# 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
[88] also presented a transition criterion for \(\Delta\)T-dependent and \(\Delta\)T-independent flow regimes. According to this transition criterion, when the dimensionless gas velocity (\(J_{G}\)) is greater than the dimensionless transition gas velocity (\(J_{G}^{T}\)) it is classified as microchannel condensation flow. This corresponds to \(\Delta\)T-independent flow regime. When the dimensionless gas velocity (\(J_{G}\)) is smaller than the dimensionless transition gas velocity (\(J_{G}^{T}\)), condensation flow is classified as \(\Delta\)T-dependent flow regime where gravity effects are dominant. \(J_{G}^{T}\) and \(J_{G}\) are expressed as in Equations (45) and (46). \[Re_{eq}=\varnothing_{lo}^{\frac{8}{2}}Re_{lo} \tag{18}\]0  
\[C_{T}=\left\{ \begin{array}{cc}1.6,&for\text{ }hydrocarbons\\ 2.6,&for\text{ }other\text{ }refrigerants\end{array} \right. \tag{46}\]\[J_{G}=\frac{xG}{\sqrt{g\rho_{v}(\rho_{l}-\rho_{v})D_{h}}} \tag{47}\]  
The correlation proposed by [PERSON] et al. [88] is given below for \(\Delta\)T-independent flow regimes (\(J_{G}>J_{G}^{T}\));  
\[h_{\rm A}=h_{lo}\bigg{[}1+1.128x^{0.817}\bigg{(}\frac{\rho_{l}}{\rho_{v}}\bigg{)} ^{0.3685}\bigg{(}\frac{u_{v}}{\mu_{l}}\bigg{)}^{0.2363}\bigg{(}1-\frac{\mu_{v}} {\mu_{l}}\bigg{)}^{2.144}Pr_{l}^{-0.1}\bigg{]} \tag{48}\]  
\[h_{lo}=0.023 Re_{lo}^{0.8}Pr_{l}^{0.4}\frac{k_{l}}{D_{h}} \tag{49}\]  
For \(\Delta\)T-dependent flow regimes (\(J_{G}<J_{G}^{T}\)), the heat transfer coefficient is provided in Equations (50) and (51). \[h_{\rm D}=\left[h_{\rm A}\left(\frac{J_{G}^{T}}{J_{G}}\right)^{0.8}-h_{STRAT} \right]\frac{J_{G}}{J_{G}^{T}}+h_{STRAT} \tag{50}\]  
\[h_{STRAT}=0.725\bigg{\{}1+0.741\bigg{(}\frac{1-x}{x}\bigg{)}^{0.3321}\bigg{\}} ^{-1}\times\left[\frac{k_{l}^{3}\rho_{l}(\rho_{l}-\rho_{v})g\Delta h_{vl}}{ \mu_{l}D_{h}\Delta\rm T}\right]^{0.25}+(1-x^{0.087})h_{lo} \tag{51}\]  
[PERSON] and [PERSON] [89] carried out experiments to determine the heat transfer characteristics of the condensation flow of R22, R134a, and R410A in tubes with inner diameters of 1.77, 3.36, and 5.35 mm, at mass flux between 200 and 400 kg/m\({}^{2}\)s and at a saturation temperature of 40 \({}^{\circ}\)C. The authors proposed a new correlation as another form of the [PERSON] and Chato [84] model. They reported that they modified the [PERSON] and [PERSON] [84] model because the model could well predict the condensation flow heat transfer characteristics of R22, R134a, and R410A at varying tube diameters. Regression analysis of the experimental data obtained by using the Dittus-Boelter [85] correlation to determine the single-phase Nusselt number gave the expression in Equation (52). \[Nu=0.034 Re_{l}^{0.8}Pr_{l}^{0.3}f_{c}(X_{tt}) \tag{52}\]  
where \(f_{c}(X_{tt})\) is a two-phase multiplier, and it can be found by the following expression:  
\[f_{c}(X_{tt})=\left[3.28\bigg{(}\frac{1}{X_{tt}}\bigg{)}^{0.78}\right] \tag{53}\]  
[PERSON] et al. [83] experimentally investigated the effect of oil on the condensation flow of R410A in a small-scale horizontal tube with an inner diameter of 1.6 and 4.18 mm. As a result of experiments conducted at 40 \({}^{\circ}\)C saturation temperature, [PERSON] et al. [83] presented a new correlation for the heat transfer coefficient of the R410A-oil mixture. The correlation proposed by the researchers is as in Equation (54):  
\[Nu=0.0152\bigg{(}-0.33+0.83\,Pr_{l}^{0.8}\bigg{)}\frac{\varnothing_{v}}{X_{tt }}Re_{l}^{0.77} \tag{54}\]  
\[\varnothing_{v}=1+0.5\left[\frac{G}{\sqrt{g\rho_{v}(\rho_{l}-\rho_{v})D_{h}}} \right]X_{tt}^{0.35} \tag{55}\]  
where \(\varnothing_{v}\) is a two-phase multiplier. [PERSON] et al. [73] experimentally compared and examined the condensation flow of the new refrigerant R1234 ze with the condensation flows of R134a and R236 fa. The experiments were carried out in a tube with vertically arranged rectangular microchannels with a 50-260 kg/m\({}^{2}\)s mass flux and under 25-70 \({}^{\circ}\)C saturation temperature conditions.