**Glossary**

**2. Specifics of thermophysical properties of SCFs**

*Advanced Supercritical Fluids Technologies*

**No. Literature source**

1 Pioro et al. [19]

3 Mann and Pioro [20]

4 Gupta et al. [21]

5 Pioro and Mokry [22]

6 Pioro and Duffey [9]

*reduced-pressure scaling: <sup>P</sup>*

*Pcr* 

*Fluid* <sup>¼</sup> *<sup>P</sup> Pcr SCW.*

*\**

**6**

**Table 4.**

Prior to a general discussion on specifics of forced-convective heat transfer at critical and supercritical pressures, it is important to define special terms and expressions used at these conditions [6, 9]. For a better understanding of these

> Properties of selected metals, alloys, and diamond Properties of selected insulating materials Radiative properties of selected materials Properties of selected nuclear fuels

Properties of selected gases at atmospheric pressure

Thermophysical properties of nuclear-reactor coolants 2 Handbook [6] H2O, CO2, He ‑ ‑ *<sup>T</sup>*-*<sup>s</sup>* diagrams

H2O (SCW) *P*cr, 25, 30, 35,

CO2 (SC CO2) *P*cr, 8.4, 10.0,

FLiNaK (MSR) 0.1 H2O/SCW (PWR/SCWR) 15.5/25 He (VHTR, GFR) 7, 9 Na, Pb, Pb-Bi (SFR, LFR) 0.1

SC R-134a *P*cr, 5, 10, 13,

He *P*cr and other

40

11.7

pressures

15

25.0 8.4\* 4.6\*

*Pressures for SC carbon dioxide, R-134a, and R-12 are equivalent for SCW pressure of 25 MPa, based on, so-called,*

*Selected list of literature sources on thermophysical properties of fluids, gases, and other materials.*

CO2 (AGR) 4 250‑<sup>1000</sup> *<sup>ρ</sup>*, *<sup>k</sup>*, *<sup>μ</sup>*, *<sup>c</sup>*p, *<sup>H</sup>*, **Pr**, *<sup>β</sup>*

H2O ‑ ‑ *<sup>T</sup>*-*<sup>s</sup>* diagram H2O (SCW) *<sup>P</sup>*cr, 25, 30, 35 350‑<sup>600</sup> *<sup>ρ</sup>*, *<sup>k</sup>*, *<sup>μ</sup>*, *<sup>ν</sup>*, *<sup>c</sup>*p, *<sup>H</sup>*, **Pr**, *<sup>β</sup>* R-12 (SC R-12) *<sup>P</sup>*cr, 4.65 0‑<sup>350</sup> *<sup>ρ</sup>*, *<sup>k</sup>*, *<sup>μ</sup>*, *<sup>ν</sup>*, *<sup>c</sup>*p, *<sup>H</sup>*, **Pr**, *<sup>β</sup>*

R-134a (SC R-134a) *<sup>P</sup>*cr, 4.6 70‑<sup>150</sup> *<sup>ρ</sup>*, *<sup>k</sup>*, *<sup>μ</sup>*, *<sup>ν</sup>*, *<sup>c</sup>*p, *<sup>H</sup>*, **Pr**, *<sup>β</sup>*

Properties of selected cryogenic gases Properties of selected fluids on saturation line Properties of selected supercritical fluids Properties of selected liquid alkali metals

H2O (BWR, PHWR, PWR)

Air, Ar, CO2, He, H2, Kr (gases)

SCW SC CO2 SC R-134a (three fluids on same graph)

**Fluid** *P***, MPa** *T***, °C Properties**

7, 11, 15 50‑<sup>375</sup> *<sup>ρ</sup>*, *<sup>k</sup>*, *<sup>μ</sup>*, *<sup>ν</sup>*, *<sup>c</sup>*p, *<sup>H</sup>*, **Pr**, *<sup>β</sup>*

<sup>350</sup>‑<sup>600</sup> *<sup>ρ</sup>*, *<sup>k</sup>*, *<sup>μ</sup>*, *<sup>ν</sup>*, *<sup>c</sup>*p, *<sup>H</sup>*, **Pr**, *<sup>β</sup>*

<sup>0</sup>‑<sup>165</sup> *<sup>ρ</sup>*, *<sup>k</sup>*, *<sup>μ</sup>*, *<sup>ν</sup>*, *<sup>c</sup>*p, *<sup>H</sup>*, **Pr**, *<sup>β</sup>*

