDI Heat Atlas), Verein Deutscher Ingenieure, DI-Gesellschaft
Verfahrenstechnik und Chemieingenieurwesen (GCV), Düsseldorf, Chapter Hbb, 1993.
[39] R. Grönnerud, Investigation in liquid holdup, flow resistance and heat transfer in circular typeevaporators, Part IV: two-phase resistance in boiling refrigerants, bulletin de l’Inst. Du Froid, Annexe
1972-1.
[40] S.M. Ghiaasiaan, Two-phase flow, boiling, and condensation in conventional and miniaturesystems, Cambridge University press, 2008, p. 261.
[41] H. Müller-Steinhagen, K. Heck, A simple friction pressure drop correlation for two-phase flow
pipes, Chem. Eng. Process. 20 (1986) 297-308.
[42] L. Friedel, Improved friction pressure drop correlations for horizontal and vertical two-phase pipe
flow, in: European Two-Phase Flow Group Meeting, Ispra, Italy, 1979, paper E2.
[43] Y.W. Hwang, M.S. Kim, The pressure drop in microtubes and the correlation development,International Journal of Heat and Mass Transfer 49 (2006) 1804-1812.

9
T = 15 o C at x = 0.5

8

HFO1234yf + HFC32
HFO1234yf+ R32

Temperature glide (oC)7

HFC134a+R32+ HFC32
R134a

6
5
4
3
2
1
0
0

0.2

0.4

0.6

0.8

1

Mass concentration of HFC32
R32
Figure 1 Temperature glides of HFC134a + HFC32 and HFO1234yf + HFC32 mixtures.

Mass fraction

Thermal boundary

Diffusion shell
R

Temperature

BubbleTbk

Tsat
Radius, R

Figure 2 Composition and temperature distribution around bubble in mixture.

2000

HFO1234yf(T (T= 303.15
K) K)
HFO1234yf / R32
HFC32= 303.15
1800

Pressure (kPa)

1600

1400

1200
Measured (Liquid)
Measured (Vapor)This Work (Liquid)This Work (Vapor)
REFPROP (Liquid)
REFPROP (Vapor)

1000

800

600
0.0

0.2

0.4

0.6

0.8

1.0

Mass Fraction of R32
HFC32

Figure 3 Comparison of the Peng–Robinson model from Kamiaka et al. [20] and REFPROP [32].

Heat transfer coefficient ( kW/m2 K )8Measurement

7

Ideal

6
5
4
3

G = 200 kg/m 2 s,
q = 12 kW/m 2
Ts = 15 o C
x = 0.49~0.52
D = 2 mm

2
1
0
0

0.2

0.4

0.6

0.8

1

Mass concentration of R32
HFC32

Figure 4 Heat transfer coefficient of mixture at different concentrations.

100

100

R32,
D = 2Dmm
HFC32,= 2 mmHFO1234yf , D = 2 mm

h exp /h l =8.1(1/Xtt )0.55

h exp /h l =2.90(1/Xtt )0.72

10

hexp /hl

hexp /hl

h exp /h l=6.81(1/Xtt)0.53

G = 100kg/m2s
kg/m2 s,q=12kW/m2
q = 12 kW/m2
G=1002
G = 200 kg/m s,q=6kW/m2
q = 6 kW/m2
G=200kg/m2s,
G=200kg/m2s,q=12kW/m2
G = 200 kg/m2 s, q = 12 kW/m2
G=200kg/m2s,q=24kW/m2
G = 200 kg/m2 s, q = 24 kW/m2
G=400kg/m2s,q=12kW/m2
G = 400 kg/m2 s, q = 12 kW/m2

h exp /h l =2.92(1/Xtt )0.72

10

G = 100 kg/m2 s, q = 6 kW/m2
G=100kg/m2s,q=6kW/m2
G = 100 kg/m2 s, q = 12 kW/m2
G=100kg/m2s,q=12kW/m2
G = 200 kg/m2 s, q = 6 kW/m2
G=200kg/m2s,q=6kW/m2
G = 200 kg/m2 s, q = 12 kW/m2
G=200kg/m2s,q=12kW/m2
G = 200 kg/m2 s, q = 24 kW/m2
G=200kg/m2s,q=24kW/m2
G=400kg/m2s,q=12kW/m2
G = 400 kg/m2 s, q = 12 kW/m2

