Prediction of Critical Heat Flux of Mixtures Flowing in Channels

Abstract

Boiling of mixtures in channels is involved in many chemical processes, and refrigerant mixtures are finding a rapidly increasing use in the refrigeration industries. Hence, reliable prediction of CHF (critical heat flux) is needed. There is no published method that has been verified over a wide range of parameters. In this study, available data for CHF in tubes and annuli were compared to general correlations for tubes and annuli, which are well-verified for single-component fluids. This paper presents the results of this comparison. It was found that general correlations for single-component fluids were in satisfactory agreement with data for mixtures. The data included mixtures of refrigerants and chemicals, reduced pressure 0.02 to 0.8597, mass flux 200 to 3798 kgm⁻²s⁻¹, temperature glide 2.1 to 21.9 K, and critical quality −0.46 to 0.99. The data for annuli were predicted with a MAD (mean absolute deviation) of 13.6%, and the data for tubes had a MAD of 13.9% when compared to the Shah correlations for single-component fluids. Based on the results of the present data analysis and results of research on pool boiling, a range is identified in which pure fluid correlations can be used for mixtures. This will be useful in the design of heat exchangers involving the boiling of mixtures in channels.

1. Introduction

Many applications involve the boiling of mixtures inside tubes. These include chemical processes and refrigeration where mixtures are being increasingly used to replace the refrigerants that cause damage to the environment. Methods to accurately predict CHF (critical heat flux) are therefore needed for designing such heat exchangers. A literature survey showed that no well-verified prediction method is available. Development of such a prediction method is therefore desirable. In order to develop one, it was decided to first compare available data with correlations that have been found reliable for single-component fluids. Data for only those mixtures could be analyzed, which are supported by REFPROP [1]. This comparison showed that data for tubes and annuli were in satisfactory agreement with proven correlations for single-component fluids using mixture properties. The data included mixtures of refrigerants (R-407C, R-12, R-114) and chemicals (benzene, acetone, toluene), reduced pressure 0.02 to 0.8597, mass flux 200 to 3798, temperature glide 2.1 to 21.9 K, and critical quality −0.46 to 0.99. From the results of this data analysis and the study of CHF during pool boiling of mixtures, a range is identified in which pure fluid correlations can be used for mixtures without the need of any correction. The results of the present research are presented, and suggestions are made for further research. Previous work related to this topic is first briefly discussed.

2. Previous Work

The topic of CHF of mixtures has been reviewed by Collier and Thome (1994) [2], Celata et al. (1994a) [3], and Shah (2021) [4]. While there are numerous studies on CHF in pool boiling, there are only a few for flow boiling. A couple of those on pool boiling pertinent to the present work are first discussed.

To help in the following discussions, the phase equilibrium diagram of a typical binary mixture is shown in Figure 1. Point A is the bubble point, point C is the dew point. The difference in temperature between points A and C is the glide. Points A and B show the mole fractions of the more volatile component in the liquid and vapor phases, respectively, at the same temperature. The symbols for these are x’ and y’, respectively.

2.1. Pool Boiling CHF

Fujita and Bai (1997) [5] performed pool boiling CHF tests on seven mixtures and compared their measured CHF with the Zuber (1959) [6] hydrodynamic theory. They noted that the deviation from the Zuber model was related to Δσ = (σ_A − σ_B) where the subscripts “A” and “B” refer to the points in Figure 1. This is the difference in surface tensions at the composition in the liquid phase and the vapor phase at the bubble point temperature. When it is positive, CHF is higher than that given by the Zuber model. When it is negative, CHF is lower than that by the Zuber model. All mixtures showed these trends, but a strong effect was found only in aqueous mixtures. Mixtures of water with alcohols showed up to 2.5 times higher CHF than the Zuber formula. A water–ethylene glycol mixture had a CHF up to 50% lower than the Zuber formula. The four other mixtures were of methanol, ethanol, n-butanol, benzene, and n-heptane. The CHF of these mixtures was close to the Zuber theory. They attributed the variations of CHF to Marangoni flow induced at the vapor–liquid interface as a consequence of the surface tension gradient due to a concentration difference and correlated their data in terms of the Marangoni number. They have also discussed other hypotheses to explain the trends of CHF of mixtures, including those of Van Stralen and Sluyter (1969) [7] and Reddy and Lienhard (1989) [8].