Range of *T k*, *c*p, *β*

‑100‑<sup>175</sup> *<sup>k</sup>*, *<sup>c</sup>*p, *<sup>β</sup>*

*ρ*, *k*, *μ*, *c*p, *H*, **Pr**

ð Þ <sup>0</sup>*:*<sup>5</sup> � <sup>1</sup>*:*<sup>6</sup> *<sup>T</sup> Tcr*

0.1 0‑<sup>1000</sup> *<sup>ρ</sup>*, *<sup>k</sup>*, *<sup>μ</sup>*, *<sup>c</sup>*p, **Pr**, *<sup>β</sup>*

*Compressed fluid* is the fluid at a pressure above the critical pressure, but at a temperature below the critical temperature (see **Figure 10**).

*Critical point (also called a critical state)* is the point in which the distinction between the liquid and gas (or vapor) phases disappears (see **Figure 10**), that is, both phases have the same temperature, pressure, and specific volume or density. The critical point is characterized with the phase-state parameters: *T*cr, *P*cr and *v*cr (or *ρ*cr), which have unique values for each pure substance.

*Deteriorated heat transfer (DHT)* is characterized with lower values of the HTC compared to those for normal heat transfer (NHT); and hence, has higher values of wall temperature within some part of a heated channel (see **Figures 12, 13a, 24b, 25b, 27, 31**, and **35**) or within the entire heated length (see **Figure 14b**).

*Improved heat transfer (IHT)* is characterized with higher values of the HTC compared to those for NHT; and hence, lower values of wall temperature within some part of a heated channel (see **Figures 12, 21, 25, 27b, 33**, and **34**) or within the entire heated length. In our opinion, the IHT regime or mode includes peaks or "humps" in the HTC profile near the critical or pseudocritical points.

*Normal heat transfer (NHT)* can be characterized in general with HTCs similar to those of subcritical convective heat transfer far from the critical or pseudocritical regions, when they are calculated according to the conventional single-phase Dittus-Boelter-type correlations: **Nu** = 0.0243 **Re**0.8**Pr**0.4 (see **Figures 12, 13a, 14a, 21, 24, 25, 27**, and **30**–**34**).

*Overheated vapor* is the vapor at pressures below the critical pressure, and at temperatures above the saturation temperature, but below the critical temperature (see **Figure 10**).

*Pseudocritical line* is the line, which consists of pseudocritical points (see **Figure 10**).

*Pseudo-boiling* is a physical phenomenon similar to subcritical-pressure nucleate boiling, which may appear at SCPs. Due to heating of an SCF with a bulk-fluid temperature below the pseudocritical temperature (high-density fluid, i.e., "liquidlike") (see **Figures 10, 11, 13b** and **15**), some layers near the heated surface may attain temperatures above the pseudocritical temperature (low-density fluid, i.e., "gas-like"). This low-density "gas-like" fluid leaves the heated surface in a form of variable density volumes (bubbles). During the pseudo-boiling, the HTC usually increases (IHT regime).

*Pseudocritical point* (characterized with *P* and *Tpc*) is the point at a pressure above the critical pressure and at a temperature (*Tpc* > *Tcr*) corresponding to the maximum value of specific heat at this particular pressure (see **Figures 10, 11**, and **13b**).

*Pseudo-film boiling* is a physical phenomenon similar to subcritical-pressure film boiling, which may appear at SCPs. At pseudo-film boiling, a low-density fluid (a fluid at temperatures above the pseudocritical temperature, i.e., "gas-like") prevents a high-density fluid (a fluid at temperatures below the pseudocritical temperature, i.e., "liquid-like") from contacting ("rewetting") a heated surface. Pseudo-film boiling leads to the DHT regime.

*Supercritical fluid* is the fluid at pressures and temperatures that are higher than the critical pressure and critical temperature (see **Figure 10**). However, in the

present paper, the term *supercritical fluid* usually includes both terms—*supercritical fluid* and *compressed fluid*.

*Supercritical "steam"* is actually supercritical water, because at supercritical pressures fluid is considered as a single-phase substance (see **Figure 10**). However, this term is widely (and incorrectly) used in the literature in relation to supercritical-"steam" generators and turbines.