1

1
1

10

1

100

10

1/Xtt

(a) HFO1234yf
100(b) HFC32
400

HFO1234yf:R32 = 0.8:0.2,
D =D2 =mm
HFO1234yf:HFC32= 0.8:0.2,
2 mm

HFO1234yf:HFC32= 0.5:0.5,DD= =2 2mm
mm
HFO1234yf :R32 = 0.5:0.5,

h exp /h l =6.76(1/Xtt )0.56
h exp /h l =2.34(1/Xtt )0.72

10

G=100kg/m2s,q=6kW/m2
G = 100 kg/m2 s, q = 6 kW/m2
G = 100 kg/m2 s, q = 12 kW/m2
G=100kg/m2s,q=12kW/m2
G = 200 kg/m2 s, q = 6 kW/m2
G=200kg/m2s,q=6kW/m2
G=200kg/m2s,q=12kW/m2
G = 200 kg/m2 s, q = 12 kW/m2
G = 200 kg/m2 s, q = 24 kW/m2
G=200kg/m2s,q=24kW/m2
G = 400 kg/m2 s, q = 12 kW/m2
G=400kg/m2s,q=12kW/m2
G=400kg/m2s,q=24kW/m2
G = 400 kg/m2 s, q = 24 kW/m2

h exp/h l

h exp/h l

h exp /h l =4.22(1/Xtt )0.63

h exp /h l =3.12(1/Xtt )0.70

20

G = 100 kg/m2 s, q = 6 kW/m2
G=100kg/m2s,q=6kW/m2
G = 100 kg/m2 s, q = 12 kW/m2
G=100kg/m2s,q=12kW/m2
G = 200 kg/m2 s, q = 6 kW/m2
G=200kg/m2s,q=6kW/m2
G = 200 kg/m2 s, q = 12 kW/m2
G=200kg/m2s,q=12kW/m2
G = 200 kg/m2 s, q = 24 kW/m2
G=200kg/m2s,q=24kW/m2
G = 400 kg/m2 s, q = 12 kW/m2
G=400kg/m2s,q=12kW/m2
G = 400 kg/m2 s, q = 24 kW/m2
G=400kg/m2s,q=24kW/m2

1

1
1

100

1/Xtt

10

1/Xtt

(c) HFO1234yf:HFC32 = 0.8:0.2

100

1

20

400

1/Xtt

(d) HFO1234yf:HFC32 = 0.5:0.5

Figure 5 Boiling heat transfer coefficients as function of the Lockhart–Martinelli parameter.

9
8
7

7

+20%

6

-20%

5
4
3

Yoshida et al.
Saitoh et al.
Chen

2
1

+20%

6
5
4

-20%

3
2

Zhang et al.
Shah
Gunger and Winterton

1

0

0
0

20

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

h cal (kW/m2K)

h cal (kW/m2K)(a) HFO1234yf(b) HFO1234yf
20

HFC32,
mm
R32, DD==22 mm

18
16
12

-20%

10
8
6

Yoshida et al.
Saitoh et al.
Chen

4
2

9

16

+20%

14

8

HFC32,
mm
R32, DD== 22 mm

18h exp ( kW/m2K )h exp ( kW/m2K )HFO1234yf, D = 2mm

8h exp (kW/m2K)

h exp ( kW/m2K )9

HFO1234yf, D = 2mm

+20%

14
12

-20%

10
8
6

Zhang et al.
shahGunger and Winterton

4
2
0

0
0

2

4

6

8 10 12 14 16 18 20

hcal (kW/m2K)

0

2

4

6

8 10 12 14 16 18 20

h cal (kW/m2K)(c) HFC32(d) HFC32

Figure 6 Experimental heat transfer coefficients for HFO1234yf and HFC32 versus heat transfer
coefficients predicted using available correlations.

