Advances and Challenges of Boiling Heat Transfer

Abstract

Boiling is a heat-transfer process during which vapor bubbles are created on a heated surface (nucleate boiling) or inside overheated liquid (bulk boiling). Boiling has been used by humans for tens of thousands of years for cooking, however, its application in industry started somewhere in the seventeenth century. Moreover, actual research into boiling-heat-transfer phenomena started only around 1920s. In general, several major types of boiling process can be identified: natural-convection pool boiling vs. forced-convection flow boiling and nucleate boiling vs. bulk boiling. Major nucleate-pool-boiling characteristics are as the following: Onset of Nucleate Boiling (ONB); Heat Transfer Coefficient (HTC); Critical Heat Flux (CHF); HTC at film pool boiling; minimum heat flux at film pool boiling; and HTC at transition boiling. Quite similar characteristics correspond to flow-boiling: Onset of subcooled Nucleate Boiling (ONB); Onset of Significant Void (OSV); HTC; CHF; and Post-DryOut (PDO) heat transfer. In spite of more than 100 years of active research and many years of applications, boiling phenomena/heat transfer are still not fully investigated and understood. There are some attempts to develop boiling-phenomena theories, but, unfortunately, they are not so practical yet. Therefore, more or less all practical calculations of various boiling characteristics/parameters rely heavily on empirical correlations, which were obtained experimentally. Due to this sophisticated studies are performed into boiling phenomena in the world.

1. Introduction: History notes

Based on various sources (Wikipedia, 2023), there is some evidence that ancient humans have started to boil water as early as ∼30,000 years ago during the Upper Paleolithic period. Later on, i.e., about 26,000 years ago, cracked “boiling stones” were discovered in caves, which have been used by early modern humans. Around 20,000 years ago, pottery has appeared for more conventional boiling. Therefore, for tens of thousands of years, the boiling process has been used for cooking.

The earliest steam engine was the scientific novelties of Hero of Alexandria in the first century CE, called as the aeolipile (https://www.britannica.com/technology/steam-engine [Accessed: December 10, 2023]).This device is the first known one to transform steam energy into a rotary motion. However, like many other early machines, they have demonstrated basic mechanical principles and were simply regarded as a curiosity or a toy and have not been used for any practical purposes.

Only in the seventeenth century, there were attempts to made steam engines for practical purposes (https://www.britannica.com/technology/steam-engine [Accessed: December 10, 2023]). As such, in 1698 Th. Savery patented a pump with hand-operated valves to raise water from mines by suction produced with condensing steam. Somewhere around 1712, Th. Newcomen, has developed a more efficient steam engine with a piston separating the condensing steam from the water. In 1765, J. Watt quite significantly improved the Newcomen engine by adding a separate condenser to avoid heating and cooling the cylinder with each stroke. And finally, he has developed a new engine that rotated a shaft instead of providing the simple up-and-down motion of a pump and added many other improvements to produce a practical power plant.

In 1769, N.J. Cugnot has built the first steam carriage for roads in France (https://www.britannica.com/technology/steam-engine [Accessed: December 10, 2023]). After that R. Trevithick in England was the first to use a steam carriage on a railway; and, in 1803, he built a steam locomotive. In 1829, English engineer G. Stephenson has adapted a steam engine to railways, which became a commercial success. In 1802, W. Symington has built the first practical steamboat. And in 1807, R. Fulton has proposed to use a steam engine for a passenger boat in the United States.

In 1892, L.P. Perkins and W.E. Buck have patented a heat-transmitting device, which was the first two-phase thermosyphon (or, also, it can be named as a wickless heat pipe) operating with boiling-condensation cycle (for more details on these devices, see Bezrodny et al. [1]; Pioro and Pioro [2]).

And only around 1920s, actual research into boiling-heat-transfer phenomena has been started. One of the most significant results, which is important even today, was obtained experimentally by Professor Sh. Nukiyama (http://www.htsj.or.jp/en/nukiyama [Accessed: December 10, 2023]). In 1934, Professor Nukiyama published his pioneering paper entitled “The Maximum and Minimum Values of the Heat Q Transmitted from Metal to Boiling Water under Atmospheric Pressure.” In this paper he has clarified and provided an overview of the boiling phenomena in the form of the Nukiyama Curve (nowadays, quite often used just “Boiling Curve”) (updated version of this curve is shown in Figure 1). Therefore, for more than 100 years, studies into the boiling heat-transfer phenomena at various conditions within a wide range of working fluids, pressures and temperatures, surfaces, etc. are performed non-stop in many research organizations, companies, universities, laboratories, etc. around the world.

Figure 1.

Boiling curve for saturated water at atmospheric pressure (first time was obtained by Professor Sh. Nukiyama (Tohoku University, Japan) at the beginning of 1930s and for long time called as “Nukiyama’s boiling curve”). In the current view the boiling curve is updated with q_max and q_min values and melting temperatures of selected common metals/alloys.

2. Classification of boiling cases

In general, boiling is a heat-transfer process during which vapor bubbles are created on a heated surface (nucleate boiling) or inside overheated liquid (bulk boiling) (for properties of various fluids on saturation line, see [3, 4]). Boiling is only possible at subcritical pressures, because at critical and supercritical pressures fluid is a single-phase substance, therefore, there are no such terms as liquid and vapor (see Figure 2). However, due to significant variations of all thermophysical properties within critical and pseudocritical regions fluid undergoes a transition from high-density fluid (liquid-like) to low density fluid (vapor-like). Therefore, we have quite similar heat-transfer processes to those at subcritical pressures, which are called pseudo-boiling, pseudo-film-boiling, and deteriorated heat flux (for details, see [5, 6, 7]).

Figure 2.

Thermodynamics diagrams for water: (a) pressure—temperature and (b) temperature—specific entropy.

An important condition for boiling is that the temperature of a heated surface should be higher, at least, by several degrees than that of saturated liquid (see Figure 1). For subcooled boiling this difference in temperatures can be significantly higher.

Boiling process (heat transfer) can be classified in general as the following (for details, see Figures 1–16):

1. Nucleate pool boiling (classical case of boiling) (Figures 1, 5–7).

2. Transition boiling (quite rare regime) (see Figure 1).

3. Film boiling (special boiling regime, which should be usually avoided) (see Figure 1).

4. Bulk boiling (the least used type of boiling) (Figure 9).

5. Subcooled (Figure 8) and saturated boiling (Figures 3 and 4).

6. Flow boiling (the most used in industrial applications):

   • Internal boiling (inside tubes, pipes, channels, etc.) (Figures 6–8);

   • External boiling (over heated surfaces, annular channels, rod bundles, cross flow, etc.); and

   • Internal or external boiling in or on horizontal (Figure 16) or inclined flow geometries.

