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A Systematic Review on Heat Transfer and Pressure Drop Correlations for Natural Refrigerants

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06 March 2024

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08 March 2024

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Abstract
Due to environmental concerns, natural refrigerants and their use in refrigeration and air conditioning systems are receiving more attention from manufacturers, end users and the scientific community. The study of heat transfer and pressure drop is essential for accurate design and more energy efficient cycles using natural refrigerants. The aim of this work is to provide an overview of the latest outcomes related to heat transfer and pressure drop correlations for ammonia, propane, isobutane and propylene and to investigate the current state of the art in terms of operating conditions. Available data on the existing correlations of heat transfer coefficient and pressure drop for natural refrigerants have been collected through a systematic search. Whenever possible, validity intervals are given for each correlation and the error is quantified. It is the intention of the authors that this could be a valuable support for researchers and an aid to design, with particular reference to heat pumps. A procedure based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was adopted, and the Scopus database was used to query the relevant literature. A total of 135 publications qualified for inclusion in the survey; 34 articles report experimental investigations for not usual geometric conditions. Of the 101 selected papers related to usual geometric conditions, N = 50 deal only with HTC, N = 16 deal only with pressure drop and the remainder (N = 35) analyse both HTC and pressure drop. Among the 85 HTC papers (N = 53) deal with the evaporating condition, N = 30 with condensation and only N = 2 with the heat transfer correlations under both conditions. Most of the 101 articles concern propane and isobutane. The high temperatures are less widely investigated.
Keywords: 
Subject: Engineering  -   Energy and Fuel Technology

1. Introduction

Refrigeration and air conditioning play an important role in modern society, providing thermal comfort and food safety. However, the widespread use of synthetic refrigerants, particularly fluorinated gases (F-gas), has led to serious environmental concerns as they contribute significantly to the greenhouse effect and climate change. In response to these problems, international regulations have imposed restrictions on the use of F-gases, pushing industry towards the adoption of more sustainable solutions. In this context, natural refrigerants have gained increasing attention as environmentally friendly and low impact alternatives [1].
These refrigerants, such as ammonia (R717), hydrocarbons and carbon dioxide (R744), have been studied to replace CFCs, HCFCs and HFCs in refrigeration, air conditioning and heat pump systems. They have zero ozone depletion potential (ODP), and most have near-zero global warming potential (GWP) compared to CFCs and HCFCs.
However, the use of natural refrigerants will be complex, mainly due to the need to adapt refrigeration and air conditioning systems to their characteristics.
In this context, the experimental study of heat transfer and pressure drop and their correlations becomes very important to optimise the energy efficiency of the system and to ensure reliable performance. In addition, the flow pattern studies will help to determine how natural refrigerants behave under different operating conditions, contributing to a more accurate design.
Sunden et al. [2] in their systematic review presented a meta-analysis and regression analysis of the available pressure drop and heat transfer data for both single-phase and two-phase flows for several refrigerants with attention to enhanced configurations of heat exchangers.
Cavallini et al. [3] provide a comprehensive review of recent research on heat transfer and pressure drop of natural refrigerants (CO2, NH3, C3H8, R600a, nitrogen) in mini channels, with the aim of properly designing heat transfer equipment.
The review by Thome et al [4] focuses on flow boiling heat transfer, two-phase pressure drop and flow patterns of ammonia and hydrocarbons. A comparison of experimental data in smooth tubes with four flow boiling correlations is presented. It is suggested that more experimental data be obtained from properly conducted experiments and that new correlations or modified correlations be made on the basis of the existing ones.
This article presents a systematic review to evaluate the available correlations on heat transfer (HT) and pressure drop (PD) of natural refrigerants such as ammonia (R717) and hydrocarbons (R290, R600a, R1270). The most common geometries and operating conditions are analysed for each refrigerant.
Whenever possible, validity intervals are given for each correlation and the error is quantified. It is the intention of the authors that this could be a valuable support for researchers and an aid to design, with particular reference to heat pumps.

2. Materials and Methods

A systematic review of heat transfer and pressure drop correlations for natural refrigerants was conducted following the PRISMA guidelines [5]. This approach to literature review aims to collect all evidence that meets pre-defined eligibility criteria to answer a specific research question. It uses explicit, systematic methods to minimise bias and thus provide reliable findings from which conclusions can be drawn and decisions made.
The workflow consists of four phases: identification, screening, eligibility, and inclusion. In the first phase, a number of research questions were formulated to accurately identify the objectives of the systematic review and, consequently, to examine the available literature:
  • Are there heat transfer and pressure drop correlations that can predict the experimental data of natural refrigerants?
  • How accurate are the current correlations?
  • Which natural refrigerants receive more attention?
Specifically, for this research, the SCOPUS database was queried, using a combination of keywords and Boolean operators to find relevant studies. Specifically, the keywords in the following items were searched in the “Article title, Abstract and Keywords” fields:
  • "heat transfer" OR "heat transmission";
  • "pressure drop" OR "frictional pressure gradient";
  • "natural refrigerant" OR hydrocarbons OR propane OR R290 OR C3H8 OR isobutane OR R600a OR C4H10 OR propylene OR R1270 OR C3H6 OR ammonia OR R717 OR NH3;
  • Correlation OR "prediction method" OR "predictive method" OR “relationship” OR "as a function of";
  • Combustion OR kerosene OR coal (only for “Article Title and Keywords” fields).
The queries from #1 to #5 were combined as follows: #1 OR #2 AND #3 AND #4 AND NOT #5.
Inclusion and exclusion criteria were then defined and applied through the identification, screening, and inclusion steps to select the relevant studies for the review, which were then analysed in detail.
Inclusion criteria:
  • The research must include heat transfer and/or pressure drop correlations.
  • Natural refrigerants must be evaluated, in particular R717, R290, R600a, R1270.
  • The papers can be reviews but also reporting data and correlations.
Exclusion criteria:
  • The articles focus on combustion, toxicity, flammability, and risk.
  • The studies concern natural refrigerants (e.g. CO2), which are not considered in this review.
  • The papers partly deal with heat transfer and pressure drop, but no correlations are reported.
  • The studies refer to synthetic refrigerants and/or refrigerant blends.
  • The papers are conference papers.
  • The papers are purely reviews, not reporting data and correlations.
  • The language is not English.
In the screening phase, the titles, and the abstracts of all the articles identified in the first stage were rigorously assessed against the defined inclusion and exclusion criteria. The papers that met the criteria were analysed in more detail through a full reading of the text (eligibility stage).
A period of 15 years was chosen to give priority to more recent studies, and only those written in English were selected.
The division of labour consisted of a first phase in which the first author independently selected the relevant material, followed by a second stage in which both authors reviewed all papers. In cases of doubt, the senior author made the final decision.

3. Results

A total of 1366 articles were analysed in the first identification step. Duplicates of 24 articles were removed before the screening phase. As shown in Figure 1, of the 1342 original articles, N = 728 were excluded because their titles did not meet the inclusion criteria and N = 213 were excluded because of their abstracts. From the 401 articles obtained, those for which the full text was not available were subtracted. This resulted in N = 353 papers that were assessed for eligibility. A thorough reading of the full text of the articles and the application of the exclusion criteria resulted in a final sample of 135 articles that were assessed in the review.
The 135 articles included are summarised in Table 1, Table 2, Table 3 and Table 4.
It should be noted that the tables are constructed with some assumptions and conventions, which are specified below.
Table 1 shows the source of the data used for the correlation and the geometry studied, highlighting the main focus of the article. As in Table 3, the reader is referred to the citing article in this review (first column) when the number of external databases is greater than 3.
Table 2 shows the operating conditions and correlations for only the natural refrigerants of interest in this review (R717, R290, R600a, R1270). Different refrigerants appear in the table in the case of universal correlations and have therefore been developed with different refrigerants.
The most frequent dimensionless parameters used in the correlations reported in Table 2 and Table 4 are summarised in the Nomenclature section.
The “R” column refers only to the refrigerants used to develop the correlation. If the experimental data available in the literature and related to the refrigerant of interest for the present work are used to test the correlation, the corresponding error is reported in the "AAD" column.
When the experimental results related to the refrigerant of interest for the present work are coupled with an existing correlation, the corresponding error is reported in the table (column "AAD") together with the corresponding reference.
The error between the model prediction and the experimental data is reported as Average Absolute Deviation (AAD), calculated according to Equation 1:
A A D =   1 N ∑ i = 1 N y i p r e d − y i e x p y i e x p
It should be noted that some authors expressed the error in a different way: some as the percentage of data falling within a certain range, others as the coefficient of determination (R2). It is marked with an asterisk in Table 2 and Table 4. The error values related to the mean deviation without the absolute value are indicated by AD.
Table 3 shows the source of the data used for the correlation and the geometry studied, highlighting the main focus of the article in case of not usual configurations.
Table 4 shows the operating conditions and correlations for only the natural refrigerants of interest in this review, in case of not usual configurations.
As said, Table 3 and Table 4 refer to unusual configurations. In fact, among N = 135 articles included, N = 34 articles treat different geometries, or different motion or heat transfer regimes. More specifically, N = 12 articles refer to various geometrical configurations (e.g. helicoidal tubes or heat pipes etc); N = 6 articles are related to the heat transfer in case of microfin tubes; N = 6 analyse the pool boiling heat transfer; N = 6 deal with external HTC; N= 3 study falling film evaporation. One article refers to a thermosyphon configuration.
The most investigated refrigerants are propane and isobutane. The most part of the articles has been published after 2017.
The following paragraphs provide some details of the articles summarised in Table 1 and Table 2.

3.1. Distribution of Articles over Time

As mentioned above, this research focused on the last fifteen years. Figure 2 shows a sharp increase in the number of studies between 2015 and 2016. This may be due to a growing interest in natural refrigerants, perhaps as a result of technological developments, regulatory changes or increased environmental awareness. Of particular note is Regulation (EU) No 517/2014 [234], which came into force on 1 January 2015 and aims to reduce F-gas emissions in the EU by limiting gases with a high Global Warming Potential (GWP).

3.2. Research Approach

3.2.1. Data

When analysing the authors' approach to the experimental data on heat transfer coefficient and pressure drop, it can be seen that N = 71 were carried out by the authors using their own experimental data, while N = 28 used external experimental databases from other studies. As shown in Figure 3, only 2 articles used numerical simulations.
Focusing on each refrigerant (Figure 4), the use of own experimental data is predominant for R290, R600a, and R1270. For R717, both approaches are used equally.

3.2.2. HTC and PD Correlations

Figure 5 shows the authors' different approaches to the correlations. In particular, a new correlation was developed in N = 47 of the HTC evaluations, while in N = 38 the authors reported the correlation from the literature that best predicted the data.
For pressure drop, the number of best correlations already published (N = 30) outweighed the development of a new model (N = 21).

3.2.3. Test Conditions

Of the 101 selected papers, N = 50 deal only with HTC, N = 16 deal only with pressure drop and the rest (N = 35) analyse both HTC and pressure drop.
A closer analysis of the 85 HTC papers shows in Figure 6 that most of them (N = 53) deal with the evaporating condition, N = 30 with condensation and only N = 2 with the heat transfer correlations under both conditions (Figure 6).

3.3. Operating Conditions

3.3.1. Hydraulic Diameters

An analysis of the geometries used, reported in Figure 7, shows that the most commonly studied diameters range from 0.5 to 9 mm, with the largest number of evaluations in the (1,2] mm range. The (0,0.5] and (9,50] mm ranges are of less interest to the authors.

3.3.2. Saturation Temperatures

From the analysis of saturation temperatures in the evaporating condition shown in Figure 8, most of the authors' evaluations cover the range from −40 to 40 °C. Less studied are the conditions from 50 to 150 °C. On the other hand, for the condensing condition, the low temperatures (from −40 to 20 °C) are the least studied, followed by the range (50, 100] °C. The most evaluated range is 30 ÷ 40 °C, followed by 40 ÷ 50 °C and 20 ÷ 30 °C.

3.3.3. Vapour Quality

From the vapour quality data summarised in Table 2 and shown in Figure 9, it can be seen that all ranges were investigated.

3.3.4. Specific Heat Flux

The analysis of the specific heat flux data shows a higher interest in the heat flux values from 0 to 30 kW/m2, with a peak in the range from 10 to 20 kW/m2, as shown in Figure 10. For the range from 30 to 740 kW/m2, a decreasing trend in the number of evaluations is observed as the heat flux increases.
Focusing on the specific heat fluxes studied for each refrigerant, a similar trend is found for all of them.

3.3.4. Specific Mass Flux

As shown in Figure 11, the most studied specific mass fluxes range from 0 to 600 kg/m2s; the intervals from 600 to 5600 kg/m2s are less adopted.
Focusing on the specific mass fluxes adopted for each refrigerant, a similar trend is found for all of them.

3.4. Refrigerants

Among the selected articles, most concern propane and isobutane, as shown in Figure 12.

3.4.1. Hydraulic Diameters and Saturation Temperatures

An analysis of the diameters used in ammonia studies shows that diameters from 0.5 to 15 mm are all widely studied, with a greater focus on those from 1 to 3 mm. Less used are the (0,0.5] mm range and diameters from 15 to 50 mm.
From the R600a geometry data, the most studied diameter range is that from 0.5 to 12 mm, with the highest number of evaluations relating to the (7,9] and (1,2] mm ranges. Of less interest to the authors are the (0,0.5] mm range and diameters from 12 to 50 mm.
For propane, most of the authors' evaluations cover the range from 0.5 to 15 mm, with a focus on the (0.5,3] mm range. As with ammonia, the (0,0.5] mm range and diameters from 15 to 50 mm are less commonly used. The few evaluations on the R1270, take into account all the diameter ranges.
Looking more closely at the saturation temperature ranges for each refrigerant, the evaluations for ammonia cover the range from 20°C to 60°C in the condensing conditions.
For R1270, R600a and R290, the range of condensing saturation temperatures considered is wider, from −40°C to 80 °C and the most evaluated range is from 30 to 40°C.
When analysing the evaporation temperatures, it can be seen that for ammonia most of the authors' evaluations cover the range −40°C to 50°C, whereas for R1270 the studies focus on saturated temperatures from 0°C to 30°C.
For R600a and R290, the most commonly used temperatures are 0°C to 40°C and from −40°C to 40°C respectively.
For evaporating temperatures above 50°C, there are no evaluations for R717 and R1270, while there are a few for R600a and R290.

4. Correlations

Correlations for HTC and for pressure drop for each refrigerant were considered below, focusing on error ranges and best correlations. Only those articles where the error was evaluated in terms of absolute average deviation are considered, and an AAD threshold of 12% was used to identify the best models.

