# Condensation Flow of Refrigerants Inside Mini and Microchannels: A Review
## 3 Condensation Flow of Refrigerants Inside Mini/Micro-Channels
### Predictive Models for Condensation Flow of Refrigerants Inside Mini/Microchannel
#### 3.3.1 Heat Transfer Coefficient Correlations
Theypresented a modified correlation for the heat transfer coefficient according to the data they obtained as a result of their experiments. They concluded that their correlation provided a good fit for three refrigerants (R1234 ze, R134a, and R236 fa) over a wide range of operating conditions. [PERSON] et al. [73] model suggests Equations (56) and (57) to compute the Nusselt number. \[Nu=0.0055 Pr_{l}^{1.37}\frac{\varpi_{v}}{X_{tt}}Re_{l}^{0.7} \tag{56}\]  
\[h_{\rm A}=h_{lo}\bigg{[}1+1.128x^{0.817}\bigg{(}\frac{\rho_{l}}{\rho_{v}}\bigg{)} ^{0.3685}\bigg{(}\frac{u_{v}}{\mu_{l}}\bigg{)}^{0.2363}\bigg{(}1-\frac{\mu_{v}} {\mu_{l}}\bigg{)}^{2.144}Pr_{l}^{-0.1}\bigg{]} \tag{48}\]0  
[PERSON] et al. [82] comparatively examined the condensation flow of R134a and R404A refrigerants in tubes with 0.31-3.30 mm inner diameters. As a result of their experimental studies, they derived their own correlations for annular and annular layered flow under the conditions of mass flux 0-1300 kg/m\({}^{2}\)s, vapour quality 0-1, and saturation temperature 20-50 \({}^{\circ}\)C. The correlation presented by [PERSON] et al. [82] is given in Equation (58). \[h_{\rm A}=h_{lo}\bigg{[}1+1.128x^{0.817}\bigg{(}\frac{\rho_{l}}{\rho_{v}}\bigg{)} ^{0.3685}\bigg{(}\frac{u_{v}}{\mu_{l}}\bigg{)}^{0.2363}\bigg{(}1-\frac{\mu_{v}} {\mu_{l}}\bigg{)}^{2.144}Pr_{l}^{-0.1}\bigg{]} \tag{48}\]1  
\[h_{\rm A}=h_{lo}\bigg{[}1+1.128x^{0.817}\bigg{(}\frac{\rho_{l}}{\rho_{v}}\bigg{)} ^{0.3685}\bigg{(}\frac{u_{v}}{\mu_{l}}\bigg{)}^{0.2363}\bigg{(}1-\frac{\mu_{v}} {\mu_{l}}\bigg{)}^{2.144}Pr_{l}^{-0.1}\bigg{]} \tag{48}\]2  
where \(p_{r}\) is the reduced pressure ratio and is the ratio of saturation pressure to critical pressure. [PERSON] [90] proposed flow regime-based extended heat transfer coefficient correlations for condensation flow in all mini/microchannel orientations. In the study, where two alternative correlations are presented, the correlations include 33 different fluids, mass fluxes between 1.1 and 1400 kg/m\({}^{2}\)s, various geometries (circular, square, quadrangular cross-sectional areas) with hydraulic diameters between 0.1 and 49 mm, and all orientations (horizontal, vertical, inclined, etc.). The author compared correlations with a comprehensive database. [PERSON] [90] defined three different flow regimes: Regime I, which covers intermittent, annular, or mist regimes; Regime II, which covers wavy flow regimes; and Regime III, which includes stratified flow. The transition criterion between these flow regimes was determined according to the Weber number (\(We\)) of the vapour phase. The Weber number is the ratio of inertial forces to the surface tension force. In this respect, the Weber number of the vapour phase (\(We_{v}\)) can be calculated as follows:  
\[h_{\rm A}=h_{lo}\bigg{[}1+1.128x^{0.817}\bigg{(}\frac{\rho_{l}}{\rho_{v}}\bigg{)} ^{0.3685}\bigg{(}\frac{u_{v}}{\mu_{l}}\bigg{)}^{0.2363}\bigg{(}1-\frac{\mu_{v}} {\mu_{l}}\bigg{)}^{2.144}Pr_{l}^{-0.1}\bigg{]} \tag{48}\]3  
According to the [PERSON] [90] model, the transition from Regime I to Regime II occurs when \(We_{v}=100\). On the other hand, Regime I is valid when \(We_{v}>100\) and \(J_{G}>0.98(Z+0.263)^{-0.62}\). It is worth noting here that \(J_{G}\) is the dimensionless gas (vapour) velocity (Equation (47)) and \(Z\) is the correlation constant. The correlation constant, \(Z\), is expressed as follows:  
\[h_{\rm A}=h_{lo}\bigg{[}1+1.128x^{0.817}\bigg{(}\frac{\rho_{l}}{\rho_{v}}\bigg{)} ^{0.3685}\bigg{(}\frac{u_{v}}{\mu_{l}}\bigg{)}^{0.2363}\bigg{(}1-\frac{\mu_{v}} {\mu_{l}}\bigg{)}^{2.144}Pr_{l}^{-0.1}\bigg{]} \tag{48}\]4  
where \(p_{r}\) is the reduced pressure ratio (Equation (59)). Regime III occurs when \(We_{v}>20\) and \(J_{G}>0.95(1.254+2.27\times Z^{1.249})^{-1}\). According to these criteria, if the flow is not Regime I or Regime III, it can be defined as Regime II.