7. Boiling in two-phase thermosyphons (or wickless heat pipes) (Figures 9–11) [1, 2].

8. Boiling in wick structures (in application to heat pipes with wicks) (for details, see [12, 13, 14]).

9. Boiling of mixtures (Figure 12) (for details, see [15, 16]) and solutions. And,

10. Boiling on enhanced surfaces (fins, ribs, artificial cavities, special surface treatment, etc.) (for details, see [17, 18, 19]) or in flow geometries with flow obstructions or turbulizers.

Figure 3.

Nucleate pool boiling of water on horizontal copper plate (see Figure 5 for test section and electron-microscope images of boiling surfaces use in this experimental setup) at sub-atmospheric pressures: Parameters of working fluid—volume 120 ml and level 5.8 mm; height of boiling-condensation chamber 38 mm; scale—pitch between two thread-rods (black vertical posts on photos) equals to 40 mm.

No. of photo (from top)	Heat flux, kW/m^2	Temperature, °C		Pressure, kPa	HTC, W/m^2K
		Wall	Saturation
1	8.6	56	41	7.8	1343
2	12.2	62	56	16.5	2152
3	29.6	68	58	18.2	3037

Figure 4.

Nucleate pool boiling of refrigerants on horizontal high-density polyethylene plate (see Figure 5 for text section): Parameters of working fluid—volume 120 ml and level 5.8 mm; height of boiling-condensation chamber 38 mm; scale—width of photos equals to 120 mm in actual chamber. Photos 1 and 2—boiling in slots and photo 3 —boiling on surface. Polyethylene has very low surface roughness due to that only several vapor-bubble-generating centers are seen.

No. of photo (from top)	Working fluid	Heat flux, kW/m^2	Temperature, °C		Pressure, kPa	HTC, W/m^2K
			Wall	Saturation
1	R-113	5.1	32	26	46.6	850
2	R-113	5.1	32	26	46.6	850
3	R-11	10.9	95	30	126.0	168

Figure 5.

Dimensions (in mm) of boiling-condensation chamber: Heating surfaces used—Aluminum, brass, copper, st. st., and high-density polyethylene (see Figure 15a–e for electron-microscope images of boiling surfaces and Tables 3 and 4 for their thermophysical properties and surface-roughness parameters): H_b-c—height of boiling-condensation chamber.

Figure 6.

Wall- and bulk-fluid-temperature and pressure-loss-gradient profiles in uniformly heated vertical, bare tube at flow boiling (based on Figure 4 from Siemens: 25JahreBENSONbild_E.doc [Accessed: February 22, 2022]).

Figure 7.

Critical-heat-flux (CHF) profiles vs. pressure in uniformly heated vertical, bare tube at flow boiling (upper solid curve) and in pool boiling (lower dashed curve).

Figure 8.

Flow boiling of water in vertical rectangular channel (8 × 12.5 × 730 mm; two opposite walls—st. st. and other two—transparent acrylic): Pressure 0.1 MPa; inlet velocity 0.036 m/s; subcooling temperature 90°C; heat flux 167 kW/m²; scale—height of each photo equals to 150 mm in actual test section; width 12.5 mm; from left to right—portions of channel from lower to upper part starting from 130 mm of heated length. Vapor bubbles on photos are shown as black circles. Flow regimes from left bottom to right top (approximately): Bubbly flow; slug flow; annular flow; annular flow with entrainment of droplets; and single-phase steam flow. Liquid film on left and right st. st. walls moves up in photos 2–4.

Figure 9.

Bulk boiling in two-phase counter-flow thermosyphon on glass surface: Methylene chloride (R-30), atmospheric pressure, filling charge more than 100% of evaporator volume, evaporator—lower part of thermosyphon and condenser—upper part, in between—short transportation zone), and heat flux increasing from left to right.

Figure 10.

Nucleate boiling in two-phase counter-flow thermosyphon on st. st. surface: Methylene chloride (R-30), atmospheric pressure, filling charge more 40% of evaporator volume, and heat flux increasing from left to right up to critical heat flux (CHF).

Figure 11.

Nucleate boiling in two-phase counter-flow thermosyphon on metal heated rod (annular-channel evaporator): Water, atmospheric pressure, filling charge 100% of evaporator volume, and heat flux increasing from left to right up to critical heat flux (CHF).

Figure 12.

Nucleate boiling in two-phase counter-flow thermosyphon on metal heated rod (annular-channel evaporator): Water-ethylene-glycol mixture (water boiling temperature ∼ 100°C and ethylene-glycol—∼200°C), atmospheric pressure, filling charge 100% of evaporator volume, and heat flux increasing from left to right up to critical heat flux (CHF). Photo 1: no boiling—mixture not separated; photos 2–9—mixture is separated, i.e., water (liquid density—958 kg/m³) boils in the upper part of evaporator and non-boiling ethylene-glycol as liquid (density—993 kg/m³) transfers heat to boiling water with natural convection in the lower part.

Figure 13.

Universal experimental setup for boiling experiments at various operating conditions and in different flow geometries (current view—test section (to the left) is two-phase counter-flow thermosyphon: 1—condenser; 2—cooling jacket; 3—coolant (antifreezing mixture water-ethylene glycol); 4—transportation (adiabatic) zone; 5—working fluid (WF); 6—evaporator; 7—current terminals; 8—insulation; 9—sheathed thermocouples (fluid/vapor temperatures); 10—wall-temperature thermocouples; A—ammeter; G—electrical generator (power supply); V—voltmeter; and VP—vacuum pump.

Figure 14.

Test sections for boiling experiments at various operating conditions: (a) two-phase counter-flow glass thermosyphon (bulk-boiling photos—Figure 9); (b) two-phase counter-flow thermosyphon with boiling on st. st. surface (nucleate-boiling photos—Figure 10); (c) two-phase counter-flow glass thermosyphon with multiple evaporators and horizontal condenser); and (d) two-phase counter-flow thermosyphon with boiling on st. st. internal tube (annular boiling channel) (nucleate-boiling photos—Figures 11 and 12):—fluid-expansion tank; 2—cooling jacket; 3—condenser; 4—heating jacket; 5—evaporator; and 6—current (power) terminals.

