# 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  
Experimental determination of the heat transfer coefficient in small-sized channels such as microchannels brings it along with some difficulties. In particular, limited space for the placement of measurement probes, small mass flux in the microchannel corresponding to low heat transfer rates, and high heat transfer coefficients causing small temperature differences make it difficult to measure experimental data accurately [33]. For this reason, it is useful to employ condensation predictive models that form the basis of condensation flow models in microchannels. The predictive empirical correlations developed for the condensation flow of refrigerants inside small-scale channels provided in this section. The most important of these classical correlations is the model developed by [PERSON] and [PERSON] [84], which depends on the flow regime. This correlation is based on the flow regime and comprises only stratified, wavy, and annular flow regimes. According to the correlation between [PERSON] and [PERSON] [84], the heat transfer coefficient of two-phase flows corresponding to annular flow, which is controlled by shear stress, is the product of the heat transfer coefficient of the liquid calculated as a single phase with the Dittus-Boelter [85] model with a two-phase multiplier. Empirical constants and exponents of the [PERSON] and [PERSON] [84] correlation are adjusted based on experiments for R134a, R22, R32, and R125 fluids with mass velocities between 25 and 800 kg/m\({}^{2}\)s, saturation temperatures of 35 to 45 \({}^{\circ}\)C, and heat fluxes of 5 to 15 kW/m\({}^{2}\). According to the [PERSON] and [PERSON] [84] model, when the Soliman Froude (\(Fr_{So}\)) number is greater than 20 (\(Fr_{So}\) > 20), the flow is considered an annular flow regime. Otherwise, the flow is considered to be in the stratified wavy flow regime. The Soliman Froude (\(Fr_{So}\)) number can be computed as follows:  
\[Fr_{So}= \begin{cases}0.025 Re_{l}^{1.59}\left(\frac{1+1.09X_{tt}^{0.039}}{X_{tt }}\right)\frac{1}{Ga^{1.5}},&Re_{l}\leq 1250\\ \\ 1.26 Re_{l}^{1.04}\left(\frac{1+1.09X_{tt}^{0.039}}{X_{tt}}\right)\frac{1}{Ga^{ 1.5}},&Re_{l}>1250\end{cases}  \tag{14}\]  
where \(X_{tt}\) and \(Ga\) stand for the modified Martinelli parameter and Galileo number, respectively. [PERSON] and [PERSON] [84] suggest using the void fraction model of [PERSON] [35] in calculating the Galileo number (\(Ga\)). The modified Martinelli parameter and Galileo number are indicated in Equations (15) and (16):  
\[Ga=gp_{l}(p_{l}-p_{v})\frac{\left(\sqrt{\alpha}D_{h}\right)^{3}}{\mu_{l}^{2}} \tag{15}\]  
\[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]  
where subscript \(l\) and \(v\) stand for \"liquid\" and \"vapour\", respectively. According to the heat transfer coefficient model of [PERSON] and [PERSON] [84], when the regime of the flow is annular (where the gravity effect may be neglected and the shear stress force is dominant), the Nusselt number is as in Equation (17):  
\[Nu_{annular}=0.023 Re_{l}^{0.8}Pr_{l}^{0.4}\left(1+\frac{2.22}{X_{tt}^{0.89}}\right) \tag{17}\]  
[PERSON] et al. [86] proposed an analytical model on condensation in the annular flow regime, which is a shear stress-controlled flow regime, in circular cross-section tubes with hydraulic diameters between 3.14 and 20 mm. They conducted their experiments on seven different types of halocarbon refrigerants in the mass flux range of 87 to 862 kg/m\({}^{2}\)s and at temperatures between 22 and 52 \({}^{\circ}\)C. Their model is based on an equivalent Reynolds number (\(Re_{eq}\)), which requires prediction methods for the single-phase heat transfer coefficient and the two-phase frictional pressure gradient:  
\[Re_{eq}=\varnothing_{lo}^{\frac{8}{2}}Re_{lo} \tag{18}\]  
To compute the \(Re_{eq}\), the friction coefficient of each phase, it is required separately.