*Superheated steam* is the steam at pressures below the critical pressure, but at

*T-s diagram of generic subcritical-pressure Rankine steam-turbine power cycle (old coal-fired thermal power*

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering…*

*DOI: http://dx.doi.org/10.5772/intechopen.91474*

Also, profiles of the basic thermophysical properties (density, thermal conductivity, dynamic viscosity, specific heat and specific enthalpy) and Prandtl number for four SCFs: water, ethanol, methanol, and carbon dioxide; at critical and one supercritical pressure, which is 25 MPa for water and the corresponding to that equivalent pressures for all other SCFs vs. reduced temperature (temperature) are

**3. Specifics of forced-convection heat transfer at supercritical pressures**

Water is the most widely used coolant or working fluid at SCPs. The largest application of SCW is in SC "steam" generators and turbines, which are widely used in the thermal power industry worldwide. Currently, upper limits of pressures and temperatures used in the thermal-power industry are about 30–38 MPa and 600–625°C, respectively (see **Table 1**). A new direction in SCW application in the power industry has been the development of SCWR concepts (see **Table 2**), as part of the Generation-IV International Forum (GIF) [27] initiative (for details, see [6, 9–13, 28–30]; and Proceedings of the International Symposiums on SCWRs (ISSCWR) (selected augmented and revised papers from ISSCWRs have been published in the ASME Journal of Nuclear Engineering and Radiation Science in

Experiments at SCPs are very expensive and require sophisticated equipment and measuring techniques. Therefore, some of these studies (e.g., heat transfer in fuel-bundle simulators) are proprietary and, hence, usually are not published in

The majority of studies deal with heat transfer and hydraulic resistance of working fluids, mainly water, carbon dioxide, refrigerants, and helium, in circular bare tubes [9, 22, 31–34]. A limited number of studies were devoted to heat transfer

2020, Vol. 6 No. 3; in 2018, Vol. 4, No. 1, and 2016, Vol. 2, No. 1).

and pressure drop in annuli and bundles [9, 10, 35–45].

temperatures above the critical temperature (see **Figure 10**).

shown in **Figures 15–20**.

*plants and SFR NPPs) [6, 7].*

**Figure 3.**

**3.1 Vertical bare tubes**

open literature.

**9**

### **Figure 1.**

*T-s diagram of generic SCP Rankine "steam"-turbine power cycle (modern advanced coal-fired thermal power plants and future SCWR NPPs) [6, 7].*

**Figure 2.**

*T-s diagram of generic subcritical-pressure Rankine steam-turbine power cycle (older coal-fired thermal power plants and AGR Torness NPP) [6, 7].*

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering… DOI: http://dx.doi.org/10.5772/intechopen.91474*

### **Figure 3.**

present paper, the term *supercritical fluid* usually includes both terms—*supercritical*

*Supercritical "steam"* is actually supercritical water, because at supercritical pressures fluid is considered as a single-phase substance (see **Figure 10**). However, this term is widely (and incorrectly) used in the literature in relation to supercriti-

*T-s diagram of generic SCP Rankine "steam"-turbine power cycle (modern advanced coal-fired thermal power*

*T-s diagram of generic subcritical-pressure Rankine steam-turbine power cycle (older coal-fired thermal power*

*fluid* and *compressed fluid*.

**Figure 1.**

**Figure 2.**

**8**

*plants and AGR Torness NPP) [6, 7].*

*plants and future SCWR NPPs) [6, 7].*

cal-"steam" generators and turbines.

*Advanced Supercritical Fluids Technologies*

*T-s diagram of generic subcritical-pressure Rankine steam-turbine power cycle (old coal-fired thermal power plants and SFR NPPs) [6, 7].*

*Superheated steam* is the steam at pressures below the critical pressure, but at temperatures above the critical temperature (see **Figure 10**).

Also, profiles of the basic thermophysical properties (density, thermal conductivity, dynamic viscosity, specific heat and specific enthalpy) and Prandtl number for four SCFs: water, ethanol, methanol, and carbon dioxide; at critical and one supercritical pressure, which is 25 MPa for water and the corresponding to that equivalent pressures for all other SCFs vs. reduced temperature (temperature) are shown in **Figures 15–20**.