Figure 15.

a-e. Electron-microscope images (enlargement × 100) of plates made of: (a) aluminum—R_q = 4.5 μm, R_sk = 0.47 μm; (b) copper—R_q = 1.7 μm, R_sk = 0.38 μm; (c) brass—R_q = 0.7 μm, R_sk = −1.3 μm; (d) st. st.—R_q = 0.6 μm, R_sk = 0.19 μm; and (e) polyethylene high density. For thermophysical properties and surface-roughness parameters, see Tables 3 and 4, respectively, and Appendix A). Details on experimental setup with these heated plates and experimental data are presented in [8]. f. Effect of heat flux on HTC at nucleate pool boiling of R-11 on copper (R_q = 1.7 μm) (b) and plastic (PHD) (e) large-size plates.

Figure 16.

Effect of gravity on boiling heat transfer and CHF in horizontal tube: Water, P = 10 MPa, G = 500 kg/m²s, D = 24.3 mm (based on Kohler and Hein [11]) (Courtesy of NRC, USA).

In addition, the following special cases of boiling can be identified:

• Non-isothermal boiling surfaces;

• Variable heat flux along the boiling surface;

• Thin boiling films;

• Rewetting of hot surface;

• Boiling under conditions of decreased or increased gravitational fields;

• Low pressures (see Figure 3);

• Boiling of liquid metals (for details, see [20, 21]);

• Boiling of cryogenic fluids (for details, see [22]);

• Boiling in microchannels; and

• Boiling with nano- /micro-particles.

3. Nucleate pool boiling

Nucleate pool boiling is the first type of boiling to be used by humans and the first one to be investigated. Boiling curve for saturated water at the atmospheric pressure was obtained by Professor Shiro Nukiyama (Tohoku University, Japan) at the beginning of 1930s and for long time was called as the “Nukiyama’s boiling curve” (see Figure 1). In the current view the boiling curve is updated with q_max and q_min values and melting temperatures of some common metals/alloys. Photos of nucleate pool boiling are shown in Figures 3 and 4.

Major nucleate-pool-boiling characteristics (see Figure 1) are as the following:

• Onset of nucleate pool boiling (Point A);

• Heat Transfer Coefficient (HTC) at nucleate pool boiling (Regions A–B–C);

• Critical heat flux at nucleate pool boiling (Point C);

• HTC at film pool boiling (Region E–D);

• Minimum heat flux at film pool boiling (Point D); and

• Also, in special conditions of controlled experiment we can talk about HTC at transition boiling (Region C–D).

Therefore, for all these Points /Regions we need to have the appropriate correlations (for general correlations, see, for example, Chapter 10 in [9]). In general, there are three internal boiling characteristics such as (for details, see [23, 24, 25, 26, 27]; and Table 1): (1) vapor-bubble departure diameter, D_b; (2) frequency of vapor-bubbles departure, f; and (3) mean velocity of vapor-bubble growth, $\overline{u}$_b = D_b · f_b. However, these internal-boiling characteristics are not easy to estimate, and their uncertainties are quite high. Also, there are some theoretical approaches to boiling heat transfer, but, usually, only empirical correlations are used for various nucleate-pool-boiling characteristics/parameters, which are based on well-known and well-defined thermophysical properties. For example, the vapor-bubble departure diameter is usually replaced with [9]:

Fluid	Psat, MPa	P/Pcr·10^3	Boiling surface	Db, mm	fb, s^−1	ub, mm/s
Water	0.1	4.52	Permalloy	2.5	61	153
			Brass	2.3	67	157
			Copper	2.8	56	157
Freon-12	0.1	23.6	Permalloy	0.7	84	59
			Brass	0.7	99	69
			Copper	0.7	91	64
CCl4	0.1	22.0	Permalloy	1.1	110	121
			Brass	1.1	108	119
			Copper	1.1	106	117
Ethanol (96.5%)	0.1	15.6	Permalloy	1.0	114	114
			Brass	1.1	112	123
			Copper	1.2	98	118
Methanol	0.1	12.6	Permalloy	1.7	74	124
n-Butanol	0.1	20.2	Permalloy	1.1	106	111
Benzene	0.1	20.3	Permalloy	1.0	99	99

Table 1.

Internal boiling characteristics of various fluid-surface combinations [23, 24].

$$D_{\mathrm{b}}\propto \sqrt{\frac{\sigma }{g\left({\rho }_f-{\rho }_g\right)}}.$$E1

In 1952, W. Rohsenow has proposed his nucleate pool-boiling correlation, which is the most widely used correlation during the last 70+ years.

The main concept of this correlation is that the heat transfer from the wall directly to the liquid with an increased heat-transfer rate, due to the agitation of liquid by the departing vapor bubbles.

$$\frac{c_{pf}\mathrm{\Delta }{T}_b}{H_{\mathit{fg}}}=C_{\mathit{sf}}{\left[\frac{q}{{\mu }_f{H}_{\mathit{fg}}}\sqrt{\frac{\sigma }{g\left({\rho }_f-{\rho }_g\right)}}\right]}^m{\left(\frac{c_{pf}{\mu }_f}{k_f}\right)}^n,$$E2

where C_sf is constant, depending upon the nature of the heating-surface- fluid combination (see Table 2). However, some other well-known correlations do not include any heating-surface parameters/properties or impact of the heating-surface- fluid combination on HTC at boiling (for details, see [10]).

No.	Surface-fluid combination	Csf	n
1	Water-copper; Scored; Polished	0.0068; 0.0128	1.0; 1.0
2	Water-stainless steel; Chemically etched; Mechanically polished; Ground and polished	0.0133; 0.0132; 0.0080	1.0; 1.0; 1.0
3	Water-brass	0.0060	1.0
4	Water-nickel	0.0060	1.0
5	Water-platinum	0.0130	1.0
6	n-Pentane-copper; Polished; Lapped	0.0154; 0.0049	1.7; 1.7
7	Benzene-chromium	0.0101	1.7
8	Ethyl alcohol-chromium	0.0027	1.7

Table 2.

Values of C_sf for various surface-fluid combinations [9].

Detailed analysis of the data in Table 2 has shown that information on the surface-fluid combination is too simplified and, actually, misleading. A thorough analysis of original publications in which C_sf values were obtained is presented in the joint publication by I. Pioro, W. Rohsenow, and S. Doerffer [10, 23] and by Pioro [8] together with the latest Pioro correlation on the pool-boiling heat transfer. This list of C_sf values is the most comprehensive and detailed one so far (see Appendix A at the end of this Chapter).

The major problem with correlations, which account for a heating surface-fluid combination, is that these correlations can be used only for a particular heating surface and fluid used in experiments. Otherwise, uncertainties can be very high! On opposite, if correlations, which do not account on a particular heating surface and fluid combination, are used, it is impossible to predict uncertainties of HTCs calculated!