Yagov (2004) [9] extended his dry spot model of CHF in pool boiling to mixtures and arrived at the following formula.

$$q_{c,mix}=q_{c,ef}\left(1+\frac{{\sigma }_A-{\sigma }_B}{{\sigma }_A}\right)$$

(1)

where q_c,ef is the CHF of an equivalent pure fluid with properties of the mixture to be calculated by a correlation for a single-component fluid. He showed this formula to be in satisfactory agreement with mixtures of ethanol and methanol with water from many sources.

2.2. Mixture CHF in Annuli

Sterman et al. (1968) [10] studied the CHF of MIPD–benzene mixtures during boiling in an annulus, 10 mm ID, 16 mm OD. Pressure was 2 bar, subcooling was 20 to 50 K, and velocity was 4 to 12 m/s. They correlated their results by using the following equation. MIPD is the abbreviation for monoisopropyl diphenyl.

$$q_{c,mix}=q_{c,I}\left(1+\beta \right)$$

(2)

where

$$q_{c,I}=q_{C,A}\dot{x^{\prime }+q_{c,B}(1-x^{\prime }})$$

(3)

q_c,A is the CHF of pure component A, and q_c,B is that of pure component B. x′ is the mole fraction of component A in the liquid phase. The parameter β was given as:

$$\beta =1.5\frac{{\left(\left|y^{\prime }-x^{\prime }\right|\right)}^3}{{\left(\frac{GD}{{\mu }_L}\right)}_A}+6.9\frac{{\left(\left|y^{\prime }-x^{\prime }\right|\right)}^{1.5}}{{\left(\frac{GD}{{\mu }_L}\right)}_A^{0.4}} \left(\frac{T_{SAT,B}}{T_{SAT,mix}-T_{SAT,B}}\right)$$

(4)

y′ is the mole fraction of component A in the vapor phase.

Carne (1963) [11] performed tests on binary mixtures of acetone/toluene and benzene/toluene in a vertical annulus. Andrews et al. (1968) [12] tested the same mixtures in an annulus of dimensions close to that used by Carne.

Tests on mixtures of MIPD/dipheny have been performed by Naboichenko et al. (1965) [13]. Annulus ID was 2.94 mm and OD 16.37 mm, subcooling was 25 to 125 K, and velocity 4 to 8 m/s.

2.3. Mixture CHF in Tubes

Tolubinsky and Matorin (1973) [14] measured CHF for benzene–ethanol mixtures and various aqueous mixtures in a 4 mm diameter tube. Pressure was 3.3 to 13.2 bar, subcooling 10 to 110 K, and liquid velocity 2.5 to 10 m/s. They do not say whether they compared their data with the Sterman et al. correlation, Equation (2) with Equation (4) for β. They correlated their data with Equation (2) but with β as below.

$$\beta =1.5{\left(\left|y^{\prime }-x^{\prime }\right|\right)}^{1.8}+6.8\left(y^{\prime }-x^{\prime }\right)\left[\frac{T_{SAT,mix}-T_{SAT,B}}{T_{SAT,B}}\right]$$

(5)

This suggests that their data did not agree with the Sterman et al. correlation.

Celata et al. (1994b) [15] performed tests with mixtures of R-12/R-114 in a vertical tube. Data were in excellent agreement with the Sterman et al. correlation, Equations (2)–(4), using the measured values of q_c for pure R-12 and R-114. They also found good agreement with the Katto and Ohno (1984) [16] correlation for pure fluids using mixture mean properties.