4.1. R717

Out of a total of 28 studies on ammonia, only 20 that expressed the error in terms of AAD were included in this analysis. In particular, for the condensation HTC, the Tao [96] correlation predicts the experimental data well, with an AAD of 7.4%. The maximum error in terms of AAD is 41% for the Shah correlation, as reported in [77]. For the evaporation HTC the proposed correlations show errors ranging from 4.7% to 40.9%, the best being those of Fang [145], Choi [25] and Zhang [111] with AAD of 4.7%, 11.09 % and 11.4% respectively. For PD, the AAD ranges from 9.5% to 23.7%; the correlation of Moreno Quiben and Thome [132] shows a good prediction of the data with an AAD of 9.5%.

4.2. R1270

Of the 16 studies on R1270, the 9 that reported the error in terms of AAD were considered. For the condensation HTC, the errors range from 11.0% to 32.6% and the most reliable correlations are those of Dorao and Fernandino [123] and Zhang [109] with an AAD of 11.0%. For the evaporating condition the best predictions of the data are the Longo [158], Liu and Winterton [118] and Sun and Mishima [142] models, with an AAD of 6.9%, 8.5% and 8.6% respectively. The maximum error is 27.1% for the Gorenflo correlation, as reported in [155].
For PD, the average absolute deviation ranges from 4.4% to 19.8%; the correlation of Xu and Fang [120], Macdonald and Garimella [69] and Friedel [143] shows the best prediction of the data with an AAD of 4.4%, 6.4% and 7.3% respectively.

4.3. R600a

Of the 45 studies on R600a, only 23 report the AAD error. In particular, for the condensation HTC, the correlations of Dorao and Fernandino [123], Haraguchi et al. [150], Cao [23] and Shah [89] predict the experimental data well, with an AAD of 5.8%, 6.57%, 9.8% and 11.2% respectively. The maximum error in terms of AAD is 17.4%, as reported in [93].
Regarding the evaporation HTC, the proposed correlations show errors ranging from 6.2% to 40.1% and the best ones are those of Fang et al. [145], Shah [122], Shah [91] and Liu and Winterton [118] with AAD of 6.2% and 10.2% (for [65] and [39] respectively), 6.4%, 11.4 % and 11.5% respectively.
For PD, the AAD ranges from 6.6% to 32.52%; the correlations of Xu and Fang [120], Xu and Fang [125], Cao [23], Sempértegui-Tapia [87], Zhang [177] and Nualboonrueng [146] show a good prediction of the data with an AAD of 6.6%, 11.0%, 7.3%, 9.3%, 9.9% and 10.18%.

4.4. R290

Out of a total of 54 studies on propane, only 38 that reported the error in terms of AAD were included in this analysis. For the condensation HTC, the errors range from 4.9% to 25.8% and the most reliable correlations are those of Dorao and Fernandino [123], Macdonald [70], Shah [93], Moser [139], Thome [147], Akers [156], Shah [89], Macdonald [69] with an AAD of 4.9%, 5.4%, 6.5% and 11%, 7.22%, 7.27%, 9.0%, 10.5%, 11% respectively. For the evaporating condition the best predictions of the data are the models of Liu and Winterton [118], Fang et al. [145], Longo et al. [158], Lillo [60], Pamitran [81], Shah [91], Choi [25], Zhang [110] and Aizuddin et al. [116] with an AAD of 6.2% and 7.5% (for [10] and [103] respectively), 6.5%, 7.7%, 8.2%, 8.27%, 9.2%, 10.02%, 10.9% and 11.6% respectively. The maximum error is 33.16%, as reported in [75].
For PD, the Average Absolute Deviation ranges from 6.88% to 20.8%; the correlation of Sun and Mishima [160], Sempértegui-Tapia [87], Friedel [143], Macdonald and Garimella [69], Del Col et al. [141], Patel [83], Choi [24], Xu and Fang [120] show the best prediction of the data with an AAD of 6.88%, 7.2%, 7.59%, 7.9%, 9.1%, 10.08%, 10.84% and 11.7% respectively.

4. Discussion

Of the four refrigerants considered in this review, R600a has the most reliable correlation for condensing HTC, with a maximum AAD error of 17.4%. For evaporating HTC, the smallest maximum error is found for R1270 and is equal to 27.1%.
For pressure drop, for both R1270 and R290, the correlations proposed by the authors show good reliability in predicting the data, with maximum AADs of 19.8% and 20.8% respectively.
Considering the intervals studied by the authors, the widest diameter range of validity of the correlations is 2–49 mm in [89]; the widest saturation temperature range of validity is from −34.4°C to 72.1°C for condensation in [95] and from 55°C to 141°C for evaporation in [110]. For specific mass flux and specific heat flux the widest ranges of validity are 3.7–5176 kg/m2s in [92] and 3–736 kW/m2 in [26] respectively.
Among the articles reported in Table 1 and Table 2, propane and isobutane are the most studied refrigerants.
The use of the authors' own experimental data predominates over the use of external experimental databases. For HTC, most of the studies deal with the development of a new correlation, whereas for pressure drop, the number of already published best correlations prevails.
Of the 101 papers selected, 50 deal only with HTC, 16 deal only with pressure drop and the remaining 35 analyse both HTC and pressure drop; most of the HTC papers deal with the evaporating condition.
With regard to the geometries, the most commonly studied diameters range from 0.5 to 9 mm, with the largest number of evaluations concerning the (1,2] mm range.
Regarding the analysis of saturation temperatures in the evaporating conditions, most of the authors' evaluations cover the range from −40 to 40°C; for the condensing condition, most of the authors studied the temperature range from 20 to 50°C.
It should be noted that a small number of evaluations (and therefore of correlations) focus on the high temperature condensation (50–80°C). These temperature ranges could be studied in view of the high temperature applications of the heat pumps. In fact, in the near future, high temperature heat pumps could be installed in buildings that have not yet been subject to energy saving measures. Many studies are dedicated to propane, as efforts are also focused on it for domestic applications (small machines). For centralised applications in residential or public buildings, the use of high capacity and high temperature machines could be considered; in this case, propane or ammonia could be interesting and should be reconsidered and further investigated.

5. Conclusions

In this work, available data on the existing correlations of heat transfer coefficient and pressure drop for natural refrigerants have been collected through a systematic search.
Whenever possible, validity intervals are given for each correlation and the error is quantified. It is the intention of the authors that this could be a valuable support for researchers and an aid to design, with particular reference to heat pumps.
For the articles considered in this review, the operating conditions are reported in terms of diameter, saturation temperatures, vapour quality, specific heat flux, specific mass flux. More attention is paid to the evaporation behaviour with respect to condensation and two refrigerants (propane and isobutane) are diffusely studied.
In the studies reported in this review, the correlation in case of high condensation temperature is reported in a few cases. The lack of information requires further investigation in view of the applications of heat pumps in heating systems, without modification of the distribution systems in buildings that have not yet been subject to energy saving measures.

Author Contributions

Conceptualization, A.C. and A.D..; methodology, A.C. and A.D..; software, A.C. and A.D.; validation A.C. and A.D..; formal analysis, A.C. and A.D.; investigation, A.C. and A.D..; resources, A.D..; data curation, A.C. and A.D..; writing—original draft preparation, A.C. and A.D..; writing—review and editing, A.C. and A.D..; visualization, A.C. and A.D..; supervision, A.D..; project administration, S.D..; funding acquisition, A.D. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Ministero dell’Università e della Ricerca MUR, grant D.M. 1061/2021 finanziati tramite il Programma Operativo Nazionale (PON) “Ricerca e Innovazione” 2014–2020—Azione IV.4 “Dottorati e contratti di ricerca su tematiche dell’innovazione” e Azione IV.5 “Dottorati su tematiche green”.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Nomenclature

Roman
cp Specific heat capacity [J/kgK]
d Diameter [m]
g Acceleration of gravity [m/s2]
G Specific Mass flux [kg/m2s]
h Heat transfer coefficient [W/m2K]
hlv Latent heat of vaporization [J/kg]
i Specific enthalpy [J/kg]
Jv Vapour superficial velocity [m/s]
Lh Heated length [m]
M Molecular mass [kg/kmol]
p Pressure [Pa]
pr Reduced pressure, p r = p s a t / p c
q Specific Heat flux [W/m2]
Ra Mean roughness height [µm]
SV Specific volume, S V = ( V v − V l ) V = V v − V l x V v + 1 − x V l
T Temperature [°C]
x Vapour quality [–]
Greek letters
β Chevron angle [°]
δ Channel height [m]
Δp Pressure drop [Pa]
θ Winding angle [°]
λ Thermal conductivity [W/mK]
µ Dynamic viscosity [Pa·s]
ν Kinematic viscosity [m2/s]
ρ Density [kg/m3]
ρ* Density ratio, ρ * = ρ l / ρ v
ρtp Two phase density, ρ t p = x ρ v + 1 − x ρ l − 1
σ Surface tension [N/m]
Subscripts
avg Average
c Critical
cb Convective boiling
eq Equivalent
exp Experimental
flat Flattened tubes
frict Frictional
h Hydraulic
i Inner
l Liquid
lo Liquid only
loc Local
nb Nucleate Boiling
o Outer
pb Pool boiling
pred Predicted
sat Saturation
v Vapour
vo Vapour only
w Wall
Abbreviations
AD Average Deviation
aPD Adiabatic flow pressure drop
AAD Absolute average deviation
CFCs Chlorofluorocarbons
f.p.m. Fins per meter
GWP Global Warming Potential
HBHX Helically baffled shell-and-tube heat exchanger
HCFCs Hydrochlorofluorocarbons
HC Rs Hydrocarbon refrigerants
HFCs Hydrofluorocarbons
HFO Hydrofluoroolefin
HT Heat transfer
bHT Boiling heat transfer
cHT Condensation heat transfer
HTC Heat Transfer Coefficient
LHP Loop heat pipe
LNG Liquefied natural gas
MF Microfin
ODF Offset strip fin
ODP Ozone Depletion Potential
PCHE Printed circuit heat exchanger
PD Pressure drop
PHE Plate heat exchanger
R Refrigerant
ST Smooth tube
SWHE Spiral wound heat exchanger
TP Two Phase
TPCT Two-phase closed thermosyphon
VQ Vapour quality
Dimensionless numbers
Bo Boiling number, B o = q G h l v
Bd Bond number, B d = g ρ l − ρ v d 2 σ
Cn Confinement number, C n = σ / g ρ l − ρ v 0.5 d
Co Convection number, C o = 1 − x x 0.8 ρ v ρ l 0.5
Fa Fang number, F a = ρ l − ρ v σ G 2 d
ϕ f 2 Two-phase frictional multiplier (Chisholm) ϕ f 2 = 1 + C X t t + 1 X t t 2
Frl Liquid Froude number, F r l = G 1 − x 2 g d ρ l 2
f Friction Factor ≡ Darcy factor, f = 2 ∆ p ρ v 2 d L
fFann Fanning friction factor, f F a n n = ∆ p 2 ρ v 2 d L
Ja Jacob’s number, J a = h l v c p l ∆ T s
Ka Kapitza number, K a = μ 4 g / ρ σ 3
Nu Nusselt number N u = h · L λ
Pr Prandtl number, P r = c p µ λ
Reeq Equivalent Raynolds number R e e q = G d h μ l 1 + x + x ρ l ρ v 0.5
Rel Liquid Reynolds number R e l = 1 − x G d μ l
Rev Vapour Reynolds number R e v = x G d μ v
Reko Liquid only (k=l) or vapor only (k=v) Re, R e k o = G d μ k
We Weber number, W e = G 2 d ρ σ
Xtt Lockhart-Martinelli parameter X t t = ρ v ρ l 0.5 μ l μ v 0.1 1 − x x 0.9
(Turbulent-Turbulent flow)
Xvv Lockhart-Martinelli parameter X v v = ρ v ρ l 0.5 μ l μ v 0.5 1 − x x 0.5
(Laminar-Laminar flow)