The most important nucleate-pool-boiling characteristic is the Critical Heat Flux (CHF), because if the CHF is reached, the boiling-surface temperature can jump to very high values (beyond 1000°C, see Figure 1) and, eventually, the boiling surface can be damaged or even melted. Of course, this temperature rise depends on the type of heating, i.e., for electrical and nuclear heating temperature rise can go far beyond 1000°C. However, if the boiling surface is heated with hot or high-temperature medium, the surface temperature cannot be higher than that of this medium.

The mostly used CHF correlation for pool boiling is as the following (for details, see Figure 7):

$$q_{\mathrm{cr}}=C_{\mathrm{cr}}{H}_{\mathrm{fg}}{\left[\mathit{\sigma g}{\rho }_{\mathrm{g}}^2\left({\rho }_{\mathrm{f}}-{\rho }_{\mathrm{g}}\right)\right]}^{0.25},$$E3

where C_cr is constant with the average value of 0.15. However, in reality, this constant can be within the range of 0.08–0.28! This correlation was obtained through a dimensional analysis by S.S. Kutateladze in Russia in 1948 and through a hydrodynamic-stability analysis by N. Zuber in the United States in 1958 [9].

Therefore, in conclusion we can say that in spite of more than 100 years of active research into the pool-boiling phenomena, we have failed to develop universal HTC, CHF, minimum heat flux, film boiling, and other correlations with a reasonable accuracy, which can be applied to various heating surfaces with different thermophysical properties, surface-roughness parameters and microgeometry, wall thickness, orientation in space, and different boiling fluids within a wide range of operating conditions!

The thermophysical properties of boiling surfaces are listed in Table 3.

No.	Boling surface material	k; W/m K	c; J/kg K	ρ; kg/m^3
1	Copper	401	385	8933
2	Aluminum	237	903	2702
3	Brass	110	380	8530
4	St. St.	145	477	7900
5	Polyethylene High Density (PHD)	0.35–0.49	1330–2400	955–961

Table 3.

Thermophysical properties of boiling surfaces (extended plates) at 27°C (listed according to decreasing thermal-conductivity values) [9].

A laser profilometer was used to determine the surface-roughness parameters that are listed in Table 4. The characteristics of the laser profilometer itself were as follows:

Plate material	Ra	Rq	Rp	Rv	Rt	Rpm	Rz	R3z	HSC	Sm	λa	λq	Δa	Rsk
	μm	μm	μm	μm	μm	μm	μm	μm	—	μm	μm	μm	deg.	μm
Al	3.6	4.5	14	14	28	12	22	17	89	89	88	82.9	0.26	0.47
Copper	1.4	1.7	7.2	4.4	12	5.2	9	6.4	68	117	109	107	0.08	0.38
Brass	0.5	0.7	2.4	5.1	7.4	1.7	3.9	2.4	126	63	65	70.1	0.05	−1.3
St. St.	0.5	0.6	3.4	2.5	5.9	2.1	3.8	2.5	123	64	65	65.2	0.05	0.19
Minimum and maximum values of roughness parameters
Min	0.5	0.6	2.4	2.5	5.9	1.7	3.8	2.4	68	63	65	65.2	0.05	−1.3
Max	1.4	4.5	14	14	28	12	22	17	126	117	109	107	0.26	0.47

Table 4.

Average surface-roughness parameters of boiling surfaces (extended plates) (listed according to decreasing surface-roughness (R_q/R_a) values) (for descriptions of all surface roughness parameters, see below or in [10]).

Vertical measuring range          ± 300 μm.

Scanning speed                              80 mm/min

Number of measured points         2000

Wavelength cut-off (L_c)               1.0 mm

Stylus filter (N_f)                            50 μm

Scan length                                    10 mm

Explanations toTable 4.

Simple-Roughness-Amplitude Parameters.

Mean parameters.

R_a average roughness: area between the roughness profile and its mean line or its integral of the absolute value of the roughness-profile height over the evaluation length. The average roughness is the most commonly used parameter in surface-finish measurements.

R_q root-mean-square roughness (rms roughness): average roughness parameter calculated as a square root from another integral of the surface-roughness profile. Root-mean-square roughness was a commonly used parameter in the past; however, nowadays it has been replaced with R_a in metal-machining specifications. Usually (but not necessarily), R_q is 1.1–1.3 times larger than R_a.

Extreme parameters.

R_p peak roughness (height of the highest peak in the roughness profile over the evaluation length).

R_v depth roughness (depth of the deepest valley in the roughness profile over the evaluation length).

R_t total roughness (vertical distance from the deepest valley to the highest peak), R_t = R_p + R_v.

Mean-extreme parameters.

R_pm mean-peak roughness (average peak roughness over the sample length).

R_z mean-total roughness (average value of the five highest peaks plus the five deepest valleys over the evaluation length).

R_z3 mean-total roughness of third extremes parameters (average vertical distance from the third deepest valley to the third highest peak).

Mean-extreme parameters are less sensitive to single unusual features, such as artificial scratches, gouges, burrs, etc.

Roughness-spacing parameters.

HPC High-Peak Count per length (number of peaks per length that cross above a certain threshold and then go back below it).

Mean-roughness-spacing parameters.

S_m mean spacing between peaks (peaks cross above a mean line and then go back below it).

λ_a average wavelength of surface.

λ_q rms (root-mean-square) average wavelength of surface.

Roughness-hybrid parameters.

Δ_a average of absolute slope of roughness profile over the evaluation length.

L_o actual profile length (in all measurements, this was 8 mm).

Statistical parameters.

R_sk skewness (this parameter represents the profile variation symmetry over its mean line). Surfaces with R_sk < 0 have fairly deep valleys in a smoother plateau. Surfaces with R_sk > 0 have fairly high spikes, which protrude above a flatter average.

4. Flow boiling

Flow boiling is boiling with forced convection, which is the most used type of boiling in industry [28], especially, in thermal- and nuclear-power industry [29, 30] and air-conditioning and refrigeration industry [31, 32]. In the thermal-power industry gas-fired and coal-fired (or fossil-fuel-fired) power plants are used, many of which equipped with the subcritical-pressure Rankine steam-turbine cycle (see Figure 17a) [33, 34]. In nuclear-power industry of the world there are 441 nuclear-power reactors connected to electrical grids of which 60 reactors are Boiling Water Reactors (BWRs) including several Advanced BWRs (ABWRs). Moreover, all current nuclear-power reactors are connected only to Rankine steam-turbine power cycles in which boiling takes place in steam generators (in BWRs and ABWRs saturated steam is generated inside reactors (for details, see Figures 17b, 18, and 19).

