Forced Convective Boiling of Hydrocarbon Mixtures

Forced Convective Boiling of Hydrocarbon Mixtures by J. R. Barbosa, Jr. and G. F. Hewitt Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine London, SW7 2BY.

ABSTRACT This paper describes a model for evaporation of hydrocarbon mixtures in vertical pipes, the evaporation taking place mainly in the forced convective (annular flow) region where nucleate boiling is expected to be greatly suppressed. The model takes account of the detailed processes of droplet entrainment and deposition. The model is compared with recent data obtained from a large scale high pressure boiling facility [Kandlbinder, 1997, Kandlbinder et al., 1998]. It is shown that taking account of liquid phase mixing due to entrainment and deposition gives predictions closer to the observations. Key words: Boiling, evaporation, heat transfer, mixture effects, annular flow.

1. INTRODUCTION Phase change heat transfer to mixtures is of indisputable technological relevance. Operations in which boiling of multicomponent organic mixtures take place are the rule rather than the exception in the process industry. Despite the evident importance of the subject, there is a dearth of experimental data for hydrocarbon mixtures and adequately detailed predictive models. Experimental data obtained recently using a high pressure multicomponent boiling rig at the Harwell laboratory of AEA Technology revealed many new features of forced convective multicomponent evaporation [Kandlbinder, 1997, Kandlbinder et al., 1998]. For instance, the increase in the heat transfer coefficient with quality characteristic of forced convective boiling often did not occur in these systems; indeed the coefficient sometimes actually decreases with increasing quality. These trends are not predicted either quantitatively or qualitatively by existing correlations and was this failure in prediction which led to the present work. Kandlbinder et al. [1998] suggest that the effects observed may be connected to the influence of droplet entrainment. At a given location along the channel, the droplets may have a higher concentration of the more volatile component than does the liquid film. This leads to an increase in film interface temperature relative to that calculated on the assumption of an equilibrium between the (mixed) liquid and the vapour (i.e., temperature normally used in calculating the heat transfer coefficient). This makes the apparent heat transfer coefficient lower and could explain the effects observed in the Kandlbinder et al. experiments.

Though Kandlbinder et al. explored this mechanism in a qualitative way, these remained the challenge of representing the processes quantitatively. In the present study, a quantitative model has been developed including a representation of the droplet entrainment/deposition processes. In what follows, a brief literature overview of predictive models for forced convective boiling of mixtures is given in section 2. Section 3 summarises the experiment carried out by Kandlbinder [1997]. The annular flow model and the main assumptions are discussed in detail in Section 4. Results for various conditions are presented in Section 5. Finally, conclusions from these studies are drawn in Section 6.

2. PREVIOUS PREDICTION METHODS FOR FORCED CONVECTIVE BOILING OF MIXTURES Predictive methods for boiling of pure fluids form the basis for development of methods for mixtures. Of all correlations for pure fluids, the most widely used is the one proposed by Chen [1966]. Chen postulates that the heat transfer coefficient is made up the sum of two parts, (a) a micro-convective (or nucleate boiling) portion,

, and, (b) a macro-convective (or forced convective) portion,

,

,

(1)

is calculated using the Forster and Zuber [1955] correlation, , and

(2)

is given by a Dittus-Boelter relationship, .

(3)

The contributions of the nucleate boiling and of the forced convective parts are weighted by suppression, S, and two-phase enhancement factors, F, respectively. These are as follows, , if

,

, if

,

(4)

,

(5)

where, ,

(6)

The wall to saturation temperature and pressure differences are defined as . The two-phase Reynolds number is Reynolds number for the liquid flowing alone in the channel.

and , where

is the

Shock [1977] compared the performance of several correlations and concluded that the Chen correlation worked quite well for a variety of fluids including pure hydrocarbons; it could also be applied to cryogenic fluids. An upgrade to the Chen correlation for mixtures was proposed by Bennett and Chen [1980], based on data obtained with an ethylene glycol-water mixture. Modified enhancement and suppression factors, Fmix and Smix, were proposed so as to cope with mixture effects in both micro and macro-convective portions. These are shown below, ,

(7)

and .