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Figure 1. PRISMA flowchart for studies included in this review.
Figure 1. PRISMA flowchart for studies included in this review.
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Figure 2. Number of studies published in the last 15 years.
Figure 2. Number of studies published in the last 15 years.
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Figure 3. Number of articles by type of data used.
Figure 3. Number of articles by type of data used.
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Figure 4. Number of evaluations by type of data used for each refrigerant.
Figure 4. Number of evaluations by type of data used for each refrigerant.
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Figure 5. Number of evaluations related to new correlations and best correlations already published for HTC and PD.
Figure 5. Number of evaluations related to new correlations and best correlations already published for HTC and PD.
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Figure 6. Percentage distribution of HTC articles.
Figure 6. Percentage distribution of HTC articles.
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Figure 7. Number of evaluations related to each hydraulic diameter range.
Figure 7. Number of evaluations related to each hydraulic diameter range.
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Figure 8. Number of evaluations related to each saturation temperature range for evaporating and condensing conditions.
Figure 8. Number of evaluations related to each saturation temperature range for evaporating and condensing conditions.
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Figure 9. Number of evaluations related to each vapour quality range.
Figure 9. Number of evaluations related to each vapour quality range.
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Figure 10. Number of evaluations related to each specific heat flux range.
Figure 10. Number of evaluations related to each specific heat flux range.
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Figure 11. Number of evaluations related to each specific mass flux range.
Figure 11. Number of evaluations related to each specific mass flux range.
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Figure 12. Number of evaluations related to each refrigerant.
Figure 12. Number of evaluations related to each refrigerant.
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Table 1. Summary of the type of data, geometries and research highlights of the articles included in this review.
Table 1. Summary of the type of data, geometries and research highlights of the articles included in this review.
First author/Year R Data Geometry/Material/Orientation Research highlights
Aǧra
(2012) [6]		 R600a Analytical model and experimental study Horizontal smooth copper tube, di = 4 mm TP annular flow condensation HT
Ahmadpour (2019) [7] R600a Experimental study Horizontal straight copper tube, di = 8.7 mm Condensation HT,
Effect of lubricating oil on condensation HT
Horizontal U-shaped copper tube, di = 8.7 mm
Akbar
(2021) [8]		 R290 Experimental study Horizontal smooth stainless steel tube, di = 3 mm TP flow boiling HT
Ali
(2021) [9]		 R1234yf
R152a
R600a R134a		 Experimental study Vertical stainless steel tube
di = 1.60 mm, Lh = 245 mm		 Flow boiling frictional PD
Allymehr
(2020) [10]		 R290 Experimental study A smooth tube, MF1, MF2
do = 5 mm		 Flow boiling HT and PD
Allymehr
(2021) [11]		 R600a
R1270		 Experimental study A smooth tube, MF1, MF2
do = 5 mm		 Evaporation HT and PD
Allymehr
(2021) [12]		 R290
R600a
R1270		 Experimental study A smooth tube, MF1, MF2
do = 5 mm		 Condensation HT and PD
Amalfi
(2016) [13]		 R134a R245fa R236fa R717, R290
R600a R1270 R1234yf
R mixtures		 External experimental database [14] Brazed/gasketed/welded/shell and plate heat exchanger (PHE), β = 27–70°, dh = 1.7–8 mm Flow boiling HT and TP frictional PD
Anwar
(2015) [15]		 R600a Experimental study Vertical stainless steel tube
di = 1.60 mm, Lh = 245 mm		 Flow boiling HT and dryout characteristics
Arima
(2010) [16]		 R717 Experimental study Vertical plate
evaporator		 Flow patterns and forced convective boiling HT
Asim
(2022) [17]		 R600a Experimental study Vertical stainless steel tube
di = 1.60 mm, Lh = 245 mm		 Flow boiling HT
Ayub
(2019) [18]		 R717 R134a
R410A		 External experimental database (see [18]) PHE, β = 0–65° Evaporation HT
Basaran
(2021) [19]		 R600a Steady-state numerical simulations
(CFD code ANSYS Fluent 19.2)		 Horizontal smooth circular microchannel
di = 0.2–0.6 mm		 Condensation HT and TP PD
Basaran
(2021) [20]		 R600a Experimental study and thermal simulation model Microchannel
dh = 0.2–0.6 mm		 Condensation HT and PD
Butrymowicz
(2022) [21]		 R134a, R507A R600a Experimental study Horizontal copper tubular channel
di = 12 mm		 Flow boiling HT under near critical pressure
Butrymowicz
(2022) [22]		 R290 Experimental study Aluminium minichannel condenser and evaporator Condensation and evaporation frictional PD
Cao
(2021) [23]		 R600a Experimental study Aluminium minichannel
di = 8 mm, vertical/horizontal inclined angles 0°–180°		 Condensation HT and frictional PD
Choi
(2009) [24]		 R290 Experimental study Horizontal smooth stainless steel minichannels
di = 1.5, 3.0 mm		 TP flow boiling HT and PD
Choi
(2014) [25]		 R744
R717
R290
R1234yf		 Experimental study Horizontal circular stainless steel smooth tube
di = 1.5, 3 mm		 Evaporation HT
Cioncolini
(2011) [26]		 R22, R32 R134a R290 R600a
R718, R12
R236fa
R245fa		 External experimental database (see [26]) Vertical/horizontal tubes
di = 1.03–14.4 mm		 Liquid film thickness, void fraction and convective boiling HT
Da Silva
(2023) [27]		 R600a Experimental study Horizontal aluminium multiport extruded tube
di = 1.47 mm		 Flow patterns, void fraction distribution and flow boiling PD
Da Silva Lima (2009) [28] R717 Experimental study Horizontal smooth stainless steel tube, di = 14 mm Flow patterns, diabatic and adiabatic frictional PD
Dalkilic
(2010) [29]		 R600a Experimental study Horizontal smooth copper tube, di = 4 mm Annular flow condensation frictional PD
Darzi
(2015) [30]		 R600a Experimental study Horizontal copper smooth round tube, dh = 8.7 mm Condensation HT and PD
Horizontal copper flattened tubes, dh = 5.1–8.2 mm
De Oliveira (2016) [31] R600a Experimental study Horizontal smooth stainless steel tube
di = 1.0 mm, Lh = 265 mm		 TP flow patterns and flow boiling HT
De Oliveira
(2017) [32]		 R290
R600a		 Experimental study Horizontal stainless steel tube
di = 1.0 mm, Lh = 265 mm		 Flow patterns and TP flow boiling frictional PD
De Oliveira
(2018) [33]		 R290 Experimental study Horizontal smooth stainless steel tube
di = 1.0 mm, Lh = 265 mm		 Flow patterns and flow boiling HT
De Oliveira
(2020) [34]		 R1270 Experimental study Horizontal stainless-steel circular tube, di = 1 mm Flow patterns and flow boiling HT
De Oliveira
(2023) [35]		 R1270 Experimental study Horizontal stainless-steel circular tube, di = 1 mm Flow patterns and flow boiling frictional PD
Del Col
(2014) [36]		 R290 Experimental study Horizontal copper minichannel
di = 0.96 mm, Ra = 1.3 µm		 TP condensation and flow boiling HT, frictional PD
Del Col
(2017) [37]		 R1270 Experimental study Horizontal copper Minichannel
di = 0.96 mm, Ra = 1.3 µm		 Condensation and flow boiling HT, adiabatic TP PD
ElFaham
(2023) [38]		 R290
R600
R600a		 External experimental database (see [38]) Horizontal/vertical stainless steel/copper tubes
di = 0.168–7.7 mm		 TP flow boiling HT
Fang, Xiande
(2019) [39]		 R717
R290
R600a		 External experimental database (see [39]) Horizontal/vertical upward copper/ stainless steel single circular tubes
dh = 0.96–14 mm		 Saturated flow boiling HT
Fang, Xianshi
(2023) [40]		 R600a External experimental database [41] Horizontal copper circular smooth and spiral coil inserted tubes, di = 8.1 mm Condensation frictional PD
Fries
(2019) [42]		 R290 Experimental study Horizontal mild steel plain tubes, di = 14.65, 20.8 mm Condensation HT and PD
Fries
(2020) [43]		 R290
R1270		 Experimental study Copper tube, di = 15 mm
Mild steel tube, di = 14.65 mm		 PD in TP flow
Fronk
(2016) [44]		 R717 External experimental database [45] Horizontal smooth stainless steel tube, di = 0.98–2.16 mm Pure ammonia condensation HT, high-temperature-glide zeotropic ammonia/water mixtures
Gao
(2018) [46]		 R717 Experimental study Horizontal smooth stainless steel tube, di = 4 mm Flow boiling HT, adiabatic TP frictional PD
Gao
(2019) [47]		 R717 Experimental study Horizontal smooth stainless steel tube, di = 4, 8 mm TP PD
Ghazali
(2022) [48]		 R290 External experimental database (see [48]) Horizontal smooth stainless steel tubes
di = 1–6 mm		 Pre-dry out TP evaporation HT,
genetic algorithm optimization
Ghorbani
(2017) [49]		 R600a Experimental study Horizontal flattened copper tube dh = 7.29 mm Condensation HT,
R600a-oil-nanoparticle mixtures
Guo
(2018) [50]		 R1234ze(E)
R290
R161
R41		 Experimental study Horizontal smooth copper tube, di = 2 mm Condensation HT
Huang
(2012) [51]		 R134a
R507a
R12, R717		 Experimental study and external experimental database [52] Brazed PHE
β = 28–60°, dh = 3.51 mm		 TP flow boiling HT and PD
Ilie
(2022) [53]		 R717 Experimental study PHE, β = 60°, dh = 10 mm Boiling HT
Inoue
(2018) [54]		 R32, R410a R1234ze(E)
R152a		 Experimental study Horizontal smooth copper tube, di = 3.48 mm
 Condensation HT
Kanizawa
(2016) [55]		 R134a
R245fa
R600a		 External experimental database (see [55]) Horizontal smooth stainless steel tube, di = 0.38–2.60 mm Flow boiling HT
Khan, T.S.
(2012) [56]		 R717 Experimental study PHE, β = 60° TP evaporation HT and PD
Khan, M.S.(2012) [57] R717 Experimental study PHE, β = 30° TP evaporation HT and PD
Koyama
(2014) [58]		 R717 Experimental study Titanium plate evaporator
Channel height = 1, 2, 5 mm		 Flow boiling HT
Lee
(2010) [59]		 R290
R600a		 Experimental study Horizontal smooth copper tube
di = 5.80–10.07 mm		 Condensation HT
Lillo
(2018) [60]		 R290 Experimental study Horizontal circular smooth stainless steel tube
di = 6 mm, Lh = 193.7 mm		 TP flow boiling HT and PD, dry-out incipience vapor quality
Liu
(2016) [61]		 R290 Experimental study Horizontal square stainless steel minichannel
dh = 0.952 mm
Ra = 3.2 µm		 Condensation HT and PD
Liu
(2018) [62]		 R600a
R227ea R245fa		 Experimental study Vertical rectangular copper mini-channel, dh = 2.76 Flow patterns and flow boiling HT
Longo
(2012) [63]		 R600a
R290
R1270		 Experimental study Brazed plate heat exchanger (PHE), β = 60°, dh = 10 mm Vaporization HT and frictional PD
Longo
(2017) [64]		 R290
R1270		 Experimental study Horizontal smooth tube
di = 4 mm		 Forced convection condensation HT, condensation frictional PD
Longo
(2020) [65]		 R600a Experimental study Horizontal smooth copper tube, di = 4 mm Flow boiling HT and frictional PD
Longo
(2023) [66]		 R290
R1270		 Experimental study Brazed Plate Heat Exchanger (BPHE), β = 65° Nucleate boiling HT
López-Belchí
(2016) [67]		 R290 Experimental study Horizontal square aluminium multiport minichannel tube, di = 1.16 mm TP condensation HT and frictional PD
Macdonald
(2016) [68]		 R290 Experimental study Horizontal smooth copper tubes, di = 7.75, 14.45 mm Condensation HT and frictional PD
Macdonald
(2016) [69]		 R290 Experimental study Horizontal smooth copper tubes, di = 7.75, 14.45 mm Flow visualization, condensation HT and frictional PD
Macdonald
(2017) [70]		 R290 Experimental study Horizontal circular smooth tube, di = 7.75 mm Flow visualization and condensation HT
Maher
(2020) [71]		 R134а
R245fa
R125, R744
R236ea R22, R152a
R32, R410a
R1234ze(E)
R290
R600a
R1234yf		 External experimental database (see [71]) Horizontal circular tubes
di = 0.509–8.0 mm		 Two Phase Flow frictional PD
Maqbool
(2012) [72]		 R717 Experimental study Vertical circular stainless steel mini channel
di = 1.70, 1.224 mm		 Flow boiling TP PD
Maqbool
(2012) [73]		 R717 Experimental study Vertical circular stainless steel mini channel
di = 1.70, 1.224 mm		 Flow boiling HT
Maqbool
(2013) [74]		 R290 Experimental study Vertical circular stainless steel minichannel
di = 1.70 mm, Ra = 0.21 µm, Lh = 245 mm		 TP flow boiling HT and frictional PD
Mohd-Yunos
(2020) [75]		 R290 External experimental database (see [75]) Vertical /horizontal tubes
di = 1–6 mm		 TP Evaporation HT and genetic algorithm optimization
Moreira
(2021) [76]		 R134a
R600a
R290
R1270		 Experimental study Horizontal smooth stainless steel tube, di = 9.43 mm Flow patterns and convective condensation HT
Morrow
(2021) [77]		 R717
R290
R600a		 External experimental database (see [77]) Horizontal/vertical, round/square/rectangular/flat, smooth tubes
di = 0.952–10.07 mm		 Flow condensation HT
Murphy
(2019) [78]		 R290 Experimental study Vertical aluminium minichannel, di = 1.93 Condensation HT and PD
Nasr
(2015) [79]		 R600a Experimental study Horizontal smooth copper tube, di = 8.7 mm Flow patterns and flow boiling HT
Oh
(2011) [80]		 R22, R134a R410A, R290, R744 Experimental study Horizontal circular smooth stainless steel tubes
di = 0.5, 1.5, 3.0 mm		 Flow patterns and TP flow boiling HT
Pamitran
(2009) [81]		 R290 Experimental study Horizontal smooth stainless steel minichannels
di = 1.5, 3.0 mm		 TP flow boiling HT
Pamitran
(2011) [82]		 R290
R717		 Experimental study Horizontal circular stainless steel smooth tube
di = 1.5, 3 mm		 Evaporation HT
Patel
(2018) [83]		 R290, R22
R1234yf, R1234ze, R410a, R32		 External experimental database (see [83]) Horizontal minichannel
dh = 0.952–1.150 mm 		Condensation TP frictional PD
Pham
(2019) [84]		 R22, R32, R410a R290 Experimental study Horizontal aluminium multiport rectangular minichannel, dh = 0.83 mm Condensation HT and TP frictional PD
Qiu
(2015) [85]		 R600a Experimental study Horizontal smooth copper tube, di = 8 mm Saturation flow boiling HT and adiabatic frictional PD
Sempértegui-Tapia (2017) [86] R134a
R1234ze(E)R1234yf R600a		 Experimental study Horizontal stainless-steel tube, di = 1.1 mm Flow boiling HT
Sempértegui-Tapia
(2017) [87]		 R134a R1234ze(E) R1234yf R600a Experimental study Horizontal circular/square/triangular stainless steel tube
dh = 0.634–1.1 mm		 TP frictional PD
Shafaee
(2016) [88]		 R600a Experimental study Horizontal copper smooth tube, di = 8.1 mm Flow boiling HT, effect of coiled wire inserted tubes on HT
Shah
(2009) [89]		 R718
Halocarbon Rs
HC Rs
Organics		 External experimental database (see [89]) Horizontal/vertical/downward-inclined tubes
dh = 2–49 mm		 Condensation HT
Shah
(2016) [90]		 R718, R744 Halocarbon Rs,
HC Rs		 External experimental database (see [90]) Horizontal round/square/ rectangle/semi-circle/triangle/barrel shaped single and multi channels
dh = 0.1–2.8 mm		 Condensation HT
Shah
(2017) [91]		 R718
R744
R717
Halocarbon Rs
Cryogens
HC Rs		 External experimental database (see [91]) Horizontal/vertical, round/rectangular/triangular single and multi-port channels, dh = 0.38–27.1 mm Saturated boiling HT prior to critical heat flux
Shah
(2017) [92]		 R718, R744
cryogens, R12, R113 R22, R134a
HC R (R50, R290)		 External experimental database (see [92]) Horizontal/vertical tubes
dh = 0.98–25 mm		 Dispersed flow film boiling HT
Shah
(2021) [93]		 R718, HC Rs, R717, halocarbon Rs External experimental database (see [93]) Plate heat exchanger (PHE), β = 30–75° Condensation HT
Shah
(2022) [94]		 R718, R744
Halocarbon R,
HC, R717 cryogens, chemicals		 External experimental database (see [94]) Horizontal/vertical, round/rectangular/triangular single and multi-port channels, dh = 0.38–41 mm Saturated boiling HT
Tao
(2019) [95]		 HFCs
HC Rs
HFOs
R744		 External experimental database (see [95]) Brazed/gasketed plate heat exchanger (PHE), β = 25.7–70°, dh = 3.23–8.08 mm Condensation HT and frictional PD
Tao
(2020) [96]		 R717 External experimental database [97] PHE, β = 63°, dh = 2.99 mm Flow patterns, condensation HT and TP frictional PD
Turgut
(2016) [98]		 R717 External experimental database [99] Horizontal circular smooth stainless steel tube
di = 14 mm		 Flow pattern map, flow boiling TP PD
Turgut
(2021) [100]		 R290 External experimental database (see [100]) Vertical/horizontal smooth stainless steel/copper tubes
dh = 0.3–7.7 mm		 Saturated TP flow boiling HT
Turgut
(2022) [101]		 R717 External experimental database (see [101]) Horizontal smooth stainless steel tube, dh = 3–14 mm Flow boiling HT
R600a Horizontal smooth stainless steel tube, dh = 1.1–8.0 mm
Umar
(2022) [102]		 R290 Experimental study Horizontal stainless steel smooth tube, di = 3 mm TP flow boiling PD
Wang, S.
(2014) [103]		 R290 Experimental study Horizontal smooth copper tube, di = 6 mm TP saturated flow boiling HT and frictional PD
Wang, H.
(2016) [104]		 R717 External experimental database (see [104]) Horizontal/vertical stainless steel/aluminium/carbon steel tube, di = 1.224–32 mm Flow boiling HT
Wen
(2018) [105]		 R290 Numerical simulation
CFD software ANSYS Fluent 		Horizontal circular smooth mini-channel, dh = 1 mm Condensation HT and frictional PD
Yang
(2017) [106]		 R600a Experimental study Horizontal smooth copper tube, di = 6 mm Flow patterns, flow boiling HT and TP frictional PD
Yuan
(2017) [107]		 R134a, R22 R717, R744 R236fa R245fa
R1234ze		 External experimental database (see [107]) Horizontal smooth circular stainless steel/aluminium/copper tube
di = 0.5–14.0 mm		 Annular flow boiling HT
Zhang, Y.
(2019) [108]		 R290
R600a		 External experimental database (see [108]) Horizontal smooth stainless steel/copper tube
di = 1–6 mm		 Boundary layer theory and flow boiling HT
Zhang, J.
(2021) [109]		 R134a
R236fa R245fa R1233zd (E)
R1234ze(E)
R290 R600a		 Experimental study Brazed plate heat exchanger (PHE),
β = 65°, dh = 3.4 mm		 Condensation HT and frictional PD
Zhang, J.
(2021) [110]		 R134a
R236fa R245fa R1233zd (E)
R1234ze(E)
R290
R600a		 Experimental study Brazed plate heat exchanger (PHE),
β = 65°, dh = 3.4 mm		 Flow boiling HT and frictional PD
Zhang, R.
(2021) [111]		 R717 Experimental study Horizontal smooth stainless steel tube, di = 3 mm Flow patterns, TP Flow boiling HT and frictional PD, dryout phenomenon
Zhang, R.
(2022) [112]		 R717 Experimental study Horizontal smooth steel tube, di = 3 mm Flow boiling TP HT and TP frictional PD, dryout phenomenon
R = refrigerant, TP = two phase, HT = heat transfer, PD = pressure drop, PHE = plate heat exchanger, β = chevron angle, ST = smooth tube, MF = microfin, di, dh, do = inner, hydraulic, outer diameter, Lh = heated length, Ra = roughness, HC Rs = hydrocarbon refrigerants.
Table 2. Summary of the operating conditions, HTC and PD correlations of the papers included in this review.
Table 2. Summary of the operating conditions, HTC and PD correlations of the papers included in this review.
First
author/Year		 R ST/SP/VQ Heat Flux (kW/m2) Mass Flux (kg/m2s) Best reported HTC correlation/New HTC correlation AAD (%) Best reported PD correlation/New PD correlation AAD (%)
Aǧra
(2012) [6]		 R600a Tsat = 30–43 °C
–
–		 – G = 47–116 h = − k d T d y y = 0 ( T s a t − T w )
T w = t u b e   w a l l   t e m p e r a t u r e 		*±20% – –
Ahmadpour (2019) [7] R600a –
psat = 510–630 kPa
x = 0.04–0.80		 – G = 140–280 Straight tube: Cavallini and Zecchin [113], Shah [114] *±20 – –
U shaped tube: Traviss et al. [115]
Shah [89]
Akbar
(2021) [8]		 R290 Tsat = 0–11 °C
–
x = 0–1		 q = 5–20 G = 50–180 Aizuddin et al. [116] 11.6 – –
Ali
(2021) [9]		 R1234yf
R152a
R600a R134a		 Tsat = 27, 32 °C
–
–		 – G = 50–500 – – Based on Cavallini et al. [117]
F =   x 0.9525 ·   1 − x 0.414 3.25 		*71.78 %±30%
Allymehr
(2020) [10]		 R290 Tsat = 0, 5, 10 °C
–
x = 0.14–1		 q = 15–33 G = 250–500 ST: Liu & Winterton [118]
MF1: Rollmann & Spindler [119]
MF2: Rollmann & Spindler [119]		 6.2
14.8
26.3		 ST: Xu & Fang [120]
MF1: Diani et al. [121]
MF2: Diani et al. [121]		 11.7
3
12.7
Allymehr
(2021) [11]		 R600a Tsat = 5, 10, 20 °C
–
x = 0.11–1		 q = 15–34 G = 200–515 ST: Shah [122]
MF: Rollmann & Spindler [119]		 6.4
–		 ST: Xu & Fang [120]
MF: Diani et al. [121]		 6.6
–
R1270 ST: Liu & Winterton [118]
MF: no reliable correlation		 8.5
–		 ST: Xu & Fang [120]
MF: Diani et al. [121]		 4.4
–
Allymehr
(2021) [12]		 R290 Tsat = 35 °C
–
x = 0.12–0.89		 – G = 200–500 ST: Dorao and Fernandino [123]
MF1: Cavallini et al. [124]		 4.9
7.9		 ST: Macdonald and Garimella [69]
MF: Diani et al. [121]		 7.9
–
R600a ST: Dorao and Fernandino [123]
MF1: Cavallini et al. [124]		 5.8
7.8		 ST: Xu and Fang [125]
MF: Diani et al. [121]		 11.0
–
R1270 ST: Dorao and Fernandino [123]
MF1: Cavallini et al. [124]		 11.0
13.6		 ST: Macdonald and Garimella [69]
MF: Diani et al. [121]		 6.4
–
Amalfi
(2016) [13]		 R134a R245fa R236fa R717, R290
R600a R1270 R1234yf
mixtures		 Tsat = −25–39 °C
–
x = 0–0.95		 q = 0.1–50.0 G = 5.5–610 For Bd < 4
N u t p = 982 · β * 1.101 W e m 0.315 B o 0.320 ρ * − 0.224