Figure 17.

Temperature (T) vs. specific entropy (s) simplified diagram of subcritical-pressure Rankine power cycle: (a) fossil-fuel-fired thermal power plant with superheated primary- and secondary-steam reheat and (b) advanced boiling water reactor (ABWR) with saturated primary steam and overheated secondary-steam (see Figure 19). Abbreviations: HPT—high-pressure turbine; LP—low pressure; MS—moisture separator; RH—re heater; SG—steam generator; and SHS—super heated steam.

Figure 18.

Heat-transfer tubes are installed into steam generator (SG) of PWR (1110 MW_el and 3060 MW_th) (in total four SGs per one reactor) (courtesy of Rosatom): https://www.flickr.com/photos/rosatom/36999718643/in/album-72157675727427445/ [Accessed: December 10, 2023]; Photo by E. Lyadov, Atommash, 2016.

Primary reactor-coolant pressure, MPa (Tsat = 348.4°C)	16.2
Coolant temperature at reactor inlet, °C	298
Coolant temperature at reactor outlet, °C	329
Steam-generator pressure, MPa (Tsat = 285.8 °C)	7.0

Reactor coolant is inside tubes and Rankine-cycle feedwater heated and boiling outside tubes.

Figure 19.

Simplified layout of typical boiling water reactor (BWR) NPP (courtesy of U.S. NRC): General basic features—(1) thermal neutron spectrum; (2) uranium-dioxide (UO₂) fuel; (3) fuel enrichment about 3%; (4) direct cycle with steam separator (steam generator and pressurizer are eliminated), i.e., single-flow circuit (single loop); (5) reactor pressure vessel (RPV) with vertical fuel rods (elements) assembled in bundle strings cooled with upward flow of light water (water and water-steam mixture); (6) reactor coolant, moderator and power-cycle working fluid are the same fluid; (7) reactor coolant outlet parameters: Pressure about 7 MPa and saturation temperature at this pressure is about 286°C; and (8) power cycle—subcritical-pressure regenerative Rankine steam-turbine cycle with secondary-steam reheat (for details, see Figure 17b). The largest BWR has installed capacities: 1435 MW_el and ∼ 4500 MW_th.

More information on all current and future nuclear-power reactors and their power cycles can be found in [29].

The main advantage of using flow or forced-convection boiling is very high HTCs compared to other types of heat transfer (see Table 5).

No.	Coolant	Heat Transfer Coefficient, kW/m^2K
1	Na (forced convection)	55–85
2	Boiling water (flow boiling)	60
3	CANDU reactor	50
4	Pb (forced convection)	25–35
5	Water (single-phase forced convection)	30
6	Pb-Bi (forced convection)	20–30
7	SuperCritical Water (SCW)	10–25
8	He (rough surface)	10
9	CO2 (high pressure)	2–5

Table 5.

Selected typical heat-transfer-coefficient (HTC) ranges of various coolants [35].

Major flow-boiling characteristics (see Figure 6) are as the following:

• Onset of subcooled nucleate boiling;

• Onset of significant void;

• Heat transfer at flow boiling;

• CHF at flow boiling (for details, see Figure 7); and

• Post-DryOut (PDO) heat transfer.

In general, these flow-boiling characteristics are quite similar to those of pool boiling. It is impossible to provide correlations for all cases of pool boiling as well as of flow boiling. However, this Chapter contains a list of references and bibliography, which have quite a large number of various cases covered and correlations provided.

Figures 20–23 show specifics of flow boiling in circular tubes, and the experimental setup for these experiments is shown in Figure 24. This study covers only two fluids: water and R-134a. To enable a comparison of CHF results between water and R-134a, the R-134a results were converted to their water-equivalent values using the following CHF fluid-to-fluid modeling relationships. It has been shown for vertical tubes (see in [36]) that if the fluid-to-fluid modeling relationships are satisfied, i.e., L_R = L_W, D_R = D_W (geometric similarity),

Figure 20.

CHF vs. critical quality at flow boiling in vertical bare circular tube (ID 6.92 mm, OD 7.93 mm, heated length 0.45–1.98 m, material Inconel): R-134a, P = 1.67 MPa, and G = 1000 kg/m²s. (a) Full scale and (b) the same as in (a), but in enlarge scale. (For details, see [36]).

Figure 21.

CHF vs. critical quality at flow boiling in vertical and horizontal circular tubes (ID 6.92 mm, OD 7.93 mm, heated length 0.45–1.98 m, material Inconel): R-134a, P = 1.31 MPa, and G = 2000 kg/m²s. (For details, see [37]).

Figure 22.

CHF vs. critical quality at flow boiling in vertical and horizontal tubes (ID 6.92 mm): R-134a, P = 1.67 MPa and G = 500 kg/m²s.

Figure 23.

(a) CHF vs. critical quality and (b) CHF enhancement vs. critical quality—Flow boiling in vertical circular tubes (ID 6.92 mm, OD 7.93 mm, heated length 0.45–2 m, material Inconel) without flow obstructions (i.e., bare) and with various flow obstructions: R-134a, P = 1.67 MPa, and G = 3000 kg/m²s. (For details, see [38]).

Figure 24.

Experimental thermalhydraulics R-134a loop: 1—gear pump; 2—coriolis-type mass flow meter; 3—preheater; 4—dielectric fittings, 5—Current (power) terminals; 6—electrical preheater; 7—sight glass; 8—condenser; 9—pressurizer; 10—pressure-relief valve; 11—refrigerant filter-dryer; 12—ball valve; 13—vacuum pump; 14—refrigerant storage tank; 15—pressure reducer; and 16—N₂ container.

${\left[\frac{G}{{\left(\frac{{\rho }_f\sigma }{D}\right)}^{0.5}}\right]}_R={\left[\frac{G}{{\left(\frac{{\rho }_f\sigma }{D}\right)}^{0.5}}\right]}_W$and ${\left(\frac{{\rho }_f}{{\rho }_g}\right)}_R={\left(\frac{{\rho }_f}{{\rho }_g}\right)}_W$ (hydrodynamic similarity),

$x_{\mathit{cr}R}=x_{\mathit{cr}W}$ (thermodynamic similarity), then the dimensionless CHF expressed as ${\left[\frac{q_{\mathit{cr}}}{G{h}_{\mathit{fg}}}\right]}_R={\left[\frac{q_{\mathit{cr}}}{G{h}_{\mathit{fg}}}\right]}_W$ will also be the same for both fluids. Even though the study deals with experiments in R-134a, the water CHF look-up table is also used as a reference, as this table represents an already normalized CHF database for water.