(8)

,the mass transfer coefficient for the liquid, are calculated via a Dittus-Boelter relationship using a modified two-phase Reynolds number in the form, (9) Celata et al. [1993] compared both Chen [1966] and Bennett and Chen [1980] correlations for boiling of refrigerant mixtures. They found that the performance of the correlation for pure fluids is very similar to that for mixtures. The Chen [1966] correlation having only a slightly larger scatter in the data for an error band greater than ± 20 %. The correlation by Mishra et al. [1981] was also implemented, but it showed lower accuracy. Palen [1983] also suggests the use of a modified form of the correlation by Chen [1966] for boiling of mixtures. In this case, no correction is made for the forced convective contribution. The heat transfer coefficient is given by, , where

(10)

is a mixture correction factor defined by Palen and Small [1964] as , ,

and

(11)

is the boiling range (difference between the dew point and the bubble point temperatures).

Kandlbinder[1997], after comparing the performance of several correlations for boiling of binary mixtures, concluded that, though none of the existing correlations performed well, the correlation by Palen [1983] gave the best results. Thus, the correlation by Chen [1966] with the correction by Palen [1983] was chosen for the comparisons to be carried out in the present paper. Other examples of correlations based on expressions for boiling of single components are those by Jung et al. [1989] and Kandlikar [1991]. In forced convective evaporation of binary mixtures in annular flow, the interface concentration of each component will normally be different to their concentrations in the bulk vapour. The interface concentrations must be such to allow the diffusion of the evaporating material from the interface into the bulk. This leads to a mass transfer resistance effect analogous to that found in condensation. Thus,

whereas in condensation of multicomponent mixtures, the interface temperature is reduced relative to the equilibrium value, the interface temperature is increased relative to the equilibrium value. Two main types of methods have been used for estimating these mass transfer effects. The first class of methods is based on the approximate methods for condensation developed by Silver [1947] and Bell and Ghaly [1973] (the SBG methods); the studies of Palen et al. [1980], Sardesai et al. [1982] and Murata and Hashizume [1993] fall into this category. A more refined class of models are those based on the socalled Colburn film theory. Shock [1976] investigated theoretically the purely convective region by writing balances for the components over an element as the sum of diffusive and net flow portions. Closure relationships for heat and mass transfer on the vapour side were given by the Chilton-Colburn analogy. In the liquid film, mass transfer was calculated via an extension of the method of Hewitt [1961] for heat transfer in single component flows. The model was applied to water-ethanol mixtures and, as the main conclusion, it can be said that the role of mass transfer resistance within the phases was found to be not very important in the cases studied. However, an evaluation of the model for mixtures with wider boiling ranges is still needed and this is currently being pursued by the present authors. For the study reported here, however, it is assumed that the temperature difference between the interface and the bulk vapour is negligible, in line with Shock's conclusions. In the present study, attention is focused on the influence of mixing processes between entrained droplets and film on the effective heat transfer coefficient.

3. EXPERIMENTS As was mentioned in the Introduction, the focus for the present work was on predicting newly-observed trends in forced convective evaporation of mixtures based on data obtained using a high pressure multicoponent boiling facility at the AEA Technology plc site at Harwell, Oxfordshire, UK. Details of the apparatus and of the data obtained are given by Kandlbinder [1997] and Kandlbinder et al. [1998]. However, it was felt worthwhile to give a brief description of the experiment in the present paper since this forms important background information to the development and exploitation of the model. A schematic of the HTFS High Pressure Boiling facility is shown in Fig. 1. The rig consists of three loops, namely the circulating, pressurising and degassing loops. The main circuit contains the vertically oriented test section, a shell and tube condenser, a circulating pump a 75 kW electrical pre-heater, a density meter and a flow meter. The pressure is generated by two centrifugal pressurising pumps, pumping against a partly open control valve in the main loop. Fine adjustment of pressure is possible by speed control of the pressurising pumps. The test section is a 8.5 m long, 321 stainless steel tube with a nominal inner diameter of 25.4 mm and an outer diameter of 38.0 mm. Uniform heating can be achieved by Joule effect, passing a large DC current (up to 4000 A) at a low voltage (up to 30 V) through the test section wall. The non-uniformity of the heat generation due to changes in the electrical resistivity can be neglected because of the small changes in the wall temperature along the test section for boiling experiments. The test section is equipped with 70 thermocouples attached to the outer wall at a spacing of 100 to 150 mm. The inner wall temperature is calculated from the one-dimensional steady-state conduction equation, correcting for heat losses. The bulk temperature is measured at 12 locations along the test section (spaced at 750 mm intervals).To achieve that, thermocouple pockets were created out of 2 mm diameter hypodermic tubes which were bent at a right angle and positioned at the centreline of the