For Bd >= 4
N u t p = 18.495 · β * 0.248 R e v 0.135 R e l o 0.351 B d 0.235 B o 0.198 ρ * − 0.223 		22.1 (all data) f t p = C · 15.698 · W e m − 0.475 B d 0.255 ρ * − 0.571
C = 2.125 β * 9.993 + 0.955 		21.5 (all data)
Anwar
(2015) [15]		 R600a Tsat = 27, 32 °C
–
x = 0–0.8		 q = 20–130 G = 50–350 Li and Wu [126] −0.48 (AD) – –
Arima
(2010) [16]		 R717 Tsat = 13.9, 17.9, 21.6 °C
psat = 0.7, 0.8, 0.9
x = 0.1–0.4		 q = 15, 20, 25 G = 7.5, 10, 15 h l o c h l o = 16.4 1 X v v 1.08
h l o = 0.023 λ l d h G 1 − x d h μ l 0.8 P r l 0.4 		*±25% – –
Asim
(2022) [17]		 R600a Tsat = 27, 32 °C
–
–		 q = 5–245 G = 50–500 Mahmoud and Karayiannis [127] 14.17 – –
Ayub
(2019) [18]		 R717 R134a
R410A		 –
psat = 0.136–1.445 MPa
–		 – – N u = 1.8 + 0.7   β β m a x R e e q 0.49 − 0.3 σ R e f σ a m m o n i a B o e q − 0.2
β m a x = 65 ° 		*±30% (all data) – –
Basaran
(2021) [19]		 R600a Tsat = 40 °C
–
x = 0.3–0.9		 q = 40 G = 200–600 N u = H T C · d h λ l
N u = 0.2516 × R e e q 0.6860 , f o r   R e e q < 2300 0.3215 × R e e q 0.6548 , f o r   R e e q > 2300 		10.22 f = ∆ p d h L 2 ρ t p G 2
f = 0.8393 × R e e q − 0.2200 ,   f o r   R e e q ≤ 2300 0.7344 × R e e q − 0.2260 ,   f o r   R e e q > 2300 		17.42
Basaran
(2021) [20]		 R600a Tsat = 0.82056 °C
–
–		 – G = 200–600 N u = 0.2963 × R e e q 0.6642 **6.8 (Po) Sakamatapan and Wongmisses [128] –
Butrymowicz
(2022) [21]		 R134a, R507A R600a –
pr = 0.501–0.985
x = 0.1–1		 q = 0.4–10 G = 60–200 Based on Gungor–Winterton [129]
h = h G W e x p − 45.8 1 − B o m − 0.016
h G W = h c o n v E + h p b S
h c o n v = 0.023 λ D i R e l 0.80 P r 0.40
h p b = 55 p r 0.12 − l o g p r − 0.55 M − 0.50 q 0.67
E = 1 + 24000 B o 1.16 + 1.37 X − 0.86
S = 1 + 1.15 · 10 − 6 E 2 R e r i 1.17 − 1 		*R2 = 0.51 (all data) – –
Butrymowicz
(2022) [22]		 R290 Tsat,e = 8 °C
Tsat,c = 34 °C
–
–		 – G = 50–160 – – Based on Müller-Steinhagen [130]
∆ p = ∆ p v o β
β = C f 1 + ζ
Condensation:
ζ = 64 0.3164 μ l μ v 0.25 ρ v ρ l G d h − 0.75
C f = 1.858 + 6.154 · 10 − 5 R e v o 		*R2 = 0.832
Evaporation
C f = 3.925 + 4.120 · 10 − 5 R e v o 		*R2 = 0.555
Cao
(2021) [23]		 R600a –
psat = 530–620 kPa
–		 – G = 25–41.25 h t p = 0.012 R e l 0.81 P r l 1.42 Φ l λ l d h
ϕ l 2 = 1 + C X t t + 1 X t t 2
C = 21 1 − e − 0.319 d h 		9.8 f l = 0.35 R e l − 0.36 w h e r e   R e l < 2000 7.3
Choi
(2009) [24]		 R290 Tsat = 0, 5, 10 °C
–
x = 0–1		 q = 5–20 G = 50–400 h = 55 p r 0.12 − 0.4343 l n   p r − 0.55 M − 0.5 q 0.67
F = M A X 0.5 ϕ f , 1
S = 181.485 ϕ f 2 0.002 B o 0.816
ϕ f 2 = 1 + C X + 1 X 2
C = 1732.953 × R e t p − 0.323 W e t p − 0.24 		9.93 C = ϕ f 2 − 1 − 1 X 2 X = 1732.953 × R e t p − 0.323 W e t p − 0.24 10.84
Choi
(2014) [25]		 R744
R717
R290
R1234yf		 Tsat = 0–10 °C
–
x = 0–1		 q = 5–60 G = 50–600 h t p = F h l o + S h p b
h l o = 0.023 k l D G 1 − x d µ l 0.8 c p l µ l k l 0.4
F = M a x 0.007 φ l 2 1.15 + 0.95 , 1
h p b = 55 p r 0.12 ( − 0.4343 l n p r ) − 0.55 M − 0.5 q 0.67
S = C r e f ( ɸ f 2 ) 0.3421 B o 0.0469
C r e f , R 717 = 0.5018
C r e f ,   R 290 = 0.12 		12.28 (all data)
11.09 (R717)
10.02 (R290) 		– –
Cioncolini
(2011) [26]		 R22, R32 R134a R290 R600a
R718, R12
R236fa
R245fa		 –
p =0.1–7.2 MPa
x = 0.19–0.94		 q = 3–736 G = 123–3925 1 + α t + = h t k l N u = 77.6 × 10 − 3 t + 0.90 P r l 0.52
10 ≤ t + ≤ 800 ;         0.86 ≤ P r l ≤ 6.1
t = 1 − e 1 − x G d 4 μ l 		13.0
(all data)		 – –
Da Silva
(2023) [27]		 R600a Tsat = 24 °C
psat = 340.3 kPa
x = 0.09 – 0.98		 q = 4.5–18.5 G = 35–170 – – Hwang and Kim [131] 7.96
(AD)
Da Silva Lima (2009) [28] R717 Tsat = −14–14 °C
–
x = 0.05–0.6		 q =12–25 G = 50–160 – – Moreno Quibén and Thome [132] 9.5
Dalkilic
(2010) [29]		 R600a Tsat = 30–43
psat = 4–5.73 bar
x = 0.45–0.9 		– G = 75–115 – – Chen et al. [133]
Mishima and Hibiki [134]		 *±30%
Darzi
(2015) [30]		 R600a –
–
x = 0.1–0.8		 q = 17 G = 154.8–265.4 Based on Shah [89]
h f l a t = 1.3   d d h 0.8 x 1 − x − 0.0008 G − 205 h s h a h 		*90%±17 Jung and Radermacher [135] *80%±25
De Oliveira (2016) [31] R600a Tsat = 25 °C
–
x = 0–0.92		 q = 5–60 G = 240–480 Kim and Mudawar (2013) [136] 4.4
(AD)		 – –
De Oliveira
(2017) [32]		 R290 Tsat = 25 °C
–
–		 q = 5–60 G = 240–480 – – Zhang et al. [137] 21.66 (AD)
R600a Mishima and Hibiki [134] −5.54 (AD)
De Oliveira
(2018) [33]		 R290 Tsat = 25 °C
psat = 952.2 kPa
–		 q = 5–60 G = 240–480 Li and Wu [126] −8.5
(AD)		 – –
De Oliveira
(2020) [34]		 R1270 Tsat = 25°C
psat = 1154.4 kPa
x = 0.01–0.99		 q = 5–60 G = 240–480 Bertsch et al. [138] 22.8
(AD)		 – –
De Oliveira
(2023) [35]		 R1270 Tsat = 25°C
psat = 1154.4 kP
a–		 q = 5–60 G = 240–480 – – Hwang and Kim [131] 2.65
(AD)
Del Col
(2014) [36]		 R290 Tsat,aPD,cHT = 40°C
Tsat,bHT = 31°C
–
x = 0.05–0.6		 q,bHT = 10–315 G,aPD = 200–800
G,cHT = 100–1000
G,bHT = 100–600 		cHT: Moser et al. [139]
bHT: Thome et al. [140]		 7.22
3.9 (AD)		 Del Col et al. [141] 9.1
Del Col
(2017) [37]		 R1270 Tsat,aPD,cHT = 40°C
Tsat,bHT = 30°C
–
–		 q,bHT = 10–244 G,aPD = 400, 600
G,cHT = 80–1000
G,bHT = 100–600 		cHT: Moser et al. [139]
bHT: Sun and Mishima [142]		 16.4
8.6		 Friedel [143] 7.3
ElFaham
(2023) [38]		 R290
R600
R600a		 Tsat = −35–43 °C
–
x = 0–1		 q = 5–315 G = 50–1100 Kew and Cornwell [144] 24.6 (all data) – –
Fang, Xiande
(2019) [39]		 R717 Tsat = 1.06–31°C
psat = 2.15–11.06 bar
x = 0–0.99		 q = 5–130 G = 20–600 Fang et al. [145] 4.7 – –
R290 6.5
R600a 10.2
Fang, Xianshi
(2023) [40]		 R600a Tsat = 38.5 °C
–
x = 0.05–0.79		 – G = 115–365 – – Nualboonrueng et al. [146] Non-annular flow 32.52
Annular flow 10.18
Fries
(2019) [42]		 R290 –
psat = 12–16 bar
–		 – G = 300–400 Thome [147] (for low x)
Cavallini and Zecchin [113] (for high x)		 –
– 		Friedel [143] –
Fries
(2020) [43]		 R290
R1270		 –
pr = 0.25
–		 – G = 300, 450, 600 – – Friedel [143] *±20% (all data)
Fronk
(2016) [44]		 R717 Tsat = 30–60 °C
pr = 0.10–0.23
–		 – G = 75–225 Annular flow model :
N u a =   h D k l = 0.023 · R e l 0.8 P r l 0.4 1 + 0.27 U v U l 0.21 f i − 0.46
U v U l =   x 1 − x ρ l ρ v 1 − ε ε
δ =   1 2 D − D i = D 2 1 − ε
ε = β 1 + V ¯ v j / j
V ¯ v j = 0.336 · X 0.25 · C a l 0.154 ρ l ρ v − 1 0.81 j
X =   d p / d z l d p / d z v
C a l = µ l 1 − q · G ρ l · σ
f = 16 R e                                             f o r   R e < 2000 0.079 R e − 0.25       f o r   R e ≥ 2000