The look-up table data were normalized to tubes with an 8 mm ID; to obtain the CHF for a different diameter, a simple correction can be applied: $\frac{{\mathit{CHF}}_D}{{\mathit{CHF}}_{D=8\mathit{mm}}}={\left(\frac{D}{8}\right)}^{-0.5}$, where D is the Inside Diameter (ID) of a circular tube in mm, D = 8 mm is the reference tube ID.

The largest by scale and the most expensive experiments are performed in nuclear-power industry to determine the abovementioned flow-boiling characteristics, because any new bundle design or even updated one requires the exact knowledge of these characteristics. Samples of several bundle-string designs and fuel channel are shown in Figures 25 and 26, respectively. Also, in nuclear reactors usually axial and radial heat fluxes are not uniform. These specifics increase significantly the complexity of manufacturing test sections/stations (directly-heated with electrical current thin-wall tubes have to be with variable wall thicknesses) (see Figures 27 and 28).

Figure 25.

Designs of fuel-bundle strings or assemblies of two pressurized water reactors (PWRs): (a) square cross section (courtesy & copyright by MHI) and (b) hexahedron cross section (courtesy of ROSATOM) (Photo by A. Antonov, 2015): https://www.flickr.com/photos/rosatom/25761756447/in/album-72157692396689951/ [Accessed: December 10, 2023].

Figure 26.

3-D image of pressurized heavy-water reactor (PHWR) fuel channel with 43-element bundle (based on AECL design; prepared by Dr. W. Peiman).

Figure 27.

Sample of stylized axial power profile (APP) or axial heat flux profile (AHFP) used for critical heat flux (CHF) tests and pressure-tube creep profiles: 3.3% for ∼10–15 years of operation and 5.1% for ∼20–30 years of operation (based on report COG-98-311) (courtesy and copyright by COG).

Figure 28.

Sample of radial power profiles (RPPs) for CANDU-reactor bundle used for critical heat flux (CHF) tests (based on report COG-98-311) (courtesy and copyright by COG).

All experiments with bundles are performed with electrically-heated bundle strings, so-called, bundle simulators (for details, see [39, 40]). Therefore, such bundle strings are usually made of Inconel or stainless steel thin-wall tubes and can cost millions of dollars. Also, experimental setups are very sophisticated in terms of measuring devices and require quite large power supplies, e.g., for water experiments with the full-scale bundle string as shown in Figure 26, it can be up to 15 MW_el, but if modeling fluid (usually, R-134a) is used for additional set of experiments, power requirement can be significantly lower, i.e., up to 1.8 MW_el (Figures 29 and 30).

Figure 29.

Simplified layout of large (full-bundle-string) thermalhydraulics R-134a loop [39, 40].

Figure 30.

General layout of horizontal test station of MR-3 R-134a thermalhydraulics loop [39, 40]: PDT—pressure differential transducer and PT—pressure transducer.

To be able to scale operating conditions in water into those of R-134a and vice versa to scale PDO results from R-134a into water data the following scaling laws have been used:

For pressure:

$${\left(\frac{{\rho }_f}{{\rho }_g}\right)}_R={\left(\frac{{\rho }_f}{{\rho }_g}\right)}_W$$E4

For mass flux:

$${\left[\frac{G{D}_{\mathit{hy}}}{{\mu }_g}\right]}_R={\left[\frac{G{D}_{\mathit{hy}}}{{\mu }_g}\right]}_W$$E5

For PDO HTC:

$${\left(\frac{h_{\mathit{PDO}}{D}_{\mathit{hy}}}{k_g}\right)}_R={\left(\frac{h_{\mathit{PDO}}{D}_{\mathit{hy}}}{k_g}\right)}_W;\text{where}{h}_{\mathit{PDO}}=\frac{q}{T_w-T_{\mathit{sat}}}$$E6

x_R = x_W, where x is the thermodynamic quality.

Dimensionless CHF expressed as:

$${\left[\frac{q_{\mathit{cr}}}{G{h}_{\mathit{fg}}}\right]}_R={\left[\frac{q_{\mathit{cr}}}{G{h}_{\mathit{fg}}}\right]}_W$$E7

It should be noted that the most important parameters for BWR/ABWR bundle-string experiments are HTC, CHF, and PDO heat transfer. Moreover, even for PWRs (the largest PWR is the EPR (Evolutionary Power Reactor) by former company Areva, currently, by EDF (France): 1670 MW_el and ∼ 4590 MW_th) and PHWRs (largest PHWR is the CANDU-9 reactor (CANada Deuterium-Uranium)) by AECL (Canada): 878 MW_el and ∼ 2750 MW_th), which are not cooled with boiling light or heavy water, CHF and PDO at flow boiling should still be determined.

Figure 31 shows the surface-temperature map for Element 35 at a pressure of 0.98 MPa and mass-flow rate of 9.6 kg·s⁻¹ with 28% overpower¹. At high overpowers, dry patches coalesced at some angular locations and the maximum axial dry patch approached the complete length of the element. A full-length axial dry patch on an element could not be measured due to the limited traveling distance of the thermocouple drive unit. Based on the variation of surface temperature with axial distance, the full-element dryout was achieved at several high-power levels.

Figure 31.

Surface-temperature map for element 35 at 28% overpower (actual power to critical power): R-134a, 37-element bundle (for details, see [40]).

Figure 32 shows a new application for boiling process such as an ultimate emergency cooling of the molten nuclear-reactor core (corium) during a severe nuclear accident (modern feature for Generation-III⁺ reactor designs) (for details, see [29]). This new safety feature is in response to the Chernobyl NNP severe accident (April of 1986), when a large pressure-channel reactor (RBMK-1000: 1000 MW_el and ∼ 3200 MW_th) was completely melted, and there was a possibility for a corium to damage a concrete foundation of the reactor).

Figure 32.

Containment heat-removal system (CHRS) (courtesy and copyright by AREVA (EDF)). Two fully redundant trains with specific diversified heat sink.

This new application of the boiling process has started to be implemented in new reactor’s designs, but this unusual type of boiling is well-known for the Mother nature for millions of years, because it is eventually quite close to the cooling of a molten volcano lava in oceans, seas, etc.

In addition, modern Generation-III⁺ reactors are equipped with Passive-Core-Cooling System (PCCS), which at high heat flux will operate as boiling circulation loop (for details, see [41] or [29]).