6
5
4
3
2
1
0
0

Heat transfer coefficient ( kW/m 2 K )Heat transfer coefficient ( kW/m2 K )HFO1234yf , D = 2 mm

16

0.2

0.4

0.6

0.8

7
6
5
4
3
2
1
0
0

0.2

0.4

0.6

0.8

1

Vapor quality

Exp G=200kg/m2s,
G = 200 kg/m 2q=6kW/m2
s, q = 6 kW/m 2
Cal G=200kg/m2s,
G = 200 kg/m 2q=6kW/m2
s, q = 6 kW/m 2
Exp G=200kg/m2s,
G = 200 kg/m 2q=12kW/m2
s, q = 12 kW/m 2
2
Cal G=200kg/m2s,
G = 200 kg/m q=12kW/m2
s, q = 12 kW/m 2
2
Exp G=200kg/m2s,
G = 200 kg/m q=24kW/m2
s, q = 24 kW/m 2
Cal G=200kg/m2s,
G = 200 kg/m 2q=24kW/m2
s, q = 24 kW/m 2

Exp G=100kg/m2s,
G = 100 kg/m 2q=12kW/m2
s, q = 12 kW/m 2
2
Cal G=100kg/m2s,
G = 100 kg/mq=12kW/m2
s, q = 12 kW/m 2
2
Exp G=200kg/m2s,
G = 200 kg/m q=12kW/m2
s, q = 12 kW/m 2
2 s, q = 12 kW/m 2
Cal G=200kg/m2s,
G = 200 kg/mq=12kW/m2
Exp G=400kg/m2s,
G = 400 kg/m 2q=12kW/m2
s, q = 12 kW/m 2
2
Cal G=400kg/m2s,
G = 400 kg/mq=12kW/m2
s, q = 12 kW/m 2(a) HFO1234yf, G = 200 kg/m2s(b) HFO1234yf, q = 12 kW/m2

12
10
8
6
4
2
0
0

HFO1234yf , D = 2 mm

8

Vapor quality

HFC32,
mm
R32, DD==22mm

14

9

1

0.2

0.4
0.6
0.8
1
Vapor quality
G = 200 kg/m 2q=6s, q kW/m2= 6 kW/m 2
Exp G=200kg/m2s,
2 s, q = 6 kW/m 2
G
=
200
kg/m
Cal G=200 kg/m2s, q=6 kW/m2
G = 200 kg/m 2q=12kW/m2
s, q = 12 kW/m 2
Exp G=200kg/m2s,2
G = 200
kg/m s, q =kW/m2
12 kW/m 2
Cal G=200kg/m2s,q=122
G = 200 kg/m q=24s, q =kW/m2
24 kW/m 2
Exp G=200kg/m2s,2
G = 200
kg/m q=24s, q =kW/m2
24 kW/m 2
Cal G=200kg/m2s,(c) HFC32, G = 200 kg/m2s

Heat transfer coefficient ( kW/m 2 K )Heat transfer coefficient ( kW/m2 K )718

HFC32,
mm
R32, DD== 22 mm

16
14
12
10
8
6
4
2
0
0

0.2

0.4
0.6
0.8
Vapor quality

1

Exp G=100kg/m2s,G = 100
kg/m 2q=12s, q =kW/m2
12 kW/m 2
2
Cal G=100kg/m2s,G = 100
kg/m q=12s, q =kW/m2
12 kW/m 2
2
Exp G=200kg/m2s,G = 200
kg/m q=12s, q =kW/m2
12 kW/m 2
2
Cal G=200kg/m2s,G = 200
kg/m q=12s, q =kW/m2
12 kW/m 22
G = 400
kg/m s,q = kW/m2
12 kW/m 2
Exp G=400kg/m2s,q=122
G = 400
kg/m q=12s, q =kW/m2
12 kW/m 2
Cal G=400kg/m2s,(d) HFC32, q = 12 kW/m2

Figure 7 Heat transfer coefficients as function of vapor quality for pure HFO1234yf and pure HFC32:
comparison of experimental results with predictions by the proposed correlation.