Non-annular flow model:
N u w a v y = 1 + 0.741 1 − x x 0.3321 − 1 N u f i l m + N u p o o l
N u f i l m = D k l 0.725 k l 3 ρ l ρ l − ρ v g h l v μ l D ( T s a t − T w , i ) 0.25
N u p o o l = 0.023 R e l 0.8 P r l 0.4 ( 1 − x 0.087 ) 		12.8 – –
Gao
(2018) [46]		 R717 Tsat = −15.8–5 °C
–
–		 q = 9–21 G = 50–100 Gungor and Winterton [148] 19.6 Müller-Steinhagen and Heck [130] 16.1
Gao
(2019) [47]		 R717 Tsat = −15.8–4.6 °C
–
x = 0–0.9		 – G = 20–200 – – Based on Müller-Steinhagen and Heck [130]
▽ p f = F 1 − x 1 / 3 + B x 3
F = A + ( 1 + 0.007695 B d − 0.03573 R e l o 0.3940   ) B − A x
A =   d p d z l o = f l o 2 G 2 ρ l D ; B = d p d z v o = f v o 2 G 2 ρ v D
I f   R e l o ≤ 1187   f l o =   16 R e l o ; I f   R e l o > 1187   f l o =   0.079 R e l o 0.25 		13.5
Ghazali
(2022) [48]		 R290 Tsat = 5–25 °C
–
x = 0.4–1		 q = 2.5–60 G = 50–500 Based on Mohd-Yunos et al. [75]
h t p = S h n b + F h l o
h n b = 55 p r 2.12 − 0.4343 l n p r − 0.55 M − 0.5 q 0.67
h l o = 0.023 R e l 0.8 P r l 0.4 k l D
S = b 1 ϕ f 2 b 2 B o b 3
F = M A X b 4 ϕ f 2 b 5 − b 6 , 1
f o r   x ≤ 1     b 1   t o   b 6 = 0.176 ,   0.096 ,   − 0.117 ,   0.1 ,   0.748 ,   − 0.076 		17.02 – –
Ghorbani
(2017) [49]		 R600a Tsat = 36.2−45.6
–
x = 0.06−0.78		 − G = 110−372 Shah [89] 13
AD		 – –
Guo
(2018) [50]		 R1234ze(E)
R290
R161
R41		 Tsat = 35–45 °C
–
x = 0–1		 q = 8–30 G = 200–400 Based on Koyama et al. [149]
ϕ v 2 = 1 + 15.6 v l v v 0.17 ×
× 1 − e − 0.6 W e 0.8 B d 0.625 X t t + X t t 2 		21.6 (R290) – –
Huang
(2012) [51]		 R134a
R507a
R12, R717		 Tsat = 1.9–13
–
xout = 0.2–0.95		 q = 1.9–10.8 G = 5.6–52.3 N u t p = 1.87 × 10 − 3 · q d 0 k l T s a t 0.56 i l g d 0 α l 2 0.31 P r l 0.33
d 0 = 0.0146   θ 2 σ g ρ l − ρ g 0.5
θ = 35 °   f o r   h y d r o c a r b o n   r e f r i g e r a n t s 		7.3 (all data) – –
Ilie
(2022) [53]		 R717 Tsat = −9–(−2) °C
–
x = 0.5		 q = 4–7.3 G = 1.8–2.6 Shah [114] 14.23 – –
Inoue
(2018) [54]		 R32, R410a R1234ze(E)
R152a		 Tsat = 35 °C
–
–		 – G = 100–400 N u = 0.17 f v ϕ v / X t t μ l / μ v 0.1 x / 1 − x 0.1 R e l 0.87
f v = 0.26 R e v − 0.38 		*±30% (all data) – –
*±30% R290
External data [65]
Kanizawa
(2016) [55]		 R134a
R245fa
R600a		 Tsat = 21.5–58.3 °C
–
x = 0.01–0.93		 q = 5–185 G = 49–2200 h t p = F h c + S h n b
h n b = 0.0546 × k l d b ρ v ρ l 0.5 q d b k l T s a t 0.670 ρ l − ρ v ρ l − 4.33 × i l v d b 2 ρ l c p l k l 2 0.248
d b = 0.51 2 σ / g ρ l − ρ v
h c = 0.023 k l d R e l 0.8 P r l 1 / 3
F = 1 + 2.50 X − 1.32 1 + W e u v 0.24
S = 1.06 B d − 8 . 10 − 3 1 + 0.12 R e 2 p , m o d / 10000 0.86 		11 (all data)
No good agreement (R600a)		 – –
Khan, T.S.
(2012) [56]		 R717 Tsat = −25–(−2)°C
–
xout = 0.5–0.9		 q = 21–44 G = 8.5–27 N u t p = 82.5 R e e q B o e q − 0.085 p r 0.21 *75%±4% f t p = 212 R e e q − 0.51 ( p r ) 0.53 *90%±5%
Khan, M.S.
(2012) [57]		 R717 Tsat = −25–(−2) °C
–
xout = 0.5–0.9		 q = 21–44 G = 5.5 N u t p = 169 R e e q B o e q − 0.04 p r 0.52 *70%±4% f t p = 673,336 R e e q − 1.3 ( p r ) 0.9 *90%±7%
Koyama
(2014) [58]		 R717 –
psat = 0.7, 0.9 MPa
–		 q = 10, 15, 20 G = 5–7.5 For δ = 1 mm:
h h l i q = 52.2 1 X v v 0.90
h l i q = 0.023   k l D h G ( 1 − x ) D h µ l 0.8 P r l 0.4 		*85%±30% – –
For δ = 2 and 5 mm:
h h l i q = 48.6 1 X v v 0.79 		*88%±30%
Lee
(2010) [59]		 R290 Tsat = 40 °C
–
x = 0–0.9		 – G = 35.5–178.8 Haraguchi et al. [150] 13.75 – –
R600a 6.57
Lillo
(2018) [60]		 R290 Tsat = 25–35 °C
–
x = 0–1		 q = 2.5–40.0 G = 150–500 Based on Wojtan et al. [151]
h w e t = h c b 3 + h n b 3 1 / 3
h c b = 0.0133 · R e δ 0.69 · P r l 0.4 · λ l δ
h n b = 0.8 · h C o o p e r
h c b , n e w = 0.5 · h c b
h n b , n e w = 1.7 · h n b 		8.2 Friedel [143] 20.8
Liu
(2016) [61]		 R290 Tsat = 40, 50 °C
psat = 1.37–1.71 MPa
x = 0.1–0.9		 – G = 200–500 Kim et al. [152] 13 Kim and Mudawar [153] ±30%
Liu
(2018) [62]		 R600a
R227ea R245fa		 Tsat = 27.5–45.5 °C
–
x = 0–0.8		 q = 3.60–10.50 G = 32.20–116.8 h t p = a B o b F r l o c B d d ρ l ρ v e k l D h
a = 17022, b = 0.939, c = 0.347,
d = 0.581, e = 0.23 		14.93 (all data)
17.09 (R600a)		 – –
Longo
(2012) [63]		 R600a Tsat = 9.8–20.2 °C
–
x = 0.21–1		 q = 4.3–19.6 G = 6.6–23.9 Cooper [154] 17.2 ∆ p f k P a = 1.525   K E / V J m − 3
K E / V = G 2 / 2 ρ m
K E / V = K i n e t i c   e n e r g y   p e r   u n i t   v o l u m e ,   J m − 3 		8.8 (all data)
R290 Gorenflo [155] 16.2
R1270 Gorenflo [155] 27.1
Longo
(2017) [64]		 R290 Tsat = 30, 35, 40 °C
psat = 1.075–1.650 MPa
x = 0.12–0.95		 – G = 75–400 Akers et al. [156] 9.0 Friedel [143] 14.5
R1270 13.0 12.4
Longo
(2020) [65]		 R600a Tsat = 5–20 °C
psat = 1.195–3.045 bar
x = 0.08–0.75		 q = 15–30 G = 100–300 Fang et al. [145] 6.2 Wang et al. [157] 15.49
Longo
(2023) [66]		 R290 Tsat = 9.9–10.4 °C
psat = 0.63–0.79 MPa
x = 0.24–1		 q = 2.9–28.3 G = 5.0–17.8 Longo et al. [158] 7.7 – –
R1270 6.9
López-Belchí
(2016) [67]		 R290 Tsat = 30, 40, 50 °C
psat = 1.08–1.71 MPa
–		 q = 15.76–32.25 G = 175–350 Koyama et al. [159] 18.44 Sun and Mishima [160] 6.88
Macdonald
(2016) [68]		 R290 Tsat = 30–94 °C
–
–		 – G = 150–450 Cavallini et al. [161] 24 Garimella et al. [162] 26
Macdonald
(2016) [69]		 R290 Tsat = 30–94 °C
–
–		 – G = 150–450 h a d j u s t e d = h c o n d e n s a t i o n · Χ L M
h c o n d e n s a t i o n = h f i l m θ + h p o o l 2 π − θ 2 π
Χ L M = k l , w a l l − s u b c o o l k l , s a t 2 − 0.3 · 1 p r 0.1 		11 d p d z = d p d z l + C d p d z l d p d z v 0.5
d p d z l = 1 2 f l ρ l v l 2 d h   w h e r e :   v l = G 1 − x ρ l
d p d z v = 1 2 f v ρ v v v 2 d h   w h e r e :   v v = G 1 − x ρ v
C = 20 R e − 0.15 S r 1.15 B d − 0.2
S r = v v / v l 		18
Macdonald
(2017) [70]		 R290 Tsat = 30–75 °C
pr = 0.25–0.67
–		 – G = 150–450 Based on Macdonald and Garimella [69]
h c o r r e c t e d = h c o r r e l a t i o n · χ ∆ T
χ ∆ T = k l , w a l l − s u b c o o l k l , s a t 2 − 0.3 · 1 p r 0.1 		5.4 – –
Maher
(2020) [71]		 R134a
R245fa
R125, R744
R236ea R22, R152a
R32, R410a
R1234ze(E)
R290 R600
aR1234yf		 Tsat = 25–55 °C
–
–		 – G = 35.5–2094 – – ∆ p ∆ L t p = G t p 2 2 D ρ t p 0.79 R e t p − 0.25 1.4 + 0.17 0.69 l n R e t p − 2.2 − 1.5 1 / 0.7  
R e t p = G t p D 1 − x μ l + x μ v 0.94 1 − x μ l + x μ v 1 − 0.94 		30
(all data)
Maqbool
(2012) [72]		 R717 Tsat = 23, 33, 43 °C
–
–		 q = 15–355 G = 100–500 – – Based on Tran et al. [163]
d p d z f =   d p d z L o Φ L O 2  
Φ L O 2 = 1 + 4.3 Y 2 − 1 · 0.2 C o 1.2 x 0.875 1 − x 0.875 + x 1.75
Y 2 = d p d z V O   d p d z L O 		16
Maqbool
(2012) [73]		 R717 Tsat = 23, 33, 43 °C
–
–		 q = 15–355 G = 100–500 Cooper [164] 20 – –
Maqbool
(2013) [74]		 R290 Tsat = 23, 33, 43 °C
–
–		 q = 5–280 G = 100–500 Cooper [165] 18 Müller-Steinhagen and Heck [130] 17
Mohd-Yunos
(2020) [75]		 R290 Tsat = −35–25 °C
–
–		 q = 5–190 G = 63.9–480 Based on Choi et al. [25]
h t p = S h n b + F h l o
C a s e   I : f o r   0.0 < x < 1.0
S = 2 ϕ f 2 − 0.073 B o 0.128
F = M A X 1.074 ϕ f 2 0.178 − 0.38 , 1
C a s e   I I : f o r   0 < x ≤ 0.6
S = 0.8 ϕ f 2 0.124 B o 0.093
F = M A X 1.226 ϕ f 2 0.107 − 0.28 , 1
f o r   0.6 < x < 1.0
S = 1.989 ϕ f 2 − 0.867 B o − 0.322
F = M A X 1.534 ϕ f 2 − 0.293 + 0.754 , 1 		33.16
25.26		 – –
Moreira
(2021) [76]		 R134a
R600a
R290
R1270		 Tsat = 35 °C
–
x = 0–1		 q = 5–60 G = 50–250 h t p = N u   λ l d
N u = J h P r l 1 / 3
J h = 0.0053   R e e q         R e e q ≥ 25,000   0.79   R e e q 0.51       R e e q < 25,000 		– – –
Morrow
(2021) [77]		 R717 Tsat = 24–60 °C
–
x = 0–1		 – G = 20–800 Shah [90] 41 – –
R290 Kim [152] 14
R600a Shah [166] 15
Murphy
(2019) [78]		 R290 Tsat = 47, 74 °C
psat = 1.6, 2.8 MPa
x = 0.1–0.9		 – G = 75–150 N u = 0.0841 P r l R e l 1.329 T + F 1.263
F = f v 8 0.5 x 1 − x 0.5 1 − 2.85 X 0.523
T + = . 707 P r l R e l 0.5                                                                                           R e l < 50 5 P r l + 5 l n 1 + P r l 0.09636 R e l 0.585 − 1           50 < R e l < 1125 5 P r l + 5 l n 1 + 5 P r l + 2.5 l n 0.00313 R e l 0.812         R e l > 1125 		13.4 d p d z f = 1 2 f i n t G x 2 ρ v α 2.5 1 D
f i n t f l = 0.0019 X 0.6 R e l , a c t u a l 0.930 φ − 0.121 		12
Nasr
(2015) [79]		 R600a –
pavg = 5–6 bar
x = 0–0.7		 q = 10–27 G = 130–380 Gungor–Winterton [129] 12.23 – –
Oh
(2011) [80]		 R22, R134a R410A, R290, R744 Tsat = 0–15 °C
–
x = 0–1		 q = 5–40 G = 50–600 h t p = S h n b c + F h l
S = 0.279 ϕ f 2 − 0.029 B o − 0.098
F = M A X 0.023 ϕ f 2.2 + 0.76 , 1
h n b c = 55 p r 2.12 − 0.4343 l n p r − 0.55 M − 0.5 q 0.67
h l = 4.36 k l D                         i f   R e l < 2300 = R e l − 1000 P r l f l 2 k l D 1 + 12.7 P r l 2 / 3 − 1 F f 2 0.5     i f   3000 ≤ R e l ≤ 10 4 = R e l P r l f l 2 k l D 1 + 12.7 P r l 2 / 3 − 1 F f 2 0.5     i f   10 4 ≤ R e l ≤ × 10 6 = 0.023 k l D G 1 − x D μ l 0.8 C p l μ l k l 0.4 R e l ≤ × 10 6 		15.28 (all data) – –
Pamitran
(2009) [81]		 R290 Tsat = 0, 5, 10 °C
–
x = 0–1		 q = 5–20 G = 50–400 h t p = S h n b c + F h l o
S = 0.6226 ϕ f 2 0.1068 B o 0.0777
h n b c = 55 p r 0.12 − 0.4343 l n p r − 0.55 M − 0.5 q 0.67
F = 0.023 ϕ f 2 + 0.977
h l o = 0.023 λ l D G 1 − x D μ l 0.8 C p l μ l k l 0.4
ϕ f 2 = 1 + C X + 1 X 2
C t t = 20 ,   C v t = 12 , C t v = 10 , C v v = 5 		8.27 – –
Pamitran
(2011) [82]		 R290
R717
R744		 Tsat = 0–10 °C
–
x = 0–1		 q = 5–70 G = 50–600 h t p = F h l o + S h p b
h l o = 0.023 k l D G 1 − x D µ l 0.8 c p l µ l k l 0.4
F = M a x 0.009 φ l 2 2 + 0.76 , 1
h p b = 55 p r 0.12 ( − 0.4343 l n p r ) − 0.55 M − 0.5 q 0.67
S = C r e f ( ɸ f 2 ) − 0.2093 B o 0.7402
C r e f , R 717 = 0.45
C r e f ,   R 290 = 0.38 		19.81 (all data)
17.94 (R290)
22.52 (R717)		 – –
Patel
(2018) [83]		 R290, R22
R1234yf, R1234ze, R410a, R32		 Tsat = 30–50 °C
–
x = 0.1–0.9		 – G = 150–800 – – ϕ N e w 2 = 1 + C X + 1 X 2
C N e w = 0.3572 R e l o 0.05021 S u v o 0.099 F 0.025 H 0.015
S u v o c = ρ v σ d h μ v 2 ,               d p d z t p = d p d z l ϕ l 2 		10.08
Pham
(2019) [84]		 R22, R32, R410a R290 Tsat = 48 °C
–
x = 0.1–0.9		 q = 3–15 G = 50–500 h = 2.76 B o 0.053 R e e q 0.528 1 − x P r l − 0.386 1 − x 0.8 + x p r − 0.76
g G h l v A o A i 0.305 Φ v X t t − 0.045 k l d
ϕ v 2 = 1 + C X t t + X t t 2
C = λ x 0.35 1 − x 0.25 p p c 0.31 R e t p 0.09 W e t p 0.09
λ = 24 1 − 1.355 β + 1.947 β 2 − 1.701 β 3 + 0.956 β 4 − 0.254 β 5 		18.14 – –
Qiu
(2015) [85]		 R600a Tsat = 20 °C
–
x = 0.05–0.85		 q = 5–10 G = 200–400 Shah [122] 21.75 Groennerud [167] 19.07 (G=400)
28.55 (G=200)
Sempértegui-Tapia (2017) [86] R134a
R1234ze(E)R1234yf R600a		 Tsat = 31, 41 °C
–
x = 0–0.93		 q = 15–145 G = 200–800 Based on Kanizawa et al. [168]
h t p = F · h l 2 + S · h n b 2 0.5
h l   a c c o r d i n g   t o   D i t t u s   a n d   B o e l t e r ,