tube with the tip facing the flow. The tips were sealed before the tubes were welded into position. In these pockets, sheathed thermocouples could be fed right into the tip. Three absolute pressure transducers were located at the bottom, middle and top of the test section, with differential pressure cells located every 750 mm along the test section. The bulk and wall thermocouples were checked against a calibrated dry block calibrator which had an accuracy of ± 0.3K. It was found that the thermocouple outputs were within the accuracy of the calibrator.

Fig. 1. The High Pressure Boiling experimental facility. 4. MODELLING The model described here is for forced convective heat transfer in annular flow; the effect of nucleate boiling is taken into account using the method of Palen [1983] (see Equation 10). However, it should be noted that nucleate boiling has a relatively minor role, contributing typically 10-30% of the total heat transfer coefficient. The model proceeds by the following steps: (1) At the onset of annular flow, the liquid phase is assumed fully mixed and it is assumed that a fixed fraction of the liquid was entrained at this point. The onset of annular flow is assumed to occur at a value of

of 1.0, where

is the Wallis parameter;

(2) From the point of onset of annular flow until the end of the channel, the channel is divided into a number of successive zones (typically 100). For each given zone, the entrainment rate of drops is

determined and these drops are convected along the channel. The entrained drops arising from the zone are assumed to have the same composition as the film from which they were created. Simultaneously, droplets from upstream zones (which have different compositions) are deposited in the given zone. Balance equations can then be written for the liquid flow and for the components. From these balances, the liquid film flowrate and the composition of each component in the liquid film can be determined; (3) For a given location, the heat transfer process can then be predicted. Transfer from the wall to the interface is calculated on the basis of a film heat transfer correlation; the forced convective element of the Chen [1966] correlation is used for convenience. The interface temperature is calculated as that at which the interface and the bulk vapour are at equilibrium (temperature differences arising from mass transfer in the vapour are neglected, as discussed above). The liquid film is considered to be well mixed such that the liquid composition at the interface is considered identical with the mean liquid concentration in the film. This is the most commonly used assumption in condensation calculations and is used here for the evaporation case also. The assumption has some background justification through the work of Shock [1976], mentioned above. The liquid film heat transfer coefficient is calculated by adding the forced convective and (much smaller) nucleate boiling coefficients. The nucleate boiling coefficient is estimated by calculating

from Equation 2 and

multiplying this by the suppression factor S (Equation 5) and by the Palen [1983] mixture factor (Equation 11); (4) Since the interface temperature and the film heat transfer coefficient are known from the above, the wall temperature may be calculated and compared with the measured values. The details of the droplet entrainment/deposition calculation and of the associated component movement are given by Barbosa and Hewitt [1999]. The methodology will be only summarised here. The following differential equations are obtained through mass balances over an element of tube of length dz (see Fig. 2). Equations (12)-(14) represent overall mass conservation for the liquid film, vapour core and liquid entrained as droplets. Equation (15) is a component mass balance for the liquid film. ,

(12)

,

(13)

,

(14)

.

D and E are the deposition and entrainment rates, respectively. The operator

(15)

, introduced by Barbosa

and Hewitt [1999], expresses the effect of deposition, at a certain co-ordinate, of droplets having different concentrations.