More information on boiling, its characteristics, specifics, etc. can be found in the following publications: Boiling: Research and Advances [42]; Pioro et al. [43]; Naterer [44]; Pioro et al. [45, 46, 47]; Handbook of Phase Change: Boiling and Condensation [48]; Groeneveld et al. [49]; Convective Flow Boiling [50]; Collier and Thome [51]; Lahey and Moody [52]; Whalley [53]; Hanne and Grigull [54]; Davis and Anderson [55]; Thorn et al. [56]; and Bergles and Rohsenow [57].

5. Conclusion

In spite of more than 100 years of active research and even more years of applications, boiling phenomena/heat transfer are still not fully investigated and understood. There are some attempts to develop boiling-phenomena theories, but, unfortunately, they are not so practical yet. Therefore, more or less all practical calculations of various boiling characteristics/parameters rely heavily on empirical correlations, which were obtained experimentally. Due to this sophisticated studies are performed into boiling phenomena in the world.

A. Appendix

Explanations to Table A.

No	Fluid-Surface	Csf	n	Tsat; °C	ΔTb; °C	q; kW/m^2	hb; kW/m^2K
1	Water/Copper (plate oxidized, Ra = 1.37, Rq = 1.73)	0.015	0.81	23–82	4.2–14	1.8–72	0.26–6.1
2	Water/Copper (thin disk emery polished and paraffin treated)	0.0147	1	100	9.4–18.3	41–950	3.7–57
3	Water (internal forced convection)/Copper (vertical tube)	0.013	1.7	100	4–15	18–190	4.5–12.7
4	Water/Copper (disk emery polished) (thin copper disk (circular plate) (D = 25.4 mm, thickness 0.5 mm)	0.0128	1	100	5.5–15.5	28–530	3.4–34
5	Water/Copper (disk scored)	0.0068	1	100	1.7–8.3	1.6–190	8.5–19
6	Water/Aluminum (disk polished, Rq = 0.33)	0.011	1	100	5–8.3	28–126	5.6–15.1
7	Water/Aluminum (plate oxidized, Ra = 3.61, Rq = 4.52)	0.011	1.26	3.5–103	5–22	1.3–90	0.1–10
8	Water/Brass (plate, Ra = 0.47, Rq = 0.66)	0.015	0.81	14–103	4–15	1.2–144	0.2–11
9	Water/Brass (tube external)	0.009; 0.006	1.1; 1.7	28–112	2.3–14	8–43	1–11
10	Water/Chromium (polished thin layer on copper disk)	0.019	0.45	100–205	8–18	140–655	14.6–51
11	Water/Platinum (wire)	0.013	1	100–355	1–28	3–3200	1.8–480
12	Water/St. St. (plate, Ra = 0.75, Rq = 1.2)	0.015	0.69	30–103	4–13	5–40	1–6.2
13	Water/St. St. (disk polished, Rq = 0.13)	0.01	1	100	4.4–7.2	28–126	6.4–17.5
14	Water/St. St. (disk grounded, Rq = 0.53)	0.008	1	100	3.3–6.7	22–158	6.7–23.6
15	Water/St. St. (disk grounded, Rq = 3.6)	0.007	1	100	3.3–5.6	37–160	11.5–29
16	Water/St. St. (disk grounded and polished)	0.008	1	100	3–8.3	17–90	6–34
17	Water/St. St. (thin strip pitted with Teflon coating in pits	0.0058	1	100	0.5–8.3	1.6–265	3.1–31.8
18	Ethanol/Copper (plate oxidized, Ra = 1.37, Rq = 1.73)	0.00079	2.3	30–82	13–20.2	2.1–26	0.1–2
19	Ethanol/Aluminum(plate oxidized, Ra = 3.61, Rq = 4.52)	0.008	1.18	16–78	11–21	2.7–32	0.16–2.3
20	Ethanol/Brass (plate, Ra = 0.47, Rq = 0.66)	0.011	0.92	40–78	9–14	4.3–56	0.7–4.7
21	Ethanol/Chromium (polished thin layer on copper disk	0.0045; 0.0027	1.47; 1.7	78–210	3–34	15–800	3.2–72
22	Ethanol/St. St. (plate, Ra = 0.75, Rq = 1.2)	0.00053	2.28	49–90	7–14	10–45	0.7–6
23	Methanol/Brass (tube external boiling)	0.0026	1.7	13–72	5–19	7.8–43	0.7–6
24	iso-Propanol (internal flow boiling)/Copper (vertical tube)	0.0022	1.7	82.5	5–20	5.7–95	1.1–4.8
25	n-Butanol (internal flow boiling)/Copper (vertical tube)	0.03	1.7	117	7–17	9.5–95	1.4–5.6
26	R-11/Copper (plate oxidized, Ra = 1.37, Rq = 1.73)	0.0009	3.47	23–49	6.4–11.2	1.4–12	0.22–1.2
27	R-11/Copper (tube external) Ra = 0.17; Ra = 0.45; Ra = 2.30	0.0019; 0.0014; 0.00089	2.8	—	—	—	—
28	R-11/St. St. (tube external) Ra = 0.02; Ra = 0.16	0.0031; 0.0023	2.8	—	—	—	—
29	R-12/Copper (tube external)	0.016 [Pioro]	1.7	2–15	6.6–10	1.5–5	0.2–0.5
30	R-12/Copper (tube external) Ra = 0.06; Ra = 0.51	0.0031; 0.00018	5	—	—	—	—
31	R-113/Copper (plate oxidized, Ra = 1.37, Rq = 1.73)	0.0022	2.25	32–80	9–16	3.2–21	0.24–1.9
32	R-113/Aluminum (plate oxidized, Ra = 3.61, Rq = 4.52); /Brass (plate, Ra = 0.47, Rq = 0.66); /St. St., (plate, Ra = 0.75, Rq = 1.2)	0.013	1.2	20–71	6–15	1.3–24	0.2–2
33	R-123/Copper (tube external) Ra = 0.16; Ra = 0.47; Ra = 3.30	0.0067; 0.0055; 0.0036	1.7	—	—	—	—
34	R-123/St. St. (tube external, Ra = 0.16)	0.0084	1.7	—	—	—	—
35	R-1234a/St. St. (tube external) Ra = 0.08	0.0025	2.5	—	—	—	—
36	R-134a/Copper (tube external) Ra = 0.07; Ra = 0.50; Ra = 2.50	0.0023; 0.0016; 0.00098	2.5	—	—	—	—
37	CCl4 (internal flow boiling)/Copper (vertical tube)	0.013	1.7	76.7	10–28	5.5–63	0.55–2.3
38	CCl4/ Copper (disk emery polished)	0.007	1.7	76.7	12–22	10.2–194	0.85–14
39	CCl4/Copper (disk lapped)	0.0031	1.7	76.7	8–13	22–280	2.6–25
40	CCl4/Brass (tube external)	0.0022	2.1	33–86	6.5–25	7.8–43	0.6–4
41	Propane/Chromium (polished thin layer on copper disk)	0.0069	2.17	34–83	3.3–22	27–400	8–28
42	n-Pentane/Copper (disk mirror finishing)	0.0171	1.7	36	16.7–44.4	22–252	1.3–5.7
43	n-Pentane/Copper (plate emery polished, Rq = 0.15)	0.0154	1.7	36	17–22	15–90	0.85–4
44	n-Pentane/Copper (disk emery rubbed)	0.0074	1.7	36	6.7–15.6	31.5–284	4.7–18.2
45	n-Pentane/Copper (disk lapped)	0.0049	1.7	36	5–8.3	31.5–284	6.3–34
46	n-Pentane/Zinc(disk polished)	0.0088	1.7	36	4–38	6.3–284	1.6–7.5
47	n-Pentane/Chromium (polished thin layer on copper disk)	0.015	1.7	48–147	4–31	29–440	2–35
48	n-Pentane/Nickel (disk mirror finishing)	0.0154	1.7	36	6.1–9.4	28–284	4.6–30.2
49	n-Pentane/Nickel (plate emery polished)	0.0127	1.7	36	11–22	13–112	0.85–5.7
50	n-Pentane/Nickel (disk lapped)	0.0043	1.7	36	15.5–39	31.5–284	2–7.3
51	n-Pentane/Inconel (disk mirror finishing)	0.018	1.7	36	19.4–43.3	31.5–221	1.6–5.1
52	n-Pentane/Inconel (disk lapped)	0.0072	1.7	36	9.4–15.6	31.5–252	3.4–16.2
53	Benzene/Chromium (polished thin layer on copper disk)	0.01	1.7	80–214	4–45	25–600	2.5–41
54	n-Heptane/Chromium(polished thin layer on copper disk)	0.0014	1.37	95–185	10–32	40–440	2.8–25
55	Acetone/Copper (disk emery polished)	0.0096	1.7	56	14.4–22.2	16.4–252	1.1–11.4
56	35% K2CO3 (internal flow boiling)/Copper (vertical tube)	0.0054	1.7	106	8–15	19–95	2.4–6.3
57	50% K2CO3 (internal flow boiling)/Copper (vertical tube)	0.0028	1.7	72.4	10–17	25–95	2.5–5.6

