## 4 Empirical Modeling  
The experimental values of the heat transfer coefficient and frictional pressure drop were used to verify some empirical models available in the literature. In particular, for R450A and R515B, since their experimental data during flow boiling inside microfin tubes are new in the literature, there is a need to verify empirical correlations to be confidently used for the design of enhanced evaporators implementing these new refrigerants as working fluids. To evaluate the accuracy of the implemented correlations, the relative deviation (\(dev_{rel}\)) and the absolute deviation (\(dev_{abs}\)) were used and defined in the following:  
\[dev_{rel}=\frac{1}{N}\sum_{i=1}^{N}\left(\frac{y_{calc}-y_{exp}}{y_{exp}} \right)\times 100 \tag{10}\]  
\[dev_{abs}=\frac{1}{N}\sum_{i=1}^{N}\left|\frac{y_{calc}-y_{exp}}{y_{exp}} \right|\times 100 \tag{11}\]  
\(y_{calc}\) and \(y_{exp}\) are the calculated and experimental generic quantities (heat transfer coefficient or frictional pressure drop), respectively. The experimental data of the heat transfer coefficient were compared against the values estimated by the following empirical models taken from the open literature: [PERSON] et al. (2019) and [PERSON] (2019). Only data prior to a fully dryout condition were considered for the comparison, as well as only data having a wall-to-saturation temperature difference higher than 0.8 K, in order to exclude experimental values with higher uncertainty. Considering all the three fluids, the model of [PERSON] et al. (2019) was able to estimate the experimental values with a relative and absolute deviation of \(-5.5\%\) and \(8.9\%\), respectively, and the model of [PERSON] and [PERSON] (2019) with a relative and absolute deviation of 0.7% and 20.4%. Table 4 summarizes the relative and absolute deviations of the implemented models split for each tested refrigerant. Data at \(G\) = 50 and 75 kg m\({}^{-2}\) s\({}^{-1}\) were omitted in the comparison, since they were in the wavy-stratified flow regime and they were outside from the range of working conditions of the implemented correlations. Among the tested empirical models, the model developed by [PERSON] et al. [39] is the one that better predicts the experimental values of the heat transfer coefficients. The model was developed from an experimental database comprising data during flow boiling of R1234 ze(E) inside a microfin tube with an inner diameter at the fin tip of 3.4 mm, and the authors proposed a correlation for the prediction of the heat transfer coefficient in the pre-dryout region. The model was validated with data covering mass velocities from 190 to 940 kg m\({}^{-2}\) s\({}^{-1}\) and heat fluxes from 10 to 50 kW m\({}^{-2}\). The model considers the contribution of nucleate boiling and convective boiling, as well as the geometrical parameters of the microfin tube. A general overview of the accuracy of the model is given in Figure 8.  
It is worth noting that experimental data with low mass velocities below 100 kg m\({}^{-2}\) s\({}^{-1}\) are scarce in the literature. Therefore, a specific model developed by [PERSON] et al. [41] was chosen to analyze these data. Data at \(G=50\) and 75 kg m\({}^{-2}\) s\({}^{-1}\), prior to the onset of dryout, were compared against the values estimated with the correlation developed by [PERSON] et al. [41], which was later reported by [PERSON] et al. [38]. For mass velocities lower than 100 kg m\({}^{-2}\) s\({}^{-1}\), this correlation considered the contribution of capillarity for the evaluation of the heat transfer coefficient. Considering only the experimental data at \(G=50\) and 75 kg m\({}^{-2}\) s\({}^{-1}\), the correlation was able to estimate the experimental data of R450A, R515B, and R1234 ze(E), with a relative and absolute deviation of 4.3% and 29.3%, respectively. Since R450A is a zeotropic mixture, the concentration of the components in the liquid and vapor phases changes during the flow boiling process, and the local saturation temperature increases as the phase change mechanism proceeds.