Sindhuja et al. (2008) [17] studied the CHF of R-407C in a vertical tube over a wide range of flow rate, pressure, and quality. They compared their data with three pure fluid correlations. These are the CHF lookup table of Groeneveld et al. (1993) [18], the Katto and Ohno (1984) [16] correlation, and Vijayarangan et al. (2006) [19]. The first two gave large deviations while the last one gave good agreement with their data.

Mori et al. (1990) [20] performed tests with R-22/R-114 mixtures in a vertical tube of 9 mm diameter at 2.3 to 4.8 MPa. No significant effect of mol fraction of components was found.

Auracher and Marroquin (1995) [21] performed tests with R-13B1/R-114 mixtures flowing up in a vertical tube of 17 mm diameter. Pressure was 11 bar, mass flux 1000 kg/m²s, and quality −0.4 to 0.2.

Robinson and Lurie (1962) [22] performed tests with organic reactor coolant mixtures. Their tests were performed in an 8.4-mm diameter vertical tube. The pressure was 1.6 to 10.3 bar, mass flux 1088 to 7122 kg/m²s, and subcooling 19 to 157 K.

In some of the above studies, it was found that at some mixture concentrations CHF can be higher than either of the pure components by a small amount.

3. Present Data Analysis

It is clear from Section 2 that there is no well-verified correlation for the CHF of mixtures in tubes or annuli. The correlation of Sterman et al. (1968) [10] for annuli was based only on their own data and was later found to be also in good agreement with the data of Celata et al. (1994b) [15]. While this is encouraging, more verification is needed to gain confidence in its reliability. Considering the widespread and increasing use of mixtures, there is clearly a need for a well-verified correlation. To achieve this goal, it was decided to first compare the available test data to correlations that have been shown to be accurate for pure fluids over a wide range of parameters, study the deviations of the data from these correlations, and then modify an existing correlation or develop a completely new one.

3.1. Choice of Correlations for Evaluation

The first step was to choose the pure-fluid correlations for comparison with data. All the available data are for vertical upflow in channels. Hence only such correlations need to be looked into. For tubes, the most verified general correlations are Shah (1987) [23] and Katto and Ohno (1984) [16]. Shah (1987) [23] analyzed data for 23 fluids (water, refrigerants, cryogens, chemicals, and liquid metals), tube diameters 0.315 to 37.5 mm, mass flux 4 to 2905 kgm⁻²s⁻¹, reduced pressure 0.0014 to 0.96, and critical quality −0.26 to 0.96. The MAD of the Shah and the Katto–Ohno correlations were 16.0 and 22.3%. With the increasing interest in mini channels (usually considered those with D < 3 mm), Shah (2017) [24] collected a database of CHF in minichannels with diameters 0.13 to 3 mm. He compared this database with the correlations of Shah (1987) [23], Katto–Ohno (1984) [16], Zhang et al. (2006) [25], and Wojtan et al. (2006) [26]. Their MAD for all data were, respectively, 18.9, 33.2, 23.4, and 59.7%. In view of the poor performance of the Wojtan et al. correlation, it was decided to compare the tube data only to the correlations of Shah, Katto–Ohno, and Zhang et al.

For annuli, only two general correlations, i.e., those applicable to a wide range of fluids and parameters, have been published. These are Shah (2015a) [27] and Katto (1979) [28]. The Shah correlation is applicable to internally, externally, and bilaterally heated annuli while the Katto correlation is essentially limited to internally heated annuli. The Katto correlation has three regimes, namely L, H, and N. The correlation requires a factor K for each regime, which was provided for regimes L and H but was not provided for regime N. Shah (2015a) compared these two correlations to a wide-ranging database that included all three heating types. The Shah correlation had a MAD of 16.5% for all data while that of the Katto correlation for internally heated annuli in the L and H regimes was 233%. Doerffer et al. (1994) [29] and Hung and Yao (1983) [30] had also found it unsatisfactory. It was therefore decided to compare the annuli CHF data to only the Shah correlation.

The Shah correlations for CHF in tubes and annuli [23,27] are given in Appendix A and Appendix B.