### **3. Specifics of forced-convection heat transfer at supercritical pressures**

### **3.1 Vertical bare tubes**

Water is the most widely used coolant or working fluid at SCPs. The largest application of SCW is in SC "steam" generators and turbines, which are widely used in the thermal power industry worldwide. Currently, upper limits of pressures and temperatures used in the thermal-power industry are about 30–38 MPa and 600–625°C, respectively (see **Table 1**). A new direction in SCW application in the power industry has been the development of SCWR concepts (see **Table 2**), as part of the Generation-IV International Forum (GIF) [27] initiative (for details, see [6, 9–13, 28–30]; and Proceedings of the International Symposiums on SCWRs (ISSCWR) (selected augmented and revised papers from ISSCWRs have been published in the ASME Journal of Nuclear Engineering and Radiation Science in 2020, Vol. 6 No. 3; in 2018, Vol. 4, No. 1, and 2016, Vol. 2, No. 1).

Experiments at SCPs are very expensive and require sophisticated equipment and measuring techniques. Therefore, some of these studies (e.g., heat transfer in fuel-bundle simulators) are proprietary and, hence, usually are not published in open literature.

The majority of studies deal with heat transfer and hydraulic resistance of working fluids, mainly water, carbon dioxide, refrigerants, and helium, in circular bare tubes [9, 22, 31–34]. A limited number of studies were devoted to heat transfer and pressure drop in annuli and bundles [9, 10, 35–45].

### **Figure 4.**

*T-s diagram of generic subcritical-pressure Rankine saturated-steam-turbine power cycle (PWR and BWR NPPs) [6, 7].*

New experiments in the 1990s–2000s were triggered by several reasons: (1) thermophysical properties of SCW have been updated from the 1950s–1970s, for example, a peak in thermal conductivity in the critical/pseudocritical points was "officially" introduced in the 1990s; (2) experimental techniques have been improved; (3) in SCWRs various bundle flow geometries will be used instead of bare-tube geometry; and (4) in SC "steam" generators of thermal power plants larger diameter tubes/pipes (20–40 mm) are used, however, in SCWRs hydraulic-

*T-s diagram for 600-MWth VHTR NPP with SC-CO2 (S-CO2) power cycle (based on* **Figure 5***) [18].*

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering…*

*DOI: http://dx.doi.org/10.5772/intechopen.91474*

Accounting that SCW, SC carbon dioxide and SC R-12 are the most widely used fluids, specifics of heat transfer, including generalized correlations, will be discussed in this paper. Specifics of heat transfer and pressure drop at other conditions and/or for other fluids are discussed in the book by Pioro and

All primary sources (i.e., all sources found by the authors from a total of 650 references dated mainly from 1950 till beginning of 2006) of heat transfer experimental data for water and carbon dioxide flowing inside circular tubes at supercrit-

In general, three major heat transfer regimes (for their definitions, see Section 2,

Glossary) can be noticed at critical and supercritical pressures (for details, see

equivalent diameters of proposed bundles will be within 5–12 mm.

ical pressures are listed in the book by Pioro and Duffey [9].

**Figures 12, 13a, 14, 21, 24, 25, 27, 30–35**):

Duffey [9].

**11**

**Figure 6.**

**Figure 5.** *Layout of 600-MWth VHTR NPP with SC-CO2 power cycle (based on figure from Bae et al. [17]) [18].*

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering… DOI: http://dx.doi.org/10.5772/intechopen.91474*

### **Figure 6.**

**Figure 4.**

**Figure 5.**

**10**

*NPPs) [6, 7].*

*Advanced Supercritical Fluids Technologies*

*T-s diagram of generic subcritical-pressure Rankine saturated-steam-turbine power cycle (PWR and BWR*

*Layout of 600-MWth VHTR NPP with SC-CO2 power cycle (based on figure from Bae et al. [17]) [18].*

*T-s diagram for 600-MWth VHTR NPP with SC-CO2 (S-CO2) power cycle (based on* **Figure 5***) [18].*

New experiments in the 1990s–2000s were triggered by several reasons: (1) thermophysical properties of SCW have been updated from the 1950s–1970s, for example, a peak in thermal conductivity in the critical/pseudocritical points was "officially" introduced in the 1990s; (2) experimental techniques have been improved; (3) in SCWRs various bundle flow geometries will be used instead of bare-tube geometry; and (4) in SC "steam" generators of thermal power plants larger diameter tubes/pipes (20–40 mm) are used, however, in SCWRs hydraulicequivalent diameters of proposed bundles will be within 5–12 mm.

Accounting that SCW, SC carbon dioxide and SC R-12 are the most widely used fluids, specifics of heat transfer, including generalized correlations, will be discussed in this paper. Specifics of heat transfer and pressure drop at other conditions and/or for other fluids are discussed in the book by Pioro and Duffey [9].