9
8
7

16

+20%

6

HFC32,
R32, DD == 2 mm
mm

18

5

hexp ( kW/m2K )h exp ( kW/m2K )20

HFO1234yf , D = 2 mm

-20%

4
3
2

+20%

14
12
10

-20%

8
6
4

1

2

0

0

0

1

2

3

4

5

6

7

h cal ( kW/m2K )G=100kg/m2s,q=12kW/m2
G = 100 kg/m 2 s, q = 12 kW/m 2
G=200kg/m2s,q=6kW/m2
G = 200 kg/m 2 s, q = 6 kW/m 2
G=200kg/m2s,q=12kW/m2
G = 200 kg/m 2 s, q = 12 kW/m 2
G=200kg/m2s,q=24kW/m2
G = 200 kg/m 2 s, q = 24 kW/m 2
G=400kg/m2s,q=12kW/m2
G = 400 kg/m 2 s, q = 12 kW/m 2(a) HFO1234yf

8

9

0

2

4

6

8 10 12 14 16 18 20

h cal ( kW/m2K )G = 100 kg/m 2 s, q = 12 kW/m 2
G=100kg/m2s,q=12kW/m2
G = 200 kg/m 2 s, q = 6 kW/m 2
G=200kg/m2s,q=6kW/m2
G = 200 kg/m 2 s, q = 12 kW/m 2
G=200kg/m2s,q=12kW/m2
G=200kg/m2s,q=24kW/m2
G = 200 kg/m 2 s, q = 24 kW/m 2
G=400kg/m2s,q=12kW/m2
G = 400 kg/m 2 s, q = 12 kW/m 2
G=400kg/m2s,q=24kW/m2
G = 400 kg/m 2 s, q = 12 kW/m 2(b) HFC32

Figure 8 Experimental heat transfer coefficients for HFO1234yf and HFC32 versus heat transfer
coefficients predicted using the proposed correlation.

9

7
+20%

5
4
3
-20%

2

+20%

8

hexp (kW/m2 K)

h exp ( kW/m2K )

6

7
6

-20%

5
4
3
2

HFO1234yf:HFC32
80:20
HFO1234yf:R32 ==80:20

1

HFO1234yf:HFC32
50:50
HFO1234yf:R32 == 50:50

1
0

0
0

1

2

3

4

5

6

0

7

1

2

h cal ( kW/m2K )

9
7
5
4

-20%

3

8

9

HFO1234yf:R32 = 50:50

8

+20%

7
6

-20%

5
4
3

2

2

1

1

0

7

HFO1234yf:HFC32 = 50:50

9

6

6

(b) HFO1234yf:HFC32 = 50:50
10

+20%

hcal

(kW/m2 K)

Bivens and YoKozeji’s Correlation

hexp ( kW/m2K )h exp ( kW/m2K )8

5

Sam et al.'s correlation(a) HFO1234yf:HFC32 = 80:20
HFO1234yf:HFC32 = 80:20
HFO1234yf:R32 = 80:20

4

Mishra et al.'s correlation

Mishra et al.'s correlation
Sam et al.'s correlation
Bivens and YoKozeji’s Correlation

10

3

0

0

1

2

3

4

5

6

7

8

9 10

hcal (kW/m2K)

0

1

2

3

4

5

6

7

hcal ( kW/m2 K )8Yoshida et al.'s correlation
Chen's correlation
Zhang et al.'s correlation
This work for pure refrigerants

Yoshida et al.'s correlation
Chen's correlation
Zhang et al.'s correlation
This work for pure refrigerants(c) HFO1234yf:HFC32 = 80:20(d) HFO1234yf:HFC32 = 50:50

9

10

Figure 9 Results predicted for HFO1234yf + HFC32 mixtures by seven correlations.

