## 3 Experimental Results  
### Preliminary Considerations  
The experimental results are shown in terms of the heat transfer coefficient and the frictional pressure gradient at the corresponding mean vapor quality. The heat transfer coefficient is calculated as:  
\[HTC=\frac{q_{TS}}{A_{D}\cdot\left(t_{wall}-t_{sat}\right)} \tag{1}\]  
where \(A_{D}\) is the internal surface area of a smooth tube having an inner diameter equal to the diameter at the fin tip of the studied microfin tube (\(A_{D}=D_{i}\times\pi\times L_{HT}\)), \(t_{wall}\) is the mean wall temperature, and \(t_{sat}\) is the mean saturation temperature calculated using the knowledge of inlet and outlet pressures with the software REFPROP10 [24]. In the case \begin{table}
\begin{tabular}{c c} \hline \hline
**Instrument** & **Accuracy** \\ \hline Coriolis mass flow meter (refrigerant side) & \(\pm\)0.10\% of the reading \\ Magnetic volumetric flow meter (water at pre-condenser) & \(\pm\)0.25\% of the reading \\ Magnetic volumetric flow meter (water at test section) & \(\pm\)0.50\% of the reading \\ T-type thermocouples & \(\pm\)0.05 K \\ Absolute pressure transducer & \(\pm\)1950 Pa \\ Differential pressure transducer & \(\pm\)25 Pa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Accuracy of the implemented instruments. Figure 2: Schematic of the test section. of R450A, whose temperature glide is 0.64 K at 6.77 bar, the saturation temperature was calculated using REFPROP10 [24] with the knowledge of the pressure and specific enthalpy, as already reported, for instance, by [PERSON] and [PERSON] [25]. It is worth highlighting that even if the outer wall temperature is measured by the thermocouples, since the wall thickness is about 0.25 mm and the tube is made of copper, the temperature difference across the outer and inner surface is well below the experimental accuracy of the thermocouples. \(q_{TS}\) is the heat flow rate, exchanged in the test section, calculated on the water side using the knowledge of the water flow rate (\(\dot{m}_{w,TS}\)) and of its inlet and outlet temperatures (\(t_{w,TS,in}\) and \(t_{w,TS,out}\)), as:  
\[q_{TS}=\dot{m}_{w,TS}\cdot c_{w}\cdot(t_{w,TS,in}-t_{w,TS,out}) \tag{2}\]  
where \(c_{w}\) is the water specific heat capacity. The uncertainty (\(i_{y}\)) on a general physical quantity \(y\), which is a function of \(n\) independent parameters \(x_{i}\), can be calculated, as suggested by [PERSON] and [PERSON] [26] as:  
\[i_{y}=\sqrt{\sum_{i=1}^{n}\biggl{(}\frac{\partial y}{\partial x_{i}}\cdot i_{ i}\biggr{)}^{2}} \tag{3}\]  
where \(i_{i}\) is the uncertainty on the \(i\)-th parameter. Following this procedure, the mean uncertainty of the heat transfer coefficient was \(\pm\)4.1%, with a minimum and maximum value of \(\pm\)1.5% and \(\pm\)10.1%, respectively. The mean vapor quality is the arithmetic average between inlet and outlet vapor qualities. The difference between outlet and inlet vapor qualities depends on the working conditions (mass velocity and heat flux): it varies from 0.486 at the lowest mass velocity and the highest heat flux to 0.023 at the highest mass velocity and the lowest heat flux. The inlet and outlet vapor qualities can be derived from energy balances at the pre-condenser and test section, respectively:  
\[x_{in}=\frac{h_{ref,TS,in}-h_{L}}{h_{V}-h_{L}}=\frac{\left[h_{ref,pc,in}-\frac {\dot{m}_{w,pc}\cdot c_{w}\cdot\Delta T_{w,pc}}{\dot{m}_{ref}}\right]-h_{L}}{ h_{V}-h_{L}} \tag{4}\]  
\[x_{out}=\frac{h_{ref,TS,out}-h_{L}}{h_{V}-h_{L}}=\frac{\left[h_{ref,TS,in}+ \frac{q_{TS}}{\dot{m}_{ref}}\right]-h_{L}}{h_{V}-h_{L}} \tag{5}\]  
where \(h_{ref,TS,in}\) is the refrigerant specific enthalpy at the inlet of the test section, \(h_{ref,PC,in}\) is the refrigerant specific enthalpy at the inlet of the pre-condenser, and \(\Delta T_{w,pc}\) is the water temperature difference at the pre-condenser, which is measured with a T-type thermopile. \(\dot{m}_{ref}\) is the refrigerant mass flow rate.