## 3 Data Analysis  
The experimental results will be given in the next paragraph in terms of heat transfer coefficient and frictional pressure gradient at the correspondent mean vapor quality. The heat transfer coefficient, \(HTC\), is calculated as:  
\[HTC=\frac{q_{TS}}{A_{i}\cdot\left(\overline{t}_{wall}-\overline{t}_{sat} \right)} \tag{1}\]  
where \(q_{TS}\) is the net heat flow rate exchanged in the test section, \(A_{i}\) is the inner surface area of the tube, \(\overline{t}_{wall}\) is the mean wall temperature, i.e., the arithmetic average between the twenty wall temperatures. \(\overline{t}_{sat}\) is the mean saturation temperature, i.e., the arithmetic average between inlet and outlet saturation temperatures, calculated from inlet and outlet pressures with REFPROP 10 [6]. Preliminary tests were run in vacuum conditions with the aim of estimating the heat losses through the external ambient. Results showed that heat losses are linearly dependent on the difference between wall temperature and ambient temperature. Therefore, \(q_{TS}\) can be calculated as the difference between the supplied electrical power and the heat loss, as:  
\[q_{TS}=P_{el}-q_{loss}=P_{el}-\left(0.1399\cdot\left(\overline{t}_{wall}-t_{ amb}\right)-0.0832\right) \tag{2}\]  
where \(P_{el}\) is the electrical power supplied by the heater, \(q_{loss}\) are the heat losses, and \(t_{amb}\) is the ambient temperature. The frictional pressure drop \(\Delta p_{f}\) is calculated as:  
\[\Delta p_{f}=\Delta p_{tot}-\Delta p_{m} \tag{3}\]  
where \(\Delta p_{tot}\) is the total measured pressure drop, and \(\Delta p_{m}\) is the momentum pressure drop. \(\Delta p_{m}\) is calculated as:  
\[\Delta p_{m}=G^{2}\cdot\left(\left(\frac{x^{2}}{\rho_{V}\cdot\epsilon}+\frac{ \left(1-x\right)^{2}}{\rho_{L}\cdot\left(1-\epsilon\right)}\right)_{out}- \left(\frac{x^{2}}{\rho_{V}\cdot\epsilon}+\frac{\left(1-x\right)^{2}}{\rho_{L }\cdot\left(1-\epsilon\right)}\right)_{in}\right) \tag{4}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Type B Uncertainty** \\ \hline Refrigerant mass flow rate & \(\pm\)0.1\% of the reading \\ Water volumetric flow rate & \(\pm\)0.25\% of the reading \\ Temperature & \(\pm\)0.05 K \\ Temperature difference & \(\pm\)0.03 K \\ Electric power & \(\pm\)0.13\% of the reading \\ Absolute pressure & \(\pm\)1950 Pa \\ Pressure drop & \(\pm\)25 Pa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Type B experimental uncertainty of measured parameters. where \(G\) is the mass velocity, \(x\) the vapor quality, \(\rho_{V}\) and \(\rho_{L}\) are the saturated vapor and liquid densities, respectively, and \(``out\"\) and \(``in\"\) mean that the properties are evaluated at the outlet and at the inlet of the test section, respectively. The void fraction, \(\varepsilon\), is calculated as suggested by [PERSON] and [PERSON] [20]. The refrigerant thermodynamic properties needed for the implementation of the model of [PERSON] and [PERSON] [20] are calculated with REFPROP 10 [6]. The mean thermodynamic vapor quality \(x_{mem}\) is the arithmetic average between inlet and outlet vapor qualities. The inlet vapor \(x_{in}\) is calculated as:  
\[x_{in}=\frac{h_{TS,in}-h_{L,in}}{h_{V,in}-h_{L,in}} \tag{5}\]  
where \(h_{TS,in}\) is the specific enthalpy of the refrigerant at the inlet at the test section, and \(h_{L,in}\) and \(h_{V,in}\) are specific enthalpies of saturated liquid and vapor, respectively, calculated with REFPROP 10 [6] from the knowledge of the inlet pressure.