h n b   a c c o r d i n g   t o   S t e p h a n   a n d   A b d e l s a l a m
F = 1 + 2.55 X t x − 1.04 1 + W e u G − 0.194
S =   1.427 B d 0.032 1 + 0.1086 10 − 4 R e l F 1.25 0.981 		11.4 (all data)
14.0 (R600a)		 – –
Sempértegui-Tapia
(2017) [87]		 R134a, R1234ze(E) R1234yf
R600a		 Tsat = 31,41 °C
–
x = 0.05–0.95		 – G = 100–1600 – – Based on Müller-Steinhagen and Heck [130]
d p d z t p = F · 1 − x 1 / λ + d p d z v o · x λ
F = d p d z l o + ω · d p d z v o − d p d z l o · x
ω = 3.01 e − 0.00464 · R e v o / 1000 ;   λ = 2.31
D e q = 4 A π ;   d p d z k o = 2 f k o G 2 D e q · ρ k
f k o = 16 R e k o   l a m i n a r   f l o w ,   c i r c u l a r   c h a n n e l
10.2 (all data)
9.3 (R600a)
7.2 (R290, external data [36])
Shafaee
(2016) [88]		 R600a –
pavg = 4–6 bar
x = 0.08–0.7		 q = 18.6–26.1 G = 109.2–505 Shah [122] 15 – –
Shah
(2009) [89]		 R718
Halocarbon Rs
HC Rs
Organics		 –
pr = 0.0008–0.9
x = 0.01–0.99		 – G = 4–820 h I = h L T μ l 14 μ g n 1 − x 0.8 + 3.8 x 0.76 1 − x 0.04 p r 0.38
n = 0.0058 + 0.557 p r
h N u = 1.32 R e l o − 1 / 3 ρ l ρ l − ρ g g k l 3 μ l 2 1 / 3
Boundary between Regime I and II:
J g ≥ 0.98 Z + 0.263 − 0.62
h t p = h t p = h I                                                                               i n   R e g i m e   I h t p = h I + h N u                                                   i n   R e g i m e   I I h t p = h N u       v e r t i c a l   t u b e s   i n   R e g i m e   I I I 		14.4 (all data)
11.2,13.7
(R600a)
16.4,15.210.5,20.5
(R290)17.2,32.6 (R1270) 		– –
Shah
(2016) [90]		 R718, R744 Halocarbon Rs, HC Rs –
pr = 0.0055–0.94
x = 0.02–0.99		 – G = 20–1400 h I = h L T 1 + 1.128 x 0.817 ρ l ρ v 0.3685 μ l μ v 0.2363 1 − μ v μ l 2.144 P r l − 0.1
h L T = 0.023 R e l t 0.8 P r l 0.4 k l / D
Preprints 100744 i001 		15.5 (all data)
21.3
(R290)		 – –
Shah
(2017) [91]		 R718
R744
R717
HalocarbonRs
Cryogens
HC Rs		 –
pr = 0.0046– 0.787
–		 – G = 15–2437 h t p = F · h S h a h
F = h t p / h S h a h = 2.1 − 0.008   W e G T − 110 B o ≥ 1
F o r   h o r i z o n t a l   c h a n n e l s  
w i t h   F r l < 0.01 ,   F = 1
18.6 (all data)
21.6 (R717)
9.2 (R290)
11.4,40.1 (R600a)		 – –
Shah
(2017) [92]		 R718, R744
cryogens, R12, R113 R22, R134a
HC Rs (R50, R290)		 –
pr = 0.0046–0.99
x = –		 – G = 3.7–5176 h t p = q / T w − T s a t
q = h v F d c T w − T v
F o r   p r > 0.8 ,       F d c = 2.64 p r − 1.11 F o r   p r ≤ 0.8 ,     F d c = 1 		19.4 (all data)
28.3
(R290)		 – –
Shah
(2021) [93]		 R718, HC Rs, R717, halocarbon Rs –
pr = 0.0083–0.8
x = 0–1		 q = 2.5–93.5 G = 2.3–165 Based on Longo et al. [169]
h g r a v = 1.32 ɸ R e l o − 1 / 3 ρ l ρ l − ρ g g k l 3 μ l 2 1 / 3
h f c = 1.875 ɸ R e e q 0.445 P r l 1 / 3 k l
f o r   R e e q < 1600 ,   h t p = l a r g e r   o f h g r a v a n d h f c   f o r   R e e q ≥ 1600 , h t p = h f c 		20.9 (all data)
16.6,23.6 (R717)
13.5,17.4 (R600a)
6.5,11.0,25.8 (R290)
13.8 (R1270)		 – –
Shah
(2022) [94]		 R718, R744
Halocarbon Rs, HC Rs, R717 cryogens, chemicals		 –
pr = 0.0046–0.787
–		 – G = 15–2437 h t p = F s t ѱ h l
ѱ = h t p / h l
h l o = 0.023 G 1 − x d μ l 0.8 P r l 0.4 λ l d
ѱ c b = 2 / J 0.8
ѱ b s = ѱ 0 1 + 0.16 J 0.87
ѱ 0 = 1 + 560 B o 0.65
F s t = 2.1 − 0.008 W e v − 110 B o ≥ 1 		18.8 (all data)
18.2
(HC Rs)		 – –
Tao
(2019) [95]		 HFCs
HC Rs
HFOs
R744		 Tsat = −34.4–72.1°C
psat = 1.0–24.2
x = 0–1		 q = 2.5–66.5 G = 2–150 Longo et al. [169] 25.5 (all data) f T P = 4.207 − 2.673 β − 0.46 × 4200 − 5.41 B d 1.2 R e e q − 0.95 p s a t p c r 0.3 31.2 (all data)
Tao
(2020) [96]		 R717 –
psat = 630–930 kPa
x = 0.05–0.65		 – G = 21–78 h g c = 0.36 C o − 0.28 g ρ l ( ρ l − ρ g ) ∆ h l g λ l 3 µ l ∆ T d h 0.25 P r l 0.333 7.4 ∆ P T P =   ∆ P L + 2 ∆ P L ∆ P G + x ∆ P G  
∆ P L =   f L G L 2 2 ρ l L p d h = f L G 2 ( 1 − x ) 2 2 ρ l L p d h  
∆ P L =   f G G G 2 2 ρ g L p d h = f G G 2 x 2 2 ρ g L p d h 		14.6
Turgut
(2016) [98]		 R717 Tsat = −14–14 °C
x = 0.1–0.6
–		 q = 12–25 G = 50–160 – – Gronnerud [170] 13.9
Turgut
(2021) [100]		 R290 Tsat = −35–43 °C
–
x = 0.01–0.99		 q = 2.5–227.0 G = 50–600 Based on Wattelet et al. [171]
X t t = 1 − x x C 1 · ρ v ρ l C 2 · μ l μ v C 3
F = 1 + C 4 · X t t c 5
h n b = C 6 · p r C 7 · − l o g p r C 8 · M C 9 · Q C 10
h c b = C 11 · R e l C 12 · P r l C 13 · k l / D h
h t p = h n b C 14 + F · h c b C 14 1 / C 14
C 1 t o   C 14   r e p o r t e d   i n   t h e   a r t i c l e   [ x ] 		19.1 – –
Turgut
(2022) [101]		 R600a Tsat = −34.4– 43 °C
x = 0.01– 0.96		 q = 5–240 G = 16.3–500 h t p = h n b 4.1684 + F · h c b 6.8901 1 4.3074
h n b = 7.4756 · p r 0.9797 · − l n p r 1.9161 · M 0.2722 · q 0.6351
F = 1 + 4.9531 · X t t − 0.991
X t t = 1 − x x 0.6171 · ρ v ρ l 0.3111 · µ v µ l 0.2527
h c b = 0.0058 · R e l 0.5758 · P r l 0.2523 · k l / D h 		17.3 – –
R717 Tsat = 6–40 °C
–
x = 0.01– 0.94		 q = 5–140 G = =49–2200 h t p = 0.6177 · M 0.3111 · B o 0.2527 · F r l 4.9531 · B d − 0.991 · µ l µ v 7.4756 · ρ v ρ l 0.9797 · Y · k l D h
Y =   0.2722                                             i f   p r < 1.9161 0.6351 − p r 0.0058                       o t h e r w i s e 		12.4
Umar
(2022) [102]		 R290 Tsat = 8.7–10.8 °C
–
x = 0.1–0.9		 q = 5–20 G = 50–180 – – Li and Hibiki [172] 19.47
Wang, S.
(2014) [103]		 R290 Tsat = −35–(−1.9) °C
–
–		 q = 11.7–87.1 G = 62–104 Liu and Winterton [118] 7.5 Müller-Steinhagen and Heck [130] 17.0
Wang, H.
(2016) [104]		 R717 –
psat = 0.19–1.6
x = 0.002–0.997		 q = 2.0–240 G = 10–600 Kandlikar [173]
Stephan [174]		 40.9
40.9		 – –
Wen
(2018) [105]		 R290 Tsat = 40 °C
psat = 1.37 MPa
–		 – G = 400–800 Thome et al. (2003) [147] 7.27 Friedel [143] 7.59
Yang
(2017) [106]		 R600a –
psat = 0.215–0.415 MPa
–		 q = 10.6–75.0 G = 67–194 Liu and Winterton [118] 11.5 Based on Müller-Steinhagen and Heck [130]
∆ p f r i c t = a + 2 b − a x 1 − x 1 / 3 + b x 3 × 0.2875 + 0.0534 1 − x − 0.1208 W e t p 0.423 l o g 10 F r t p − 0.5222
a = f l G 2 2 d ρ l ,   b = f v G 2 2 d ρ v
I f   R e l a n d   R e v ≤ 1187 ,   f l = 64 R e l , f v = 64 R e v   I f   R e l a n d   R e v > 1187 ,   f l = 0.3164 R e l 1 / 4 , f v = 0.3164 R e v 1 / 4   		16.6
Yuan
(2017) [107]		 R134a, R22 R717, R744 R236fa R245fa
R1234ze		 –
pr = 0.01–0.77
x = 0.10–0.98		 q = 3–240 G = 50–1290 h t p = h c v 2 + h n b 2   1 / 2
h c v = 7.0 × 10 − 3 t + 1.00 R e v 0.14 P r l 0.80 k l t
h n b = 0.69   · h n b ,   S h e k r i l a d z e
h n b ,   S h e k r i l a d z e = 0.0122 × k l r 0 p ρ v − 1 − ρ l − 1 0.5 σ c l ρ l 2 T s a t µ l h l v 2 ρ v 2 0.25 r 0 2 ρ v h l g q σ k l T s a t 0.7
t + = 1 2 R e l f             f o r           R e l f ≤ 162
t + = 0.6246   R e l f 0.5244           f o r           162 ≤ R e l f ≤ 2785
t + = 0.03221   R e l f 0.8982           f o r         R e l f ≥ 2785 		13.7 (all data)
12.9 (R717)		 – –
Zhang, Y.
(2019) [108]		 R290
R600a		 Tsat = −35–40 °C
–
x = 0–0.99		 q = 5–135 G = 50–500 h t p = f c b h c b 2 + f n b h n b 2 0.5
h c b = 0.023 R e l o 0.8 P r l 0.4 λ l / D
h n b = 55 p r 0.12 − 0.2 l o g R a − l o g p r − 0.55 M − 0.5 q 2 / 3
f n b = a 1 C n a 5 1 + a 2 2 R e l a 3 f c b a 4 ( 1 + a 6 R t d a 7 P r l a 8 W e l , b a 9
f c b = b 1 1 + b 2 X t t b 3 1 + b 4 1 − P r l − 0.4 b 5 P r l b 6 W e v b 7 B o b 8 b 9
a 1 t o   a 9 = 1.758 ,   0.596 ,   0.133 ,   0.1 , − 0.137 ,
2.455 × 10 − 3 , − 0.15 ,   2.0 ,   0.677  
b 1 t o   b 9 = 0.5 ,   1.0 , − 1.0 ,   1.044 × 10 − 2 , 6.0 ,   5.5 ,   1.2 , − 0.2 ,   0.3 		−3.6
(AD all data)		 – –
Zhang, J.
(2021) [109]		 R134a
R236fa, R245fa, R1233zd (E)
R1234ze(E)
R290
R600a		 Tsat = 30–90 °C
–
xout = 0.01–0.05		 – G = 12–93 Based on Yan et al. [14]
h = 0.4703 R e e q 0.5221 P r l 1 / 3 B d 0.1674 ρ * 0.2126 k l D h
D h = 2 b / φ                 γ = π b / λ    
φ = 1 + 1 + γ 2 + 4 1 + γ 2 / 2 / 6 		8.9 (all data)
11.0 (R1270, external data [175])		 f = 11557.62 R e e q − 1.0041 B d 0.3002 ρ * − 0.426 10.3 (all data)
19.8 (R1270, external data [175])
Zhang, J.
(2021) [110]		 R134a
R236fa, R245fa, R1233zd (E)
R1234ze(E)
R290
R600a		 Tsat = 55–141 °C
–
x = 0.06–1		 q = 12.3–37.5 G = 52–137 h = h n b + h c b = S h p o o l + F h l
F, S by Chen [176]
h c o o p e r = 35 P r 0.12 − l o g 10 P r − 0.55 M − 0.5 q 0.67
h l = 0.023 R e l 0.8 P r l 0.4 k l D h
F = 2.35 X t t − 1 + 0.213 0.736
S = 1 + 2.53 · 10 − 6 R e l F 1.25 1.17 − 1 		12.8 (all data)
10.9 (R290)
8.4 (R600a)		 Zhang et al. [177] 11.1 (all data)
13.3 (R290)
9.9 (R600a)
Zhang, R.
(2021) [111]		 R717 Tsat = −10–10 °C
–
x = 0.1–1		 q = 10–30 G = 40–200 Based on Kew and Conwell [178]
Pre-dryout:
h t p = 6.56 R e l o 0.536 B o 0.274 1 1 − x 0.350 λ l D 		10.4 Based on Müller-Steinhagen and Heck [179]
d p d z f = G   1 − x 1.28 +   d p d z v o x 3.11
G =   d p d z l o + 1.68 x d p d z v o −   d p d z l o 		19.6
Post-dryout:
h t p = 34.12 R e l o 0.371 B o 0.10 1 1 − x − 0.557 λ l D 		11.4
Zhang, R.
(2022) [112]		 R717 Tsat = −10–10 °C
–
x = 0.1–1		 q = 10–30 G = 40–200 Kew and Conwell [144] 20.84 Müller-Steinhagen and Heck [130] 23.71
R = refrigerant, ST, Tsat = saturation temperature, SP, psat = saturation pressure, pr = reduced pressure, pavg = average pressure, VQ = vapour quality, HC Rs = hydrocarbon refrigerants, cHT = condensation heat transfer, bHT = boiling heat transfer, aPD = adiabatic pressure drop, AAD = Average Absolute Deviation, AD = Average Deviation.
Table 3. Summary of the type of data, geometries and research highlights of the articles included in this review in case of not usual configurations.
Table 3. Summary of the type of data, geometries and research highlights of the articles included in this review in case of not usual configurations.
First author/Year R Data Geometry/Material/Orientation Research highlights
Abbas
(2017) [180]		 R717 Experimental study Flooded triangular pitch plain tube bundle,
do = 19.1 mm		 Outside boiling HT
Abbas
(2017) [181]		 R717 Experimental study Triangular pitch plain tube bundle, do = 19.1 mm Effects of inlet vapor quality and exit degree of super heat on HT, outside boiling
Ahmadpour (2020) [182] R600a Experimental study Horizontal copper MF tube, di = 14.18 mm Condensation HT,
Effect of lubricating oil and nanoparticles on condensation HT
Aprin
(2011) [183]		 R290
R600a
R601a		 Experimental study Staggered smooth tube bundle, do = 19.05 mm Flow patterns, TP flow void fraction and convective boiling outside tube bundle
Ayub
(2017) [184]		 R717 Experimental study Triangular pitch plain tube bundle, do = 19.1 mm Effect of exit degree of super heat on HT, outside boiling
Ding
(2017) [185]		 R290 Experimental study Shell side of LNG SWHE
di = 6 mm, θ = 4°		 Flow patterns, TP downward flow boiling HT and PD
Ding
(2018) [186]		 R290 Experimental study Shell side of LNG SWHE