Fig. 2. Mass balance over an element of length dz. A physical justification for the concentration unbalance between the film and the droplets core is briefly explained as follows. As the more volatile component is preferentially depleted from the liquid stream, an axial gradient of concentration is set up in the liquid film. If the vaporisation rate of the liquid film is much higher than that of the droplets in the core, then it is not illogical to assume that, whilst in the vapour core, the droplets retain a concentration approximately equal to that of the liquid film at the point where they were created (entrained). Thus, droplets generated at distinct co-ordinates have distinct concentrations and, at a particular co-ordinate, a spectra of concentration is found in the population of depositing droplets. Closure relationships for the hydrodynamics of the model are provided by the triangular relationship between film thickness, film flowrate and interfacial shear stress. The latter is calculated via a correlation by Hewitt and Whalley [1978]. The entrainment and deposition rates are calculated using the set of correlations by Govan et al. [1988], to which modifications to account for mixture effects were made by Barbosa and Hewitt [1999]. A significant amount of liquid may be entrained as droplets at the onset of annular flow, perhaps as a result of high liquid entrainment also present in the churn flow regime [Hewitt and Hall-Taylor, 1970]. There is at present no general method for calculating the entrained fraction at the onset of annular flow. One possible assumption is that deposition and entrainment are at equilibrium (i.e. equal) at this point; for the present data, this would give entrained fractions in the range 5-10% at the onset of annular flow. However, this takes no account of the proximity to churn flow and the actual values are likely to be higher. In the present work, the approach has been to assume a series of values covering the likely range (i.e. 0, 10, 20, 40 and 50%) and to carry out calculations for each of these values. A flash calculation based on the Peng and Robinson [1976] equation of state is used to determine the film mass evaporation rate from the (known) heat flux and the film (interface) temperature.

In order to validate the analysis, comparisons with experimental data have been carried out in two different ways: (1) Comparison of predicted and measured wall temperature; (2) Comparison of heat transfer coefficients. The heat transfer coefficient in multicomponent mixtures is normally defined by the following equation, ,

(16)

where TE is the flow equilibrium bulk temperature calculated from local mean enthalpy and pressure. As a result of the postulated existence of different compositions in the film and in the droplets, by Equation (16) will be different from

as defined

as defined by the ratio of the heat flux to the temperature

difference across the film. However, since the wall temperature, Tw, is calculated by the present methodology, since TE can also be estimated using the vapour-liquid equilibrium package and since is known, it will be possible to obtain a predicted heat transfer coefficient from Equation 16 which can be compared with (a) the experimental heat transfer coefficient calculated from Equation 16 using the measured values of T w; (b) the heat transfer coefficient calculated from the Chen [1966] correlation (Equations 1-6) without taking any account of mixture effects; the heat transfer coefficient calculated from the Chen [1966] correlation but with the nucleate boiling term corrected for mixture effects using the empirical correlation of Palen [1983].

5. RESULTS 5.1. COMPARISON OF EXPERIMENTAL AND PREDICTED WALL TEMPERATURES. To asses the performance of the present model, comparisons were made with the data sets of Kandlbinder [1997] listed in Table 1. Table 1. Experimental conditions for Pentane/Octane mixture used in comparisons. Case No.

Mole fraction of n-Pentane

Pressure [MPa]

Mass flux -2 -1 [kgm s ]

Heat Flux -2 [kWm ]

1 2 3 4 5

0.7 0.7 0.7 0.7 0.35

0.23 0.32 0.61 1.02 0.22

292.8 305.0 503.8 508.9 297.1

49.8 49.3 68.4 59.6 49.3

The predictions from the present model are compared with measured wall temperatures in parts (a) of Figs. 3-7. Wall temperatures increase somewhat with increasing initial entrained fraction but the effect is relatively small. In general, the model gives encouragingly good predictions of the wall temperatures though there is a tendency to underpredict the wall temperature at higher values of z (i.e. high qualities) and at higher pressures. Introduction of the droplet mixing concept goes a long way, therefore towards explaining the reductions in heat transfer coefficients found in the Kandlbinder experiments. The parts (b) of Figs. 3-7 show calculations of wall temperature based on the simplified concept introduced by Kandlbinder et al. [1998], namely an entrained droplet flow which is fixed as a given fraction of the total liquid flow at the onset of the annular regime. In this simplified model, the concentrations of the two components in the drops are fixed at those corresponding to equilibrium at the onset of annular flow; the effect of the entrainment and deposition processes on entrained flowrate and compositions were not considered in this simple model. The wall temperatures were again calculated from the known heat flux and the calculated interface temperature using the Chen correlation with the nucleate boiling component corrected for multicomponent effects by the correlation of Palen [1983]. As will be seen by comparing the upper and lower parts of Figs. 3-7, the effect of accounting for droplet mass transfer processes is to narrow the range of predicted wall temperature. Decreased wall temperature are predicted by the present droplet interchange model (relative to the simplified model) at high initial entrained fractions and lower wall temperatures for lower initial entrained fractions. It should be noted that the simplified model, coupled with an assumption of zero entrained fraction, corresponds to a conventional application of the Chen/Palen method taking no account of entrainment. This does lead, of course, to a considerable under-prediction of wall temperature. The importance of considering entrainment is thus clearly demonstrated.

