# 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
#### 3.3.2 Pressure Drop Correlations  
Although the studies in the literature for small tubes are mostly on nitrogen-water and air-water mixtures, in recent years, experimental studies have also been carried out on the condensation flows of refrigerants in mini/microchannels. The empirical pressure drop correlations on condensation flows of refrigerants inside microchannels are provided in this section. Pressure drops of mini/microchannel condensation flows are generally modelled by applying a flow regime-based approach or by experimentally modifying the two-phase multipliers of classical correlations. In this way, flow phenomena occurring at the microscale can be taken into account [33]. For this reason, it would be useful to first examine the classical correlations that are the subject of the models developed for microchannels. The most well-known classical correlations are [PERSON] and Martinelli [34] and [PERSON] [91]. The correlation of [PERSON] and [PERSON] [34] is given in Equation (66), and it is based on the two-phase multiplier (\(\mathcal{O}_{I}^{2}\)) given in Equation (67). The two-phase multiplier is basically defined as the ratio of a two-phase pressure drop to a single-phase (liquid or vapour) pressure drop. \[\frac{\Delta P}{L}=\mathcal{O}_{I}^{2}\left(\frac{dP}{dz}\right)_{l} \tag{66}\]  
\[\mathcal{O}_{I}^{2}=1+\frac{C}{X}+\frac{1}{X^{2}} \tag{67}\]  
where \(C\) is a parameter depending on the flow regime and \(X\) is the Martinelli parameter. The parameter \(C\) and Martinelli parameter \(X\) are computed as in Equations (68) and (69), respectively. \[C=\left\{ \begin{array}{ll}20,&\text{\emph{Liquid}}:\text{\emph{Turbulent / Vapor}}:\text{\emph{Turbulent}}\\ 12,&\text{\emph{Liquid}}:\text{\emph{Laminar}}\text{\emph{/ Vapor}}:\text{\emph{Turbulent}}\\ 10,&\text{\emph{Liquid}}:\text{\emph{Turbulent}}\text{\emph{/ Vapor}}:\text{\emph{Laminar}}\\ 5,&\text{\emph{Liquid}}:\text{\emph{Laminar}}\text{\emph{/ Vapor}}:\text{\emph{Laminar}} \end{array} \right. \tag{68}\]  
\[X=\left[\frac{\left(\frac{dP}{dz}\right)_{v}}{\left(\frac{dP}{dz}\right)_{l}} \right]^{1/2} \tag{69}\]  
On the other hand, [PERSON] [91] produced the following correlation based on 25,000 data points obtained for adiabatic flow in channels with a hydraulic diameter greater than 1 mm. \[\frac{\Delta P}{L}=\mathcal{O}_{lo}^{2}\left(\frac{dP}{dz}\right)_{lo} \tag{70}\]\[\mathcal{O}_{lo}^{2}=E+\frac{0.32 FH}{Fr_{TP}^{0.045}We_{TP}^{0.035}} \tag{71}\]  
\[E=(1-x)^{2}+x^{2}\frac{\rho_{l}f_{vo}}{\rho_{v}f_{lo}} \tag{72}\]  
\[F=x^{0.78}(1-x)^{0.24} \tag{73}\]  
\[H=\left(\frac{\rho_{l}}{\rho_{v}}\right)^{0.91}\left(\frac{\mu_{v}}{\mu_{l}} \right)^{0.19}\left(1-\frac{\mu_{v}}{\mu_{l}}\right)^{0.7} \tag{74}\]  
where \(f_{vo}\) and \(f_{lo}\) are the single-phase friction factors for only vapour and only liquid, respectively. [PERSON] and [PERSON] [92], who studied the flow regime and void fraction with an air-water mixture in small channels with diameters of 1 to 4 mm, suggested using the \(C\) expression given in Equation (75) for small-scale channels using the correlation of [PERSON] and [PERSON] [34]. In this respect, the parameter \(C\) (Equation (75)) is applied to the correlation of [PERSON] and [PERSON] [34] and is given in Equations (66) and (67) according to the [PERSON] and [PERSON] [92] correlation. \[C=21\left(1-e^{-0.319D}\right) \tag{75}\]  
In addition to these classical correlations, empirical correlations were derived for the condensation flow of refrigerants in microchannels. [PERSON] et al. [93] developed an experimental correlation based on the flow regime at mass fluxes of 150-450 kg/m\({}^{2}\)s for the condensation flow of R134a in circular cross-section channels with diameters ranging from 0.5 to 4.91 mm. [PERSON] et al. [93] presented a pressure drop model for annular flow condensation in microchannels, assuming an equal pressure gradient in vapour and liquid at any cross-sectional area and uniform film thickness. According to [PERSON] et al.