All primary sources (i.e., all sources found by the authors from a total of 650 references dated mainly from 1950 till beginning of 2006) of heat transfer experimental data for water and carbon dioxide flowing inside circular tubes at supercritical pressures are listed in the book by Pioro and Duffey [9].

In general, three major heat transfer regimes (for their definitions, see Section 2, Glossary) can be noticed at critical and supercritical pressures (for details, see **Figures 12, 13a, 14, 21, 24, 25, 27, 30–35**):

### **Figure 7.**

*Schematic of 600-MWth GFR concept considered initially by GIF with direct Brayton helium cycle (Courtesy of GIF) (see also [6]).*

### **Figure 8.**

*Layout of 2400-MWth GFR NPP with He-N2 indirect combined power cycle (based on figure from Anzieu [23]) [18].*

These heat transfer regimes and special phenomena appear to be due to significant variations of thermophysical properties near the critical and pseudocritical points

*Thermodynamics diagrams for water: (a) pressure-temperature and (b) temperature-specific entropy (based*

*T-s diagrams of 2400-MWth GFR NPP combined power cycle (based on* **Figure 8***) [18].*

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering…*

*DOI: http://dx.doi.org/10.5772/intechopen.91474*

Therefore, the following conditions can be distinguished at critical and SCPs:

a. Wall and bulk-fluid temperatures are below a pseudocritical temperature within a part of (see **Figure 12**) or the entire heated channel (see **Figures 14a,**

and due to operating conditions.

**24a,** and **30**);

**Figure 9.**

**Figure 10.**

**13**

*on NIST [25]).*


Also, two special phenomena (for their definitions, see Section 2, Glossary) may appear along a heated surface: (1) pseudo-boiling; and (2) pseudo-film boiling.

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering… DOI: http://dx.doi.org/10.5772/intechopen.91474*

**Figure 9.**

*T-s diagrams of 2400-MWth GFR NPP combined power cycle (based on* **Figure 8***) [18].*

### **Figure 10.**

*Thermodynamics diagrams for water: (a) pressure-temperature and (b) temperature-specific entropy (based on NIST [25]).*

These heat transfer regimes and special phenomena appear to be due to significant variations of thermophysical properties near the critical and pseudocritical points and due to operating conditions.

Therefore, the following conditions can be distinguished at critical and SCPs:

a. Wall and bulk-fluid temperatures are below a pseudocritical temperature within a part of (see **Figure 12**) or the entire heated channel (see **Figures 14a, 24a,** and **30**);

1.Normal heat transfer;

**Figure 7.**

**Figure 8.**

*[23]) [18].*

**12**

*GIF) (see also [6]).*

*Advanced Supercritical Fluids Technologies*

2. Improved heat transfer; and

3.Deteriorated heat transfer.

Also, two special phenomena (for their definitions, see Section 2, Glossary) may

*Schematic of 600-MWth GFR concept considered initially by GIF with direct Brayton helium cycle (Courtesy of*

appear along a heated surface: (1) pseudo-boiling; and (2) pseudo-film boiling.

*Layout of 2400-MWth GFR NPP with He-N2 indirect combined power cycle (based on figure from Anzieu*

**Figure 11.**

*Profiles of selected thermophysical properties (density, specific heat, thermal conductivity, and dynamic viscosity) vs. temperature for SCW at pressure of 24.0 MPa (based on NIST [25]).*


All these conditions can affect SC heat transfer.

**Figure 13b** shows bulk-fluid-temperature and thermophysical-properties (thermal conductivity, dynamic viscosity, specific heat, and Prandtl number) profiles along the heated length of a vertical bare circular tube (operating conditions in this figure correspond to those in **Figure 13a**).

Some researchers have suggested that variations in thermophysical properties near critical and pseudocritical points result in the maximum value of HTC. Thus, Yamagata et al. [46] found that for SCW flowing in vertical and horizontal tubes, the HTC increases significantly within the pseudocritical region (**Figure 21**). The magnitude of the peak in HTC decreases with increasing heat flux and pressure. The maximum HTC values correspond to a bulk-fluid enthalpy, which is slightly less than the pseudocritical bulk-fluid enthalpy.