3.2. Selection of Test Data

The published test data have been identified in Section 2.2 and Section 2.3. It is certainly desirable to analyze all available test data. The difficulty in doing so is in not being able to calculate accurately the properties of some mixtures. The concentration of components of mixtures is different in the vapor and liquid phases, and it changes along the tube length as the liquid evaporates, the more volatile component evaporating faster. Therefore, the properties of the phases change as the evaporation progresses. Calculating mixture properties is therefore very difficult without the support of a reliable software. The present author uses REFPROP 9.1, Lemmon et al. (2013) [1]. REFPROP is the most widely used property software. Developing programs to reliably predict properties of mixtures not supported by REFPROP will itself be a major project. Therefore, data for mixtures not supported by REFPROP were not analyzed. REFPROP 9.1 and its latest version does not provide transport properties of mixtures containing water or alcohols, as reliable general models for this purpose are not available to the developers of this program (Huber 2022 [31]). Further, it does not have properties of R-13B1, MIPD, and organic reactor coolants used by Robinson and Lurie (1962) [22]. For this reason, only the data listed in

Table 1. Results of comparison of data for CHF in tubes with some correlations. All tubes are vertical, and flow is upward.

Source	D, mm	L/D	Fluid (Mol Fractions)	pr	Glide, K	Δσ, mNm−1	G	xin	xc	N	Deviation, % MAD (Above)/AD (Below)
											Shah [23]	Katto and Ohno [16]	Zhang et al. [25]
Sindhuja et al. (2008) [25]	12.7	205	R-407C	0.6632	3.5	0.248	200	−0.06	0.99	1	7.4 −7.4	4.3 4.3	11.7 11.7
Celata et al. (1994) [4]	7.57	277	R-12/R-114 (0.136/0.864)	0.3500 0.6770	2.1	0.081	393 1684	−0.6 −0.2	0.24 0.84	14	27.7 23.3	47.2 46.9	45.4 44.9
			R-12/R-114 (0.377/0.623)	0.3298 0.6770	5.5	0.374	431 1634	−0.48 −0.23	0.26 0.67	14	19.4 10.0	32.2 31.3	34.1 33.0
			R-12/R-114 (0.586/0.414)	0.3164 0.6770	6.9	0.498	402 1607	−0.41 −0.22	0.30 0.86	14	14.0 2.0	21.0 20.2	24.5 23.4
			R-12/R-114 (0.787/0.213)	0.3006 0.6770	6.5	0.503	421 1578	−0.38 −0.20	0.30 0.98	14	6.9 −3.2	15.7 13.7	21.1 19.0
			R-12	0.2910 0.6770	NA	NA	384 1571	−0.36 −0.22	0.29 0.95	14	7.0 1.2	18.8 17.8	25.5 24.2
			R-114	0.3684 0.8597	NA	NA	414 1773	−0.72 −0.26	0.01 0.73	14	9.0 7.8	22.1 22.1	24.4 16.9
All data				0.2910 0.8597	2.1 6.5	0.081 0.503	200 1773	−0.48 −0.06	0.01 0.99	85	13.9 6.7	25.9 25.1	29.0 26.7

and

Table 2. Range of data for CHF in annuli and results of comparison with the Shah correlation. Mixture composition varied between 10 and 90% of each component.