Table A.

Average values of constants in the Rohsenow pool-boiling correlation and prediction intervals (for all references and other details of experiments and boiling surfaces/conditions, see [8]).

Fluids are given in such order: water, alcohols, fluorocarbons (refrigerants by increasing in their number), hydrocarbons, and others.

Materials of surfaces are located according to the value of thermal conductivity: from highest to lower ones.

Surfaces of the same material generally are located according to the decreasing value of C_sf.

All surfaces were located horizontally except where noted.

Generally two-phase thermosyphon-type chambers were used with boiling surface (plates, disks, or strips) located on the bottom or immersed in a pool (wires or tubes) and condensing part at the top.

In the present work plates (boiling surface 411 × 51 mm) from copper (no surface treatment, naturally oxidized, thickness 6.4 mm, R_a = 1.37, R_q = 1.73), aluminum (surface machined and oxidized, thickness 12.7 mm,), brass (no surface treatment, thickness 6.4 mm), and SS304 stainless steel (no surface treatment, thickness 9.62 mm) were used.

Nomenclature

A	flow area, m^2
Al	Aluminum
c	specific heat, J/kg K
cp	specific heat at constant pressure, J/kg K
D	inside diameter, m
Db	vapor-bubble departure diameter, m
Dhy	hydraulic-equivalent diameter, m
f	frequency of vapor-bubbles departure, 1/s
G	mass flux, kg/m^2s; $\left(\frac{m}{A_{\mathit{fl}}}\right)$
g	gravitational acceleration, m/s^2
H, h	specific enthalpy, J/kg
k	thermal conductivity, W/m K
L	heated length, m
m	mass-flow rate, kg/s; $\left(\rho \cdot V\right)$
P, p	pressure, Pa
R	surface roughness parameters (for details, see Appendix A)
Q	heat-transfer rate, W
q	heat flux, W/m^2; $\left(\frac{Q}{A_h}\right)$
T, t	temperature, °C
$\overline{u}$b	mean velocity of vapor-bubble growth, (Db · fb)
V	volume-flow rate, m^3/kg or volume, m^3
x	vapor quality
Greek Letters
Δ	difference
μ	dynamic viscosity, Pa·s
ρ	density, kg/m^3
σ	coefficient of surface tension (N/m)
Subscripts or superscripts
b	boiling
cr	critical
el	electrical
f	saturated fluid
fg	fluid-gas
fl	fluid
g	gas (saturated vapor)
h	heated
hor	horizontal
hy	hydraulic equivalent
in	inlet
lim	limited
max	maximum
min	minimum
sat	saturation
th	thermal
ver	vertical
w	wall

Abbreviations and acronyms widely used in the text and list of references

ABWR	Advanced Boiling Water Reactor
AECL	Atomic Energy of Canada Limited
AHFP	Axial Heat Flux Profile
Al	Aluminum
ASHRAE	American Society of Heating, Refrigerating and Air-Conditioning Engineers
Bi	Bismuth
CE	Common Era (the same as AD (Anno Domini); represents time from year 1 and onward)
CO2	Carbon Dioxide
BWR	Boiling Water Reactor
CANDU	CANada Deuterium Uranium (reactor)
CHF	Critical Heat Flux
COG	CANDU Owners Group (Ontario, Canada)
Cu	Copper
EDF	Électricité de France S.A.
HE	Helium
hor.	horizontal
HTC	Heat Transfer Coefficient
ID	Inside Diameter
MHI	Mitsubishi Heavy Industries
NIST	National Institute of Standards and Technology (USA)
NPP	Nuclear Power Plant
NRC	Nuclear Regulatory Commission
NU	Natural Uranium
OD	Outside Diameter
ONB	Onset of Nucleate Boiling
OSV	Onset of Significant Void
PB	lead
PDO	Post-DryOut
PHD	Polyethylene High Density
PHWR	Pressurized Heavy-Water Reactor
Pt	Platinum
PWR	Pressurized Water Reactor
R	Refrigerant
RBMK	Reactor of Large Capacity Channel-type (in Russian abbreviations) cooled with boiling water)
REFPROP	REFerence PROPerties
SS, St.St.	Stainless Steel
USA	United States of America
vert.	vertical
W	Water