**Figure 13.**

**15**

**Figure 12.**

*(a) Temperature and HTC profiles along heated length of vertical bare tube with upward flow of SCW (data by Kirillov et al. [26]): D = 10 mm; Lh = 4 m; points—experimental data; curves—calculated data. Uncertainties of primary parameters are listed in* **Table 5***; and (b) temperature and thermophysical-properties profiles along heated length of vertical tube: operating conditions in this figure correspond to those in (a); and thermophysical properties based on bulk-fluid temperature. Profiles of density, specific heat, thermal conductivity, and dynamic viscosity vs. temperature for SCW at pressure of 24.0 MPa are shown in* **Figure 11***.*

*Temperature and HTC profiles along heated length of vertical bare tube with upward flow of SCW (data by*

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering…*

*DOI: http://dx.doi.org/10.5772/intechopen.91474*

*curves—calculated data; curve for HTC is calculated through Dittus-Boelter correlation (Eq. (1)). Profiles of density, specific heat, thermal conductivity, and dynamic viscosity vs. temperature for SCW at pressure of 24.0 MPa are shown in* **Figure 11***. Uncertainties of primary parameters are listed in* **Table 5***.*

*s; points—experimental data;*

*Kirillov et al. [26]): D = 10 mm; Lh = 4 m; qdht = 316 kW/m<sup>2</sup> at G = 503 kg/m2*

*Supercritical-Fluids Thermophysical Properties and Heat Transfer in Power-Engineering… DOI: http://dx.doi.org/10.5772/intechopen.91474*

### **Figure 12.**

b. Wall temperature is above, and bulk-fluid temperature is below a

*Profiles of selected thermophysical properties (density, specific heat, thermal conductivity, and dynamic*

c. Wall temperature and bulk-fluid temperature is above a pseudocritical temperature within a part of or the entire heated channel (see **Figures 12,**

or the entire heated channel (see **Figure 14b**);

*viscosity) vs. temperature for SCW at pressure of 24.0 MPa (based on NIST [25]).*

d. High heat fluxes (see **Figures 13a**, **24** and **25**);

e. Entrance region (see **Figures 12, 13a, 32,** and **34**);

h. Effect of gravitational forces at lower mass fluxes; etc.

All these conditions can affect SC heat transfer.

**13a, 21, 31**–**35**);

*Advanced Supercritical Fluids Technologies*

**Figure 11.**

**14**

f. Upward and downward flows;

figure correspond to those in **Figure 13a**).

than the pseudocritical bulk-fluid enthalpy.

g. Horizontal flows; and

pseudocritical temperature within a part of (see **Figures 13a, 31, 34,** and **35**)

**Figure 13b** shows bulk-fluid-temperature and thermophysical-properties (thermal conductivity, dynamic viscosity, specific heat, and Prandtl number) profiles along the heated length of a vertical bare circular tube (operating conditions in this

Some researchers have suggested that variations in thermophysical properties near critical and pseudocritical points result in the maximum value of HTC. Thus, Yamagata et al. [46] found that for SCW flowing in vertical and horizontal tubes, the HTC increases significantly within the pseudocritical region (**Figure 21**). The magnitude of the peak in HTC decreases with increasing heat flux and pressure. The maximum HTC values correspond to a bulk-fluid enthalpy, which is slightly less

*Temperature and HTC profiles along heated length of vertical bare tube with upward flow of SCW (data by Kirillov et al. [26]): D = 10 mm; Lh = 4 m; qdht = 316 kW/m<sup>2</sup> at G = 503 kg/m2 s; points—experimental data; curves—calculated data; curve for HTC is calculated through Dittus-Boelter correlation (Eq. (1)). Profiles of density, specific heat, thermal conductivity, and dynamic viscosity vs. temperature for SCW at pressure of 24.0 MPa are shown in* **Figure 11***. Uncertainties of primary parameters are listed in* **Table 5***.*

### **Figure 13.**

*(a) Temperature and HTC profiles along heated length of vertical bare tube with upward flow of SCW (data by Kirillov et al. [26]): D = 10 mm; Lh = 4 m; points—experimental data; curves—calculated data. Uncertainties of primary parameters are listed in* **Table 5***; and (b) temperature and thermophysical-properties profiles along heated length of vertical tube: operating conditions in this figure correspond to those in (a); and thermophysical properties based on bulk-fluid temperature. Profiles of density, specific heat, thermal conductivity, and dynamic viscosity vs. temperature for SCW at pressure of 24.0 MPa are shown in* **Figure 11***.*