Radial direction

Liquid–vapor interface

Tsat

Diffusion layer
Tin
Wall
Tw

Figure 10 Distribution of temperatures and composition of the mixture in radial direction

VaporG

I

Interface
Transfer layer21

Liquid
qhigh
q

(a)

High Bo

Vapor
G
IIInterface

Transfer layer

Liquidq(b) Low Bo

Vapor
G
II
Interface3
LiquidTransfer layerIq(c) Moderate Bo
Figure 11 Flow boiling situation of mixtures at various Bo.

Mass diffussion coefficient x10 5 (cm 2 /s)

3
2.5
2
1.5
1

P = 0.775 MPa
P = 1.117 MPa

0.5
0
0

0.2

0.4

0.6

0.8

Mass concentration of HFC32
R32

Figure 12 Mass diffusion coefficients of mixtures.

1

7

HFO1234yf:R32
D == 22mm
mm
HFO1234yf:HFC32==80:20,
80:20, D

Heat transfer coefficient ( KW/m 2 K )Heat transfer coefficient ( KW/m 2 K )

6
5
4
3
2
1
0
0

0.2

0.4
0.6
Vapor quality

0.8

HFO1234yf:R32 ==80:20,
HFO1234yf:HFC32
80:20, D = 2 mm

6
5
4
3
2
1
0

1

0

Exp G=200kg/m2s,q=6kW/m2
G = 200 kg/m 2 s, q = 6 kW/m 2
Cal G=200kg/m2s,q=6kW/m2
G = 200 kg/m 2 s, q = 6 kW/m 2
G = 200 kg/m 2 s, q = 12 kW/m 2
Exp G=200kg/m2s,q=12kW/m2
G = 200 kg/m 2 s, q = 12 kW/m 2
Cal G=200kg/m2s,q=12kW/m2
Exp G=200kg/m2s,q=24kW/m2
G = 200 kg/m 2 s, q = 24 kW/m 2
G = 200 kg/m 2 s, q = 24 kW/m 2
Cal G=200kg/m2s,q=24kW/m2

0.8

1

G = 200 kg/m 2 s, q = 12 kW/m 2
Exp G=200kg/m2s,q=12kW/m2
G = 200 kg/m 2 s, q = 12 kW/m 2
Cal G=200kg/m2s,q=12kW/m2
Exp G=400kg/m2s,q=12kW/m2
G = 400 kg/m 2 s, q = 12 kW/m 2
Cal G=400kg/m2s,q=12kW/m2
G = 400 kg/m 2 s, q = 12 kW/m 2(b) HFO1234yf:HFC32 = 80:20, q = 12 kW/m2
Heat transfer coefficient ( KW/m 2 K )Heat transfer coefficient ( KW/m 2 K )0.4
0.6
Vapor quality

G = 100 kg/m 2 s, q = 12 kW/m 2
Exp G=100kg/m2s,q=12kW/m2
G = 100 kg/m 2 s, q = 12 kW/m 2
Cal G=100kg/m2s,q=12kW/m2(a) HFO1234yf:HFC32 = 80:20, G = 200 kg/m2s
7

0.2

HFO1234yf:HFC32==50:50,
50:50, D
D = 22 mm
HFO1234yf:R32
mm

6
5
4
3
2
1

9

HFO1234yf:HFC32= 50:50,DD==2 2mm
mm
HFO1234yf:R32= 50:50,

8
7
6
5
4
3
2
1
0

0
0

0.2

0.4

0.6

0.8

1

Vapor quality
Exp G=200kg/m2s,q=6kW/m2
G = 200 kg/m 2 s, q = 6 kW/m 2
Cal G=200kg/m2s,q=6kW/m2
G = 200 kg/m 2 s, q = 6 kW/m 2
Exp G=200kg/m2s,q=12kW/m2
G = 200 kg/m 2 s, q = 12 kW/m 2
Cal G=200kg/m2s,q=12kW/m2
G = 200 kg/m 2 s, q = 12 kW/m 2
Exp G=200kg/m2s,q=24kW/m2
G = 200 kg/m 2 s, q = 24 kW/m 2
Cal G=200kg/m2s,q=24kW/m2
G = 200 kg/m 2 s, q = 24 kW/m 2(c) HFO1234yf:HFC32 = 50:50, G = 200 kg/m2s