Source	Din, mm	Gap, mm	L/DHP	Fluid	pr	Glide, K	Δσ, mNm−1	G Kgm−2s−1	xin	xc	N	Deviation MAD (Above)/AD (Below)
Andrews et al. (1968) [1]	6.3	7.2	1.2	Benzene–Toluene	0.021 0.024	3.0 6.1	−0.018 0.109	912 3723	−0.26 −0.19	−0.19 −0.17	16	10.1 9.7
				Acetone–Toluene	0.021 0.022	4.1 21.0	0.445 2.764	1705 3583	−0.15 −0.04	−0.14 −0.03	12	26.9 25.7
				Acetone	0.021	NA	NA	2450	−0.13 −0.04	−0.13 −0.04	3	30.2 30.2
				Toluene	0.024	NA	NA	850 3400	−0.22 −0.11	−0.21 −0.05	10	9.7 9.7
				Benzene	0.020	NA	NA	407 3549	−0.39 −0.20	−0.39 −0.18	9	9.6 5.1
Carne (1963) [3]	6.3	6.4	1.5	Acetone–Toluene	0.046 0.048	3.4 21.9	0.396 2.680	1633 3588	−0.28 −0.09	−0.25 −0.08	41	10.2 5.6
				Benzene–Toluene	0.047 0.053	2.8 5.8	0.007 0.034	1759 3770	−0.43 −0.21	−0.43 −0.21	46	9.3 5.7
				Acetone	0.047	NA	NA	1620 3440	−0.27 −0.10	−0.27 −0.09	16	23.7 23.7
				Toluene	0.054	NA	NA	1720 3640	−0.48 −0.13	−0.46 −0.12	13	15.6 10.7
				Benzene	0.045	NA	NA	1803 3798	−0.40 −0.21	−0.39 −0.20	16	9.6 −0.8
All	6.3	6.4 7.2	1.2 1.5		0.021 0.053	2.8 21.9	−0.018 2.764	407 3798	−0.48 −0.04	−0.46 −0.3	181	13.4 9.8

could be analyzed. These data were read from the figures in the publications.

3.3. Results of Data Analysis

The results for data analyzed for tubes are listed in Table 1, and those for annuli are in Table 2. The range of all data analyzed is listed in

Table 3. Range of parameters in the data analyzed.

Parameter	Range
Fluids	R-407C; mixtures R-12/R-114, acetone/benzene, acetone/toluene, benzene/toluene (mol fraction of components 0 to 1)
Flow channels	Vertical tubes and annuli with upflow
Tube diameter, mm	7.57 to 12.7
Annuli	Internally heated, tube diameter 6.3 mm, gap between tubes 6.4 to 7.2 mm
L/DHP	1.2 to 277
Reduced pressure	0.021 to 0.677 for mixtures. 0.02 to 0.86 for pure fluids.
Mass flux, kgm−2s−1	200 to 3798
Glide, K	2.1 to 21.9
Δσ, mNm−1	−0.02 to 2.8
Inlet quality	−0.78 to −0.03
Critical quality	−0.46 to 0.99

. The deviations listed in the tables are the mean absolute deviation (MAD) and the average deviation (AD). These are defined as below.

$$MAD=\frac{1}{N}{{\displaystyle \sum }}_1^{N}ABS\left\{\left(q_{c,predicted}-q_{c,measured}\right)/q_{c,measured}\right\}$$

(6)

Average deviation (AD) is defined as:

$$AD=\frac{1}{N}{{\displaystyle \sum }}_1^{\mathrm{N}}\left\{\left(q_{c,predicted}-q_{c,measured}\right)/q_{c,measured}\right\}$$

(7)

Results for the pure fluids have also been listed to permit comparison with those of their mixtures.

It is seen in Table 1 that the data of mixtures in tubes are in close agreement with the Shah correlation. The MAD for mixtures is comparable to that for the pure components. The other two correlations also do fairly well. Their deviations are higher than those of the Shah correlation but are comparable with their deviations for the pure components.

Table 2 for annuli shows that the data for mixtures are in good agreement with the Shah correlation, and deviations for mixtures are comparable to those of their pure components.

4. Discussion

4.1. Variation of CHF with Mixture Composition

Figure 2, Figure 3, Figure 4 and Figure 5 show the variations of CHF as a fraction of the more volatile component of the mixture varies from 0 to 1. It is seen that in some cases CHF at some composition is a little higher than of either component, but the excess is small and is within the margin of experimental uncertainty. The predictions of the Shah (2015a) [27] correlation are always close to the measured values. As is seen in Figure 2, it also predicts a CHF higher than that of either pure component. So, the variations in CHF are accounted for by the change in properties with change in composition.