do = 12 mm, θ = 4°		 TP flow boiling HT and PD
Fernández-Seara
(2016) [187]		 R717 Experimental study A plain and an integral-fin (1260 f.p.m.) titanium tube, do = 19.05 mm Pool boiling HT
Gil
(2019) [188]		 RE170 R600a
R601		 Experimental study Horizontal flat plate of a vessel, d = 72 mm Nucleate boiling HT
Gong
(2013) [189]		 R600a Experimental study Vertical stainless-steel cylinder boiling vessel, di = 75 mm Visualization study, nucleate pool boiling HT
Huang
(2020) [190]		 R717 Experimental study Microchannel
heat sink dh = 280 µm 		Saturated flow boiling HT
Jin
(2019) [191]		 R134a, R290, R600a, R32 R1234ze(E) Experimental study and data from [192,193] Horizontal smooth copper tube, do = 19.05 mm Falling film evaporation HT
Koyama
(2014) [194]		 R717 Experimental study Titanium MF plate evaporator, Channel height = 1, 2, 5 mm Flow boiling HT
Li
(2018) [195]		 R290 Numerical simulation
(ANSYS CFX 12.1)		 SWHE
dh = 14 mm, tilt angle 10°		 Numerical study on forced convective condensation HT and frictional PD
Lin
(2023) [196]		 R134a, R32
R245fa, R1234ze(E) R410a R123, R290 R600a		 External experimental database (see [196]) Horizontal smooth tube
do = 16–25.35 mm		 Falling film evaporation HT
Ma
(2017) [197]		 R600a Experimental study Smooth copper TPCT
di = 40 mm		 Evaporation and condensation HT
Moon
(2022) [198]		 R600a Experimental study Horizontal MF tube
di = 6.36 mm		 Evaporation HT and frictional PD
Pham
(2022) [199]		 R290 Experimental study Horizontal MF copper tube, di = 6.3 mm Flow patterns and flow condensation HT
Qiu
(2015) [200]		 R290 Numerical simulation
CFD software ANSYS Fluent		 Upright spiral tube
Tilt angle = 10°
di = 14 mm		 Forced convective condensation HT and frictional PD
Salman(2023) [201] R290 Experimental study Brazed PHE with OFS Saturation flow boiling HT and frictional PD
Sathyabhama
(2010) [202]		 R717 External experimental database [203,204,205] Horizontal platinum wire
d = 0.3 mm		 Nucleate pool boiling HT
Horizontal flat circular sur face of silver, d = 10 mm
Horizontal, plain stainless- steel tube, d = 19.05 mm
Shah
(2017) [206]		 R718, R717
Halocarbon Rs
HC Rs		 External experimental database (see [206]) Copper/ brass/steel, stainless steel single tubes and plain/ enhanced tube bundles
di = 3 mm		 Flow patterns, TP void fraction and flow boiling HT
Shah
(2021) [207]		 R718, R717, halocarbon Rs, HC Rs (R290, R600a) External experimental database (see [207]) Horizontal copper/brass/aluminium-brass/stainless steel/copper-nickel single tube, top tube of a column of tubes, do = 12.7–50.8 mm Falling film evaporation HT
in full wetting and partial dry-out regimes
Shete
(2023) [208]		 R134a, R32 R600a Experimental study A plain and five different reentrant cavity (REC) copper tubes, di = 16.5 mm Nucleated pool boiling HT
Tian
(2022) [209]		 R290 Experimental study A smooth, a fin-enhanced horizontal U-shaped titanium tube, di1,2 = 16.65 mm Enhanced pool boiling
Touhami
(2014) [210]		 R718, R717
Halocarbon Rs
HC RsHFC		 External experimental database (see [210]) Horizontal copper/carbon steel/stainless-steel tubes
do = 4–51 mm		 Pool boiling HT
Wen
(2014) [211]		 R600a Experimental study Circular copper tube with porous inserts, di = 7.5 mm Flow boiling HT and PD, effect of the sizes of inserts on HT and PD
Wu
(2021) [212]		 R290 Experimental study Horizontal copper MF tube, di = 6.3 mm Condensation HT
Yan
(2021) [213]		 R1270 Experimental study LHP, 2.5 mm × 2.5 mm channel Flow patterns and Condensation HT
Yang
(2018) [214]		 R290 Experimental study Shell side of horizontal stainless steel HBHX
do = 14 mm, baffle angle 40°		 Flow patterns and TP condensation HT
Yang
(2019) [215]		 R290 Experimental study Shell side of vertical stainless steel HBHX
do = 14 mm, baffle angle 40°		 Flow patterns and TP condensation HT
Yoo
(2022) [216]		 R290 Experimental study Semicircular channel PCHE
dh = 1.22 mm		 Condensation HT and PD
Yu
(2018) [217]		 R290 Experimental study Helical tube
helix angle = 10°
dh = 10 mm		 Forced convective condensation HT and frictional PD
Zhao
(2023) [218]		 R290 Experimental study Horizontal copper MF tube, do = 7 mm Flow patterns, boiling HT and frictional PD
R = refrigerant, TP = two phase, HT = heat transfer, PD = pressure drop, PHE = plate heat exchanger, MF = microfin, di, dh, do = inner, hydraulic, outer diameter, HC Rs = hydrocarbon refrigerants, LNG = liquefied natural gas, SWHE = spiral wound heat exchanger, HBHX = helically baffled shell-and-tube heat exchanger, TPCT = two-phase closed thermosyphon, PCHE = printed circuit heat exchanger, LHP = loop heat pipe, ODF = offset strip fin, θ = winding angle, f.p.m. = fins per meter.
Table 4. Summary of the operating conditions, HTC and PD correlations of the papers included in this review, in case of not usual configurations.
Table 4. Summary of the operating conditions, HTC and PD correlations of the papers included in this review, in case of not usual configurations.
First
author/Year		 R ST/SP/VQ Heat Flux (kW/m2) Mass Flux (kg/m2s) Best reported HTC correlation/New HTC correlation AAD (%) Best reported PD correlation/New PD correlation AAD (%)
Abbas
(2017) [180]		 R717 Tsat = −20–(−1.7) °C
–
–		 q = 5–45 – h t p = 70 q 0.9 − 0.4 p r 0.1 p r 0.55 − l o g p r − 0.6 *±15% – –
Abbas
(2017) [181]		 R717 Tsat = −20–(−1.7) °C
–
xin = 0–0.30		 q = 5–45 – h t p = 70 q 0.9 − 0.4 p r 0.1 p r 0.55 − l o g p r − 0.6 e − 0.075 T s u p e − 0.5 x i n *93%±20%
Ahmadpour (2020) [182] R600a Tsat = 41.4–52.3 °C
psat = 550–700
x = 0.03–0.76		 – G = 54–90 Yu and Koyama [219]
Cavallini et al. [220]
Kedzierski and Goncalves [221]		 *±20 – –
Aprin
(2011) [183]		 R290
R600a
R601a		 –
p = 0.2–12 bar
–		 q = 3–53 G = 8–15 J G < 0.15   m s − 1 ;   h 1 = 55 p r 0.12 − 0.2 l o g R a / 0.4 − l o g p r − 0.55 M − 0.5 q 0.67 J G > 0.35   m s − 1   ; N u = h 2 d o λ G = 387 p r 0.17 R e v 0.34 P r v 0.33 0.15   m s − 1 < J G < 0.35   m s − 1   ; h = m a x h 1 , h 2 *92%±20% (all data) – –
Ayub
(2017) [184]		 R717 Tsat = −20–(−1.7) °C
–
–		 q = 5–45 – h t p = 70 q 0.9 − 0.4 p r 0.1 p r 0.55 − l o g p r − 0.6 e − 0.075 T s u p *±15%
Ding
(2017) [185]		 R290 –
psat = 0.25 MPa
x = 0.2–1		 q = 4–10 G = 40–80 h t p = E · h c v + S · h n b
h c v = 0.039 λ l · v 2 g − 1 / 3 · R e 0.09 · P r 0.99
h n b = 55 p r 0.12 − 0.4343 l n R a − 0.4343 l n p r − 0.55 M − 0.5 q 0.67
E = 1 + 9.42 × 10 − 6 · ϕ 2 0.92 R e 0.81
S = 4.76 × 10 − 5 W e − 0.0047 B o 0.061 p r 0.094 		*98%±20% – –
Ding
(2018) [186]		 R290 Tsat = −19.4 °C
psat = 0.25 MPa
x = 0.2–0.9		 q = 4–10 G = 40–80 h t p = E · h c v + S · h n b
h c v = 0.039 λ l · v 2 g − 1 / 3 · R e f i l m 0.04 · P r 0.65
h n b = 55 p r 0.12 − 0.4343 l n R a − 0.4343 l n p r − 0.55 M − 0.5 q 0.67
E = 1 + 3.25 × 10 − 4 · ϕ l 2 − 0.47 P t r a d i + 1.03 R e f i l m 0.040 P t l o n g + 0.79
S = − 0.3 + 1.19 · W e 0.25 B o 0.068 P t l o n g + 0.70 P t r a d i − 0.69
P t l o n g = p l o n g + D D ; P t r a d i = p r a d i + D D 		*95%± 20% ∆ P f r i c t , t p = ϕ l 2 · ∆ P f r i c t , l
ϕ l 2 = 1 + C X t t + 1 X t t 2
∆ P f r i c t , l = 2 f l N G 1 − x 2 ρ l
C = 1416.31 R e l − 0.53 U v 0.0041 P t l o n g − 2.41 P t r a d i − 5.40 − 2 		*95%± 25%
Fernández Seara (2016) [187] R717 Tsat = 4–10 °C
–
–		 – NA h o = C q / A o 0.77 p r 1.31
q = h e a t f l o w W ; A o = π d o L
C = 87.35                                             f o r   p l a i n   t u b e C = 110.46     f o r   i n t e g r a l − f i n   t u b e 		*±5.5 – –
Gil
(2019) [188]		 RE170 R600
aR601		 Tsat = 10 °C
–
x = –		 q = 5–70 NA h n b = 42 λ l d 0 q d 0 λ l T s a t C 1 − l o g 10 p r − 1
C 1 = 0.4 p r 0.78 ρ v ρ l − 0.59
d 0 = 0.0208 β σ g ρ l − ρ v
β = c o n t a c t a n g l e = 35 ° 		3.5 (all data) – –
Gong
(2013) [189]		 R600a –
psat = 0.1–0.5 MPa
–		 q = 20–150 NA Jung et al. [222] 6.9 – –
Huang
(2020) [190]		 R717 Tsat = 25, 35 °C
–
–		 q = 60.2–134.3W/cm2 G = 165–883 h = 0.00061 S + F R e l P r l 0.4 F a 0.11 λ l d h / l n b µ l f µ l w
F = 1250 B o 0.95 R e l o 0.22 x 1 − x 1.06
S = 2000 B o 1.02 R e l o 0.22 ; b = 1.02 		5.2 – –
Jin
(2019) [191]		 R134a, R290, R600a, R32 R1234ze(E) Tsat = 6–10 °C
––		 q = 10–60 – Full wetting regime:
N u = 23.3 R e Γ 0.8174 B o 0.6331 P r − 0.0864
R e Γ = 3.92 × 10 2 − 3.5 × 10 3
B o = 5.16 × 10 − 3 − 3.30 × 10 − 1
P r = 1.77 − 4.46 		*96.7% ±30% – –
Partial dryout regime:
N u = 11.7 R e Γ 0.8931 B o 0.5278 P r − 0.0287
R e Γ = 1.95 × 10 2 − 8.33 × 10 2
B o = 2.2 × 10 − 2 − 3.56 × 10 − 1
P r = 1.77 − 4.46 		*97.5%±30%
Koyama
(2014) [194]		 R717 –
psat = 0.7, 0.9 MPa
–		 q = 10, 15, 20 G = 5–7.5 F o r δ = 1 m m
h h l = 48.0 1 X v v 0.95
h l = 0.023 λ l d h G 1 − x d h µ l 0.8 P r l 0.4 		*92%±30% – –
F o r δ = 2 a n d 5 m m
h h l = 41.8 1 X v v 0.96 1 / X v v ≥ 1
h h l = 47.1 1 X v v 0.51 1 / X v v ≤ 1 		*87%±30%
Li
(2018) [195]		 R290 –
psat = 1.2–2.0 MPa
x = 0.15–0.95		 q = 5–20 G = 150–350 h t p = 0.021 λ l d h R e l o 0.8 P r l 0.43 1 + 3.5 d h D ѱ l o
ѱ l o = 1 + ∑ i = 1 2 a i · x b i · ρ v ρ l c · F r l o d · B o 1 − x + 1 e
a 1 = 0.0830 , a 2 = − 0.076 , b 1 = 0.8161 , b 2 = 16.29
c = − 1.364 , d = 0.047 , e = − 543.1 		4.00 d p d l t p = d p d l l o + φ l v d p d l v o − d p d l l o
d p d l l o = 0.3164 R e l o 0.25 + 0.03 d h D 0.5 G 2 2 ρ l d h
d p d l v o = 0.3164 R e l o 0.25 + 0.03 d h D 0.5 G 2 2 ρ v d h
φ l v = ∑ i = 1 3 a i x i · ρ l ρ v b · ∑ i = 1 3 c i F r l o i
a 1 = 0.5311 , a 2 = 1.794 , a 3 = − 1.270 , b = − 0.1703
c 1 = 8.613 , c 2 = − 4.975 , c 3 = 0.7734 		3.37
Lin
(2023) [196]		 R134a, R32
R245fa R1234ze(E) R410a R123, R290 R600a		 Tsat = 4.85–26.7 °C
–
–		 q = 2.5–168 – N u w e t t i n g = m a x N u c v , N u c o m b
N u c v = N u l a m 5 + N u t u r 5 1 / 5
N u l a m = 2.65 R e f f − 0.158 K a f f 0.0563
N u t u r = 0.03 R e f f 0.2 P r 0.7
N u c o m b = N u n b S + N u c v E
N u n b = h n b λ l d
h n b = 10 k l d b u b b l e q d b u b b l e λ l T s a t a p r 0.1 1 − T r − 1.4 P r l − 0.25
a = 0.855 ρ v ρ l 0.309 p r − 0.437
d b u b b l e = 0.511 2 σ g ρ l − ρ v 0.5
S = P r l 0.474 R e f f 0.968 B o f f 1 K a f f 0.565 G a b u b b l e 1 p r − 0.037 π 0 − 0.883 ρ l ρ v − 1 q q c r i 0.99
E = P r l − 0.465 R e f f 0.642 B o f f 0.46 K a f f − 0.242 G a b u b b l e − 1 p r − 0.253 π 0 0.418 ρ l ρ v 1 q q c r i − 1
R e f f = 4 Γ / µ
B o f f = q π d / Γ i l v
G a b u b b l e = g d b u b b l e 3 ν l − 2
π 0 = q 2 d ρ l − ρ v / i l v 5 / 2 μ l
q c r i = π 2 60 3 0.25 2 g ρ l − ρ v ρ l + ρ v + σ ρ l + ρ v R 2 0.5 g ρ l − ρ v σ + 1 2 R 2 − 0.75
Simplified correlation
S = R e f f 0.043 B o f f − 0.182
E = R e f f − 0.496 B o f f − 0.377 		10 (all data)