0

0.2

0.4
0.6
0.8
1
Vapor quality
Exp G=100kg/m2s,q=12kW/m2
G = 100 kg/m 2 s, q = 12 kW/m 2
Cal G=100kg/m2s,q=12kW/m2
G = 100 kg/m 2 s, q = 12 kW/m 2
Exp G=200kg/m2s,q=12kW/m2
G = 200 kg/m 2 s, q = 12 kW/m 2
Cal G=200kg/m2s,q=12kW/m2
G = 200 kg/m 2 s, q = 12 kW/m 2
Exp G=400kg/m2s,q=12kW/m2
G = 400 kg/m 2 s, q = 12 kW/m 2
Cal G=400kg/m2s,q=12kW/m2
G = 400 kg/m 2 s, q = 12 kW/m 2(d) HFO1234yf:HFC32 = 50:50, q = 12 kW/m2

Figure 13 Comparison of experimental results with predictions by the proposed correlation.

45
40

+30%

(dp/dz)exp (kPa/m)

35
30
25
-30%

20

HFO1234yf

15

HFC32
R32

10

HFO:HFC32 = 80:20
HFO:R32=80:20

5

HFO:HFC32 = 50:50
HFO:R32=50:50

0
0

5

10

15

20

25

30

35

40

45

(dp/dz)cal (kPa/m)
Figure 14 Comparison of experimental pressure drops with predicted values by using
Müller–Steinhagen and Heck [41] model.

Table 1 Experimental conditions
Refrigerant

HFO1234yf

HFC32

Concentration wt%
Quality
Heat flux (kW/m2)
Mass flux (kg/m2s)
Data number

100

100

75

164

HFO1234yf +
HFC32
80:20
0.2–1.06, 12, 24
100, 200, 400
99

HFO1234yf +
HFC32
50:50

138

Table 2 Deviations in predictions of heat transfer coefficients for pure HFO1234yf

Mass flux (kg/m2s),
Heat flux (kW/m2)

Chen
[3]

Yoshidaet al.
[8]Zhang
et al.
[9]

Shah
[13]

Saitohet al.
[17]

100, 12200, 6200, 12200, 24400, 12

0.235
0.086
0.099
0.198
0.092

0.045
0.195
0.175
0.157
0.142

0.188
0.277
0.301
0.320
0.224

0.252
0.112
0.164
0.118
0.114

0.046
0.065
0.046
0.080
0.112

Note: Italicized numbers indicate that the deviation is greater than 0.2.

GungerandWinterton
[19]
0.377
0.223
0.331
0.432
0.186

This
work
0.061
0.114
0.130
0.138
0.098

Table 3 Deviations in predictions of heat transfer coefficients for pure HFC32

Mass flux (kg/m2s),
Heat flux (kW/m2)

Chen
[3]

100, 6100, 12200, 6200, 12200, 24400, 12400, 24

0.312
0.367
0.146
0.192
0.303
0.087
0.201

Yoshidaet al.
[8]
0.276
0.341
0.154
0.147
0.213
0.168
0.103

Zhang
et al.
[9]
0.225
0.278
0.183
0.066
0.141
0.195
0.082

Shah
[13]
0.483
0.525
0.286
0.344
0.406
0.197
0.301

Saitohet al.
[17]
0.424
0.426
0.211
0.321
0.319
0.148
0.292

Note: Italicized numbers indicate that the deviation is greater than 0.2.