Some data show very complex variations of CHF with composition. An example is the data of Carne (1963) [11] shown in Figure 3, in which CHF has almost sinusoidal variations with composition. Note that there was considerable scatter in the data while Figure 3 gives the data points on the curve drawn through the data by Carne. Carne himself says about this figure that in view of the data scatter, these maxima have no significance, and the existence of the turning point itself is doubtful. Note that the Shah correlation agrees fairly closely with the measured CHF values.

It can be concluded that for the data analyzed, the Shah correlations for tubes and annuli adequately predict the variations of CHF with composition. However, this may not be the case for mixtures in which surface tension differences are large, as discussed in Section 4.2.

4.2. Effect of Surface Tension Difference

As was discussed in Section 2.1, Fujita and Bai (1997) [5] measured pool boiling CHF of seven mixtures. For mixtures with Δσ variation between −2.4 to 2.0 mN/m, they found that CHF of the mixture was close to the prediction of the Zuber model. By contrast, CHF was 2.5 times the Zuber prediction when Δσ was 20 mN/m and 50% lower than the Zuber prediction when Δσ was −10 mN/m.

As seen in Table 1, Table 2 and Table 3, Δσ in the present data analysis varied from −0.02 to 2.8 mN/m, and data over the entire range are in satisfactory agreement with the Shah correlations. Deviations of the Shah (2015a) [27] correlation with annulus data are plotted against Δσ in Figure 6. There is no indication in it that deviations are related to Δσ. Deviations of a few data points are high at both small and large Δσ. All such data are for mixtures of acetone. Some data for pure acetone also had similar deviations. This behavior may be due to small amounts of impurities in acetone. No data other than those for acetone and its mixtures had deviations greater than 25%.

Based on the present data analysis and the pool boiling results of Fujita and Bai, it seems that the Shah correlations for tubes and annuli can be used without any correction in the range of Δσ from −2.4 to 2.8 mN/m.

4.3. Effect of Glide

As seen in Table 1, Table 2 and Table 3, the glide of mixtures was up to 21.9 K. Data over this entire range of the glide for tubes and annuli are in satisfactory agreement with the Shah correlations. The glide is used as a parameter in the Bell and Ghaly (1973) [32] correction factor for the heat transfer coefficient of mixtures. The larger the glide, the greater the reduction in the heat transfer coefficient compared to pure fluid. The glides of most mixtures in use or being considered for use in refrigeration systems is well below 20 K.

4.4. Mass Flux

Mass flux in the data analyzed varied from 200 to 3798 kgm⁻²s⁻¹, a very wide range. As seen in Table 1 and Table 2, the data over the entire range are satisfactorily predicted. Figure 7 and Figure 8 show the comparison of data of mixtures in tubes over a wide range of mass flux with the correlations of Shah, Katto and Ohno, and Zhang et al. The Shah correlation is seen to be in close agreement with the data. The predictions of the other two correlations are not too far off.

4.5. Reduced Pressure

Reduced pressure is a very important parameter as properties of fluids vary strongly with reduced pressure. Many correlations are known to fail at extremes of reduced pressure. The reduced pressure in the mixture data analyzed varied from 0.021 to 0.677, a wide range. For the pure components, the reduced pressure was up to 0.86. In fact, the reduced pressure in the pure fluid data analyzed in Shah (1987) [23] for tubes was up to 0.96 and in Shah (2015a) [27] for annuli up to 0.906. As the mixture data analyzed were limited to 0.677 reduced pressure, applicability to higher reduced pressures is subject to verification.

4.6. Inlet and Critical Qualities

CHF is basically of two types. One is DNB (departure from nucleate boiling) and the other is dryout. DNB occurs because of the inability of liquid to reach the tube surface due to intense vapor generation. Dryout occurs due to drying out of the liquid in contact with the surface due to evaporation. DNB occurs at a subcooled condition (negative quality) or at low vapor qualities. Dryout occurs at higher vapor qualities. As seen in Table 1, Table 2 and Table 3, critical quality varied from −0.46 to 0.99. Thus, both types of CHF are included in the data analyzed. The inlet quality varied from −0.78 to −0.03. There were no positive quality data in the present data analysis. However, the Shah (1987) [23] correlation for tubes and the Shah (2015a) [27] correlation for annuli were verified with pure fluid data that included large positive inlet qualities.

