# 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
The friction coefficients of the phases can be calculated with the following expressions:  
\[\varnothing_{lo}^{2}=A_{1}+\frac{3.24A_{2}}{Fr_{TP}^{0.045}W\epsilon_{TP}^{0.03 5}} \tag{19}\]  
\[A_{1}=(1-x)^{2}+x^{2}\bigg{(}\frac{\rho_{l}}{\rho_{v}}\bigg{)}\bigg{(}\frac{f_ {eq}}{f_{lo}}\bigg{)} \tag{20}\]  
\[A_{2}=x^{0.78}(1-x)^{0.24}\bigg{(}\frac{\rho_{l}}{\rho_{v}}\bigg{)}^{0.91} \bigg{(}\frac{\mu_{v}}{\mu_{l}}\bigg{)}^{0.19}\bigg{(}1-\frac{\mu_{v}}{\mu_{l} }\bigg{)}^{0.7} \tag{21}\]  
\[Fr_{TP}=\frac{G^{2}}{gD_{h}\rho_{TP}^{2}} \tag{22}\]  
\[W\epsilon_{TP}=\frac{G^{2}D_{h}}{\rho_{TP}\sigma} \tag{23}\]  
\[\rho_{TP}=\bigg{(}\frac{1}{\rho_{b}}+\frac{1-x}{\rho_{s}}\bigg{)}^{-1} \tag{24}\]  
where \(Fr_{TP}\) and \(We_{TP}\) are Froude and Weber numbers for two-phase condensation flow, respectively. Also, subscripts \(lo\) is liquid-only\", subscripts \(vo\) is \"vapour-only\", and \(TP\) is \"two-phase\". According to the [PERSON] et al. [86] model, the Nusselt number can be calculated as given in Equation (25):  
\[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]0  
[PERSON] et al. [40] discussed the condensation of R134a in two different extruded aluminium multi-port microchannel tubes and proposed a heat transfer model. One of the tubes they used in their experimental setup had eight microchannels (ports) with a hydraulic diameter of 1.11 mm; the other tube contained nineteen microchannels with a hydraulic diameter of 0.8 mm. They carried out their tests in the mass flux range of 100 to 700 kg/m\({}^{2}\)s at 60 \({}^{\circ}\)C. The model proposed by [PERSON] et al. [40] consists of the asymptotic sum of terms related to forced convection condensation (\(F\)) and gravity-controlled (\(B\)) condensation. \[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]1  
where \(Nu_{F}\) is the forced convection condensation term and \(Nu_{B}\) is the gravity-controlled (buoyancy) condensation term. \(Nu_{F}\) can be computed as follows:  
\[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]2  
\[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]3\[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]4  
where \(X_{tt}\) is the modified Martinelli parameter (Equation (16)). Gravity controlled condensation term (\(Nu_{B}\)) is expressed as in Equation (30):  
\[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]5  
\[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]6  
\[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]7  
where \(T_{sat}\) is the saturation temperature, \(T_{wall,i}\) is the inner wall temperature of the tube, and \(h_{fg}\) is the vaporisation enthalpy. At the same time, \(\xi\) represents the void fraction in the [PERSON] et al. (2004) model, and it is written as in Equation (33). \[X_{tt}=\left(\frac{\rho_{v}}{\rho_{l}}\right)^{0.5}\left(\frac{\mu_{l}}{\mu_{v }}\right)^{0.1}\left(\frac{1-x}{x}\right)^{0.9} \tag{16}\]8  
[PERSON] et al. (2017) and [PERSON] et al. (2017) experimentally examined the condensation of R134a in circular microchannels with hydraulic diameters ranging from 0.506 to 1.524 mm and non-circular microchannels with hydraulic diameters ranging from 0.424 to 0.839 mm. They presented a new heat transfer coefficient model with the data obtained from their experiments between 150 and 750 kg/m\({}^{2}\)s. [PERSON] et al.