## 4 Empirical Modeling
However, since the temperature glide is small (approximately 0.6 K), the increase in the bubble temperature due to temperature glide is somehow mitigated by the saturation temperature drop caused by the pressure drop, so the added heat flow rate needed to heat the liquid and vapor phases toward the dew temperature can be neglected. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Fluid** & \(\mathbf{dev_{rel}}\) & \(\mathbf{dev_{\text{abs}}}\) \\ \hline \multirow{3}{*}{[PERSON] et al. [39]} & R450A & \(-0.8\%\) & \(5.5\%\) \\  & R515B & \(-9.0\%\) & \(10.6\%\) \\  & R1234 ze(E) & \(-6.6\%\) & \(10.4\%\) \\ \hline \multirow{3}{*}{[PERSON] and [PERSON] [40]} & R450A & \(14.0\%\) & \(18.7\%\) \\  & R515B & \(-1.7\%\) & \(18.4\%\) \\ \cline{1-1}  & R1234 ze(E) & \(-10.9\%\) & \(21.0\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Accuracy of implemented correlations for heat transfer coefficient. Figure 8: Calculated vs. experimental heat transfer coefficient. Model developed by [PERSON] et al. [39]. According to [PERSON] [42], the flow boiling heat transfer coefficient can be estimated by correcting the nucleate boiling contribution for mass diffusion effects with a correction factor (\(F_{C}\)):  
\[HTC_{fb}=HTC_{nb}\times F_{C}+HTC_{cb} \tag{12}\]  
where \(F_{C}\) can be estimated as [42]:  
\[F_{C}=\left\{1+\left[HTC_{fb,id}\times\Delta T/q_{nb}\right]\times\left[1-e^{- B}\right]\right\}^{-1} \tag{13}\]  
with:  
\[B=\frac{q_{nb}}{\rho_{L}\times\Delta l_{m}\times\beta_{L}} \tag{14}\]  
The mass transfer coefficient \(\beta_{L}\) was set by [PERSON] [42] as equal to 0.0003 m s\({}^{-1}\). \(HTC_{fb,id}\) is the flow boiling heat transfer coefficient calculated as if the mixture were a pure fluid. According to [PERSON] [42], the local nucleate boiling heat flux, \(q_{nb}\), can be approximated with the total heat flux. \(\Delta T\) is the temperature glide of the mixture, and \(\Delta l_{m}\) is the enthalpy of isobaric vaporization. Considering the effect of the temperature glide of R450A on the prediction of the model developed by [PERSON] et al. [39], the relative and absolute deviations were \(-\)0.3% and 7.2%, respectively, whereas they were \(-\)0.8% and 5.5%, respectively, by neglecting \(F_{C}\). Due to the small temperature glide, the correction factor \(F_{C}\), which multiplies the nucleate boiling contribution, presented a mean value of 0.95, and as a result, it could be neglected in the case of R450A. The flow boiling heat transfer coefficient can be seen as the sum of a term due to nucleate boiling and a term due to convective boiling, but it is not possible to distinguish the two contributions from the experimental tests. Since the model of [PERSON] et al. [39] is the one that better predicts the experimental heat transfer coefficients, it was implemented here to estimate the effects of both nucleate boiling and convective boiling. Figure 9a,b show the effect of heat flux on the two contributions for a mass flux of 100 kg m\({}^{-2}\) s\({}^{-1}\) (Figure 9a) and 400 kg m\({}^{-2}\) s\({}^{-1}\) (Figure 9b) for R515B and R450A. The two contributions had an opposite trend with respect to vapor quality. Convective boiling was highly affected by the vapor quality, and it increased as vapor quality increased: the estimated heat transfer coefficient due to convective boiling at a mean vapor quality of 0.8 was about 2.2 times the value at a mean vapor quality of 0.2. On the contrary, the effect of nucleate boiling decreased as the vapor quality increased. The comparison between the fluids confirmed what highlighted from the analysis of the experimental data, i.e., R515B has a stronger convective boiling contribution compared to R450A: the convective boiling heat transfer coefficient of R515B was about 18% higher than that of R450A.