4.7. Orientations Other Than Vertical Upflow

All the data analyzed in the present study are for vertical upflow. Use of horizontal channels is widespread. In horizontal channels, stratification occurs at lower flow rates. This causes the upper part of channel to dry out and have CHF while the lower part remains in contact with liquid. Several correlations have been developed for CHF of pure fluids in horizontal channels. These were reviewed in Shah (2015b) [33] and Shah (2021) [4]. Shah (2015b) [33] developed a correlation for CHF in horizontal tubes, which is in the form of a correction factor to the CHF in vertical upflow calculated with the Shah (1987) [23] correlation. It was verified with a wide range of data and was shown to be much more accurate than other correlations. It is likely to be applicable to mixtures but needs to be verified when data become available.

For orientations other than vertical upflow and horizontal, there are no well-verified prediction methods even for pure fluids. Gong et al. (2022) [34] have reviewed the literature on the effect of orientation on the CHF of pure fluids.

4.8. Correlations for Mixture CHF

The correlation of Sterman et al. (1968) [10] was discussed in Section 2.2. It predicts the CHF of mixtures using the values of CHF of the pure components. It was shown by them to be in good agreement with their data for MIPD/benzene mixtures in a vertical tube. CHF occurred under a subcooled condition. They used their measured values of CHF of the pure components. Celata et al. (1994b) [15] found it to be in good agreement with their data for the R-12/R-114 mixture, again using the measured values of CHF of the pure components; CHF occurred at high vapor qualities. Thus, this correlation has been shown to agree with data for both DNB and dryout and could be generally applicable. As it requires the CHF of pure components to be inserted in it, its accuracy is limited by the accuracy of the correlations to predict pure fluid CHF. As the Shah (1987) [23] correlation predicted the CHF of mixtures with the same accuracy as for pure fluids, it is not possible to evaluate the accuracy of the Sterman et al. correlation using the data analyzed in the present study. Some doubts about the general applicability of the Sterman et al. correlation are raised by the fact that Tolubinsky and Matorin (1973) [14] gave their own formula for β to fit their data. This might have been because β from the Sterman et al. formula did not agree with their data.

The correlation of Tolubinsky and Matorin (1973) [14], Equation (5), was verified only with their own data. Hence, its general applicability is unknown. Note that this correlation also requires the value of CHF of the pure components, which have to be calculated by a suitable correlation.

5. Conclusions

• Data for CHF mixtures of halocarbon refrigerants (R-407C, R-12, R-114) and mixtures of chemicals (benzene, acetone, toluene) in annuli and tubes were compared to well-verified general correlations for pure fluids. The data included subcooled CHF as well as at high qualities. The range of flow rates and reduced pressures was very wide.
• Based on the results of this data analysis and results of pool boiling CHF, the best recommendation is that correlations for pure fluids can be used without any correction to predict CHF of mixtures provided that Δσ is the range −2.4 to +2.8 mN/m. Δσ is the difference between surface tension of the mixture at a vapor phase composition and that at a liquid phase composition, both at the same liquid phase temperature. The data analyzed were in this range and were in good agreement with the correlations of Shah (1987) for tubes and Shah (2015a) for annuli, both well verified for pure fluids.
• Most refrigerant mixtures have Δσ in the range stated above, and hence, this result will be particularly useful in the design of refrigerant evaporators.
• There is no verified method for calculation of CHF when Δσ is outside the range −2.4 to +2.8 mN/m.
• A number of available data sets for mixture CHF could not be analyzed due to the unavailability of software for calculating their properties. There is a need to develop software to predict properties of such fluids and mixtures.
• There is a great need for more experimental studies on the CHF of mixtures so that reliable methods to calculate the CHF of all types of fluid mixtures could be developed.