Temperature [K]

380.00

droplet interchange

370.00

50%

40% 20% 10% 0%

360.00 2.00

4.00

6.00

z [m]

8.00

10.00

(a)

Temperature [K]

no droplet interchange 50%

380.00

40%

20% 10% 0%

360.00 2.00

4.00

6.00

z [m]

8.00

(b) Fig. 3. Wall temperature predictions. Case 1.

10.00

384.00

Temperature [K]

droplet interchange

50% 40% 20%

380.00

10% 0%

376.00 4.00

5.00

6.00

z [m]

7.00

8.00

9.00

(a) 400.00

Temperature [K]

no droplet interchange

50% 40% 20% 10% 0%

380.00

360.00 4.00

5.00

6.00

z [m]

7.00


8.00

9.00

420.00

Temperature [K]

droplet interchange

50%

410.00

40% 20% 10% 0%

400.00 5.00

6.00

7.00

z [m]

8.00

9.00

(a) 420.00

Temperature [K]

no droplet interchange 50% 40%

410.00

20% 10% 0%

400.00 5.00

6.00

7.00

z [m]

8.00


9.00

450.00

Temperature [K]

droplet interchange

440.00 50%

0%

40% 20% 10%

430.00 5.00

6.00

7.00

z [m]

8.00

9.00

(a) 450.00

Temperature [K]


50%

440.00

40% 20% 10% 0%

430.00 5.00

6.00

7.00

z [m]

8.00


9.00

395.00

Temperature [K]

droplet interchange

50% 40% 20% 10% 0%

390.00

385.00 5.00

6.00

7.00

z [m]

8.00

9.00

(a) 400.00 50%

Temperature [K]


40%

20% 10%

390.00

0%

380.00 5.00

6.00

7.00

z [m]

8.00

9.00


5.2. COMPARISON OF EXPERIMENTAL AND PREDICTED HEAT TRANSFER COEFFICIENTS The measured heat transfer coefficients (calculated by introducing the known heat flux, the measured wall temperature and the calculated value of TE into Eq. 16) are compared with those calculated using the present methodology in Figs. 8-12. Parts (a) of Figs. 8-12 show the results calculated from the present (droplet interchange) model and parts (b) of Figs. 8-12 show the results calculated based on the simplified (constant entrainment flow) model of Kandlbinder et al. [1998].

Heat transfer coefficient [W/m2/K]

6000.00

droplet interchange Chen/Palen

4000.00 0% 10% 20% 40% 50%

2000.00 2.00

4.00

6.00

z [m]

8.00

10.00


(a)

8000.00

no droplet interchange 0%

4000.00

10% 20% 40% 50%

0.00 2.00

4.00

6.00

z [m] (b)

Fig. 8. Heat transfer coefficient. Case 1.

8.00

10.00

Heat tranfer coefficient [W/m2/K]

6000.00


4000.00

0% 10% 20% 40% 50%

2000.00 4.00

5.00

6.00

z [m]

7.00

8.00

9.00


(a)

8000.00


0% 10% 20%

4000.00

40% 50%

0.00 4.00

5.00

6.00

z [m]

7.00

(b) Fig. 9. Heat transfer coefficient. Case 2.

8.00

9.00


6000.00


4000.00

0% 10% 20% 40% 50%

2000.00 5.00

6.00

7.00

z [m]

8.00

9.00


(a) 6000.00

no droplet interchange 0% 10% 20%

4000.00 40% 50%

2000.00 5.00

6.00

7.00

z [m] (b)

Fig. 10. Heat transfer coefficient. Case 3.

8.00

9.00


6000.00


4000.00

0% 10% 20% 40% 50%

2000.00 5.00

6.00

7.00

z [m]

8.00

9.00


(a) 6000.00

no droplet interchange 0% 10% 20%

4000.00

40% 50%

2000.00 5.00

6.00

7.00

z [m]

8.00

9.00

(b)

Fig. 11. Heat transfer coefficient. Case 4. The results show that the present model is in encouragingly good agreement with the data for lower pressures. The simplified model of Kandlbinder et al. also spans the data at lower pressures but is much more sensitive (of course) to the choice of initial entrained fraction. The present model tends to overpredict the data at high values of z (quality) even at low pressures. As the pressure increases, both the present model and (ultimately) the Kandlbinder at al. simplified model over-predict the data. These observations are, of course, consistent with the observations regarding wall temperatures presented in Section 5.1.