14 (all data)		 – –
Ma
(2017) [197]		 R600a Tsat = 54.6 °C
psat = 0.77 MPa
–		 – NA Rohsenow [223] 10.3 – –
Moon
(2022) [198]		 R600a Tsat = −25–(−10) °C
–
x = 0.2–0.9		 q = 9–15 G = 20–40 h = h n b + h c v
h n b = 0.9664 · h C o o p e r · S
h C o o p e r = 55 p r 0.12 − l o g p r 0.55 M 0.5 q 0.67
S = 1.36 X t t 0.36
h c v = 1.0274 · h l o · 1 + 1.128 x 0.8170 ρ l ρ v 0.3685 μ l μ v 0.2363 · 1 − μ l μ v 2.144 P r l 0.1 · R x 2.14 B d · F r − 0.2531 · G 0 G 0.0677  
h l o = 0.023 λ l d R e l o 0.8 P r l 0.333 		8.26 d p d z f = ϕ l o 2 d p d z f , l o = ϕ l o 2 · 2 f l o G 2 d ρ l A
A = 2.358 G G 40 1.2464 ; f l o = 64 R e l o ; G 40 = 40  
ϕ l o 2 = Z + 1.3529 · F · H · 1 − E W
Z = 1 + x 2 + x 2 ρ l ρ v μ v μ l 0.2
F = x 0.9525 1 + x 0.414
H = ρ l ρ v 1.132 μ v μ l 0.44 1 − μ v μ l 3.542
1 − E = − 0.331 · l n μ l G x ρ v σ − 0.0919
E = 0.95       i f   E > 0.96 E = 0       i f   E < 0
W = 1.398 p r 		4.82
Pham
(2022) [199]		 R290 Tsat = 48 °C
–
–		 q = 3–9 G = 100–300 h = λ l d i 0.007079 R e 0.1112 J a − 0.232 x P r − 0.68 ·
· p r − 0.578 x 2 − l o g P r − 0.474 x 2 S v 2.531 x 		8.54 – –
Qiu
(2015) [200]		 R290 –
–
x = 0.1–0.9		 – G = 150–250 Boyko [224] 8.8 Fuchs [225] 4.05
Salman
(2023) [201]		 R290 Tsat = 5–20 °C
–
x = 0.14–0.89		 q = 7.5–15 G = 20–60 N u = Z 1 R e e q Z 2 R e l Z 3 P r Z 4
Z 1 t o Z 4 = 2.251 , 0.549 , 0.043 , 0.333
10 f t p = Z 1 R e e q Z 2 R e l Z 3 ρ l ρ v Z 4
R e e q < 2500 ; Z 1 t o Z 4 = 0.061 , 1.251 , − 0.501 , − 0.951
R e e q > 2500 ; Z 1 t o Z 4 = 0.091 , 1.101 , − 0.551 , − 1.021 		14
Sathyabhama
(2010) [202]		 R717 –
p [203] = 0.7 MPa
p [204] = 0.7 MPa
p [205] = 0.4 MPa
–		 q [203] = 72–1000
q [204] = 72–2800
q [205] = 8–60		 NA Kruzhilin [226] 7.54 (AD) – –
Mostinski [227] −3.16 (AD)
Mostinski [227] 29.8 (AD)
Shah
(2017) [206]		 R718 R717
Halocarbon Rs
HC Rs 		–
pr = 0.005–0.2866
x = 0–0.98		 q = 1–1000 G = 0.17–1391 Regime I Intense Boiling Regime (YIB > 0.0008)
Y I B = F p b B o F r 0.3
F p b = h p b , a c t u a l / h C o o p e r
F p b = 1   unless test data or an alternative correlation is used
h t p = F p b h C o o p e r
h C o o p e r = 55.1 q 0.67 p r 0.12 − l o g p r − 0.55 M − 0.55
Regime II Convective Boiling Regime (0.00021<YIB ≤0.0008)
φ = φ 0
Regime III Convection Regime (YIB ≤ 0.00021)
φ = 2.3 Z 0.08 F r 0.22
Z = 1 − x x 0.8 p r 0.4 		5.2 (all data)
24.25
(R717)
14.3
(R600a)		 – –
Shah
(2021) [207]		 R718, R717, halocarbon Rs, HC Rs (R290, R600a) –
pr = 0.00059–0.19144
–		 q = 1–208 – h t p i s   t h e   l a r g e r   o f   h c , l a m a n d   h p b + h c , t u r b  
h c , l a m = 0.821 ѵ 2 g λ 3 − 1 / 3 R e l − 0.22
h c , t u r b = 0.0038 ѵ 2 g λ 3 − 1 / 3 R e l 0.4 ѵ α 0.65
hpb from Mostinski for HC Rs:
h p b = 0.00417 q 0.7 p c 0.69 1.8 p r 0.17 + 4 p r 1.2 + 10 p r 10
hpb from Cooper for all other fluids:
h p b = 55 p r 0.12 − 0.4343 l n p r − 0.55 M − 0.5 q 0.67 		17.4 (all data)
16.9 (HC Rs)
13.0 (R717)		 – –
Shete
(2023) [208]		 R134a, R32 R600a Tsat = 7–10 °C
–
–		 q = 6.92–51.71 NA Plain: Stephan and Abdesalam [228] *±30% – –
For REC tubes:
N u = R e 0.773 P r l 0.036 p s a t p c 2.721 ρ l ρ v 2.765 β − 0.1617
β = mouth size to fin height ratio		 *±20%
Tian
(2022) [209]		 R290 Tsat = 20–40 °C
–
–		 q = 2.5–10.5 NA Smooth tube: R-J [229]
Enhanced tube: Copper [230]		 10.93
11.48		 – –
Touhami
(2014) [210]		 R718 R717
Halocarbon Rs
HC RsHFC		 –
p = 0.2–106.87 bar
–		 q = 0–670 – h = 0.5 p c 0.10 l c − 0.20 c p 0.40 H l v − 0.67 μ − 0.27 λ 0.60 p − 010 R a q 0.07 d − 0.20 q 0.67 32% (all data) – –
Wen
(2014) [211]		 R600a Tsat = 10 °C
–
x = 0.076–0.87		 q = 12–65 G = 120–1100 N u = 8.332 B o 0.35 R e 0.48 P r 0.74 ε 0.47 *95%±20% f = 21.093 R e − 0.731 ε − 6.558 *95%±20%
Wu
(2021) [212]		 R290 Tsat = 40–55 °C
psat = 1.37–1.91 MPa
x = 0–1		 q = 3–8 G = 100–250 Yu et al. [219] 15.52 – –
Yan
(2021) [213]		 R1270 Tsat = 283 K
–
–		 q = 5–70 G = 2.2–26.5 Cavallini et al. [231] *±20 – –
Yang
(2018) [214]		 R290 –
–
x = 0.1–0.9		 q = 3–7 G = 20–40 h s λ l μ l 2 ρ l ρ l − ρ v g 1 / 3 =
= 1.11 R e f i l m − 0.3 4 + 0.068 R e f i l m 0.2 4 1 / 4
R e f i l m = 4 Γ x µ l = 4 π d q x µ l i f v 		*86%±10% – –
Yang
(2019) [215]		 R290 –
–
x = 0.2–0.9		 q = 3–7 G = 20–40 h = λ l ρ l ρ l − ρ v g μ l 2 1 / 3 a R e f i l m b 1 + R e v c 1.08 R e f i l m 1.22 − 5.2
48.5 < R e f i l m < 684.6 ,   6150 < R e v < 61153
a = 0.00063 ,   b = 1.4 ,   c = 0.5 		*93%±20% – –
Yoo
(2022) [216]		 R290 Tsat = −5.47–7.92
psat = 400–600 kPa
x = 0–1		 – G = 40–90 N u = 1.18 R e e q , t e s , h 1 / 3 P r l , t e s t , h 1 / 3 *±15 Lockhart and Martinelli [232] –
Yu
(2018) [217]		 R290 Tsat = −40–27 °C
–
x = 0.1–0.9		 q = 1.4–9.6 G = 200–400 Shah [114] *±20 Müller-Steinhagen & Heck [130] *±20
Zhao
(2023) [218]		 R290 Tsat = −23.55–(−4.35) °C
psat = 0.215–0.415 MPa
x = 0–0.96		 q = 10.6–73.0 G = 70–190 Cavallini [233] 29.39 Rollmann and Spindler [119] 16.24
R = refrigerant, ST, Tsat = saturation temperature, SP, psat = saturation pressure, pr = reduced pressure, pavg = average pressure, VQ = vapour quality, HC Rs = hydrocarbon refrigerants, AAD = Average Absolute Deviation, AD = Average Deviation.
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