Gunger andWinterton
[19]
0.254
0.060
0.293
0.149
0.130
0.112
0.134

This
work
0.243
0.220
0.153
0.069
0.114
0.135
0.087

Table 4 Deviations in predictions of heat transfer coefficients for HFO1234yf + HFC32 (80/20 by
mass%)
Mass flux (kg/m2s),
Heat flux (kW/m2)

Chen
[3]

Yoshidaet al.
[8]Zhang
et al.
[9]Mishraet al.
[29]

100, 6
0.533
0.369
0.507
0.322
100, 12
0.686
0.507
0.691
0.226
200, 6
0.147
0.356
0.397
0.477
200, 12
0.345
0.344
0.489
0.226
200, 24
0.300
0.314
0.506
0.301
400, 12
0.275
0.430
0.516
0.450
400, 24
0.374
0.390
0.537
0.265
Note: Italicized numbers indicate that the deviation is greater than 0.2.

BivensandYokozeki
[30]
0.248
0.462
0.290
0.235
0.277
0.337
0.334

Sami et
al.
[33]

This
work

0.329
0.379
0.307
0.375
0.485
0.359
0.380

0.345
0.540
0.329
0.323
0.337
0.382
0.386

Table 5 Deviations in predictions of heat transfer coefficients for HFO1234yf + HFC32 (50/50 by
mass%)
Mass flux (kg/m2s),
Heat flux (kW/m2)

Chen
[3]

Yoshidaet al.
[8]Zhang
et al.
[9]Mishraet al.
[29]

100, 6
0.052
0.087
0.167
0.218
100, 12
0.155
0.394
0.299
0.269
200, 6
0.208
0.137
0.236
0.361
200, 12
0.101
0.056
0.115
0.421
200, 24
0.169
0.036
0.164
0.459
400, 12
0.078
0.099
0.138
0.619
400, 24
0.083
0.094
0.189
0.607
Note: Italicized numbers indicate that the deviation is greater than 0.2.

BivensandYokozeki
[30]
0.060
0.238
0.092
0.067
0.110
0.088
0.102

Sami
et al.
[33]

This
work

0.371
0.416
0.208
0.417
0.496
0.345
0.410

0.057
0.222
0.098
0.054
0.042
0.072
0.089

Table 6 Deviations in predictions of heat transfer coefficients for HFO1234yf + HFC32 (80/20 by
mass%) using suppression factors for mixtures
Mass flux (kg/m2s),
Heat flux (kW/m2)
100, 6100, 12200, 6200, 12200, 24400, 12400, 24

Chen [3]
0.156
0.264
0.095
0.178
0.158
0.107
0.160

Yoshidaet al. [8]
0.145
0.227
0.195
0.143
0.100
0.246
0.194

Zhang
et al. [9]
0.192
0.357
0.192
0.249
0.220
0.321
0.312

This work
0.080
0.209
0.113
0.093
0.068
0.203
0.193

Note 1: The factors Smix and Fmix are applied to all the correlations.
Note 2: Italicized numbers indicate that the deviation is greater than 0.2.

Table 7 Deviations in predictions of heat transfer coefficients for HFO1234yf + HFC32 (50/50 by
mass%) using suppression factors for mixtures
Mass flux (kg/m2s),
Heat flux (kW/m2)
100, 6100, 12200, 6200, 12200, 24400, 12400, 24

Chen [3]
0.123
0.299
0.130
0.071
0.091
0.068
0.071

Yoshidaet al. [8]
0.105
0.091
0.066
0.084
0.085
0.076
0.061

Zhang
et al. [9]
0.086
0.172
0.124
0.057
0.051
0.099
0.151

This work
0.084
0.146
0.067
0.070
0.063
0.072
0.053

Note 1: The factors Smix and Fmix are applied to all the correlations.
Note 2: Italicized numbers indicate that the deviation is greater than 0.2.

Table 8 Deviations in predictions of pressure drop for pure refrigerants and mixtures
Models

HFO:HFC32= 80:20
Grönnerud [39]
0.302
0.360
0.388
Lockhart–Matinelli [40]
0.238
0.267
0.377
Müller-Steinhagen and Heck [41]
0.203
0.268
0.221
Friedel [42]
0.632
0.614
0.606
Hwang and Kim [43]
0.572
0.613
0.623
Note 2: Italicized numbers indicate that the deviation is greater than.0.3
HFO

HFC32

HFO:HFC32= 50:50
0.249
0.259
0.220
0.660
0.650