4000.00 0% 10% 20%

droplet interchange

40% 50%

3000.00

2000.00 5.00

6.00

7.00

z [m]

8.00

9.00


(a) 4000.00 0%


10% 20%

3000.00 40%

50%

2000.00 5.00

6.00

7.00

z [m]

8.00

9.00

(b) Fig. 12. Heat transfer coefficient. Case 5. The probable reason for the discrepancy between the present model and the data at higher pressures is that mass transfer resistance in the vapour phase becomes significant as the pressure increases. The mass transfer coefficient in the vapour phase will decrease (for a given mass flux) as the pressure increases. Thus, the finding of Shock [1976] that mass transfer effects are small under forced convective situations may be no longer valid. The mass transfer effects are difficult to predict quantitatively because of the interfacial waves on the mass transfer coefficients. However, mass transfer effects are currently being evaluated in ongoing work in this project. Also shown in the upper parts of Figs. 8-12 are the predictions obtained from the Chen [1966] correlation taking account of mixture effects on the nucleate boiling coefficient using the correlation of Palen [1983].

As will be seen, this modified version of the Chen correlation overpredicts the heat transfer coefficients. Since the Chen/Palen method was also used in the present methodology for calculating the film coefficient, the difference between the Chen/Palen predictions based on a conventional interpretation and those arising from the present (droplet interchange) model give a direct indication of the importance of droplet interchange. As observed, a very significant effect is predicted. 5. CONCLUSION The new model described here has been substantially successful in predicting the reductions in forced convective heat transfer coefficient observed in the Kandlbinder et al. [1998] mixture boiling experiments. The new model tends to somewhat underpredict coefficients at high quality and pressure. This may be due to the assumption that the interface-to-bulk vapour temperature differences (due to mass transfer effects in the vapour phase) are negligible. Though this assumption arises directly from the studies of Shock [1976], further investigation is indicated. Such an investigation is now proceeding.

ACKNOWLEDGEMENTS The first author thanks the Brazilian National Research Council (CNPq) for the award of a scholarship (Grant No. 200085/97-2). The Heat Transfer and Fluid Flow Service (HTFS) of AEA Technology plc provided the laboratory facilities and the support services. The research funding was provided by the Engineering and Physical Sciences Research Council (EPSRC).

NOMENCLATURE Roman -1

cp

- specific heat capacity [J kg K];

Dm

- mass diffusivity [m s ];

D

- deposition rate [kg m s ];

dT

- inner diameter of tube [m];

E

- entrainment rate [kg m s ];

f

- friction factor [-];

F

- enhancement factor [-];

2 -1

-2 -1

-2 -1

-2 -1

- mass flux [kg m s ]; Nu

- Nusselt number,

p

- pressure [Pa];

Pr

- Prandtl number,

;

;

-2

- heat flux [W m ]; Re

- Reynolds number,

S

- suppression factor [-];

T

- temperature [-]; - Wallis parameter,

;

; x

- mass fraction in liquid phase [-];

X

- quality [-];

Xtt

- Martinelli parameter [-];

y

- mass fraction in gas phase [-];

z

- axial co-ordinate [m];

Z

- sensible to total heat flux ratio [-];

Greek -2

-1

α

- heat transfer coefficient [W m K ];

β

- mass transfer coefficient [m s ];

δ

- film thickness [m];

Δhv

- latent heat of vaporisation [J kg ];

η

- viscosity [N s m ];

κ

- thermal diffusivity [m s ];

λ

- thermal conductivity [W m K ];

ρ

- density [kg m ];

σ

- surface tension [N m ];

-1

-1

-2

2 -1

-1

-1

-3

-1

Subscripts c

- core;

C

- convective;

G

- gas/vapour;

GC

- gas core;

EV

- evaporation;

i

- component identifier (1= n-Pentane);

I

- interface;

L

- liquid;

LE

- entrained liquid;

LF

- liquid film;

mac - macro-convective; mic

- micro-convective;

mix

- mixture;

N

- nucleate boiling;

sat

- saturation;

tp - two-phase; w

- wall.

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rd

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