# Flow Condensation of Low-GWP Zeotropic Mixtures Inside 5 mm OD Micro-Finned Tube
## 3 Results and Discussions
### Empirical Models  
Owing to their geometrical complexity compared to conventional tubes, micro-finned empirical models for the prediction of two-phase heat transfer coefficients should account for geometrical parameters beyond mere tube diameter. [PERSON] et al. [24] developed a model based on a database of experimental heat transfer coefficients for micro-finned tubes ranging from 5.95 to 14.18 mm inner diameter and included the geometrical complexities by implementing two terms, namely R\({}_{\rm x}\) and C. While the former is merely a ratio of heat transfer areas in the case of the micro-finned tube to the smooth one, the latter is a coefficient that is based on whether the optimal number of fins have been implanted on the tube, a condition which is not met in the 5 mm OD tube under study. The optimum number of  
Figure 6: Frictional pressure drop per unit length versus vapor quality for various mass fluxes. (**a**) R450A and (**b**) R454B. \(G\) is expressed in [kg m\({}^{-2}\) s\({}^{-1}\)]. fins suggested by [PERSON] et al. [24] is presented in Equation (14), and the procedure to calculate the coefficient in the case of incompatibility is given in Equation (15). \[n_{opt}=4064.4\times D_{i}+23.257 \tag{14}\]  
\[C=\left(n_{opt}/n_{fins}\right)^{1.904} \tag{15}\]  
Furthermore, the correction of [PERSON] and Ghaly [25] for mass transfer resistance in the mixture can be considered as well. In the current case, it has been explored whether such correction for mass transfer resistance and the optimal number of fins could ameliorate the accuracy of the predictions made. It should be noted that the vapor heat transfer coefficient required by the model of [PERSON] and Ghaly's correction [25] is acquired using the correlation of Gnielinski [31]. Figure 8 represents the deviation of predictions for different considerations made regarding the mass resistance correction and coefficient \(C\) equal to 1. Considering Table 3--which provides detailed information by stating the average relative deviation and average absolute deviation, whose expressions are given in Equations (16) and (17)--on average, the correlation benefits from the correction introduced by [PERSON] and [PERSON] [25]. \[Dev_{rel}=\left[\sum\biggl{(}\frac{HTC_{model}-HTC_{exp}}{HTC_{exp}}\biggr{)} \right]\times 100 \tag{16}\]  
\[Dev_{abs}=\left[abs\sum\biggl{(}\frac{HTC_{model}-HTC_{exp}}{HTC_{exp}} \biggr{)}\right]\times 100 \tag{17}\]  
Figure 7: Heat transfer coefficient and frictional pressure drop per unit length versus vapor quality for various mass fluxes and two saturation temperatures of 30\({}^{\circ}\) and 40\({}^{\circ}\)C (**a**) HTC and (**b**) FPD (per unit length). \(G\) is expressed in [kg m\({}^{-2}\) s\({}^{-1}\)]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fluid** & \(C\) & _Bell and Ghaly_ & _dev\({}_{rel}\)_ & _dev\({}_{abs}\)_ \\ \hline R450A & 1 & with & 5.5\% & 22.6\% \\ R450A & 1 & without & 7.9\% & 23.8\% \\ R450A & 0.58 & with & –37.9\% & 37.9\% \\ R450A & 0.58 & without & –37.1\% & 37.1\% \\ R454B & 1 & with & 37.0\% & 40.3\% \\ R454B & 1 & without & 43.3\% & 44.9\% \\ R454B & 0.58 & with & –18.7\% & 21.2\% \\ R454B & 0.58 & without & –16.5\% & 20.8\% \\ \hline \hline \end{tabular} The coefficient C based on an optimum number of fins does not necessarily elevate the accuracy of the model as evident in Table 3 by noticing the variability of deviations.  
\end{table} 
Table 3: Average relative and absolute deviations for HTC. Regarding frictional pressure drop predictions, two models, namely [PERSON] and Spindler [35] and [PERSON] et al. [36], are taken into consideration. Both models developed for micro-finned tubes are expected to be suitable for the case under study. Figure 9 demonstrates the deviations for both models based on experimental data excluding values of FPD per unit of length below 0.4 kPa m\({}^{-1}\) as a result of high experimental uncertainty. It is clear that both models provide fair predictions that are mainly underestimations, which, in the worst case, are, on average, as high as 20%.