# Modeling Liquid Thermal Conductivity of Low-GWP Refrigerants Using Neural Networks
## 4 Experimental Settings and Results
It is evident that the network can accurately reproduce the behavior of liquid thermal conductivity of this refrigerant as a function of the temperature. However, higher deviations can be seen at some specific temperatures. From an in-depth analysis of the results, it was found that this outcome could be due to the different temperature and pressure behaviors of the experimental point provided by the two sources [39,40] presenting \(\lambda_{L}\) data for R1336 mzz(E). However, the behavior of the entire network is very satisfactory, as can also be seen in Figure 4 where an excellent agreement of the computed points with respect to the experimental data is evident. Furthermore, Figure 4 shows that for the training, validation, and test datasets, the behavior of the network is always close to the bisector of the first and third quadrants, demonstrating the good performance of the network architecture. The deviations provided using the proposed neural network were compared with that given using Equation (1) and the models used in REFPROP 10.0. The results of these models are also reported in Table 5. The results for R1336 mmz(E) provided by REFPROP 10.0 are not reported in this table since a model to calculate its thermal conductivity is currently not available in the software. This table shows that the proposed ANN ensured the lowest AARD% for all the studied low-GWP refrigerants, while REFPROP 10.0 gave the highest overall AARD% for the complete dataset. This outcome is due to high deviations obtained for R1224 yd(Z) and R1336 mzz(Z), for which preliminary models for thermal conductivity are available in the software. Instead, REFPROP 10.0 ensured accurate results for the other selected fluids. Despite its simplicity, Equation (1) generally provided good \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Training Set** & **Test Set** & **Training Set** & **Test Set** \\  & **Point N.** & **Point N.** & **AARD\%** & **AARD\%** \\  & **Point N.** & **RMSE** & **RMSE** \\ \hline Cross Validation 1 & 2553 & 851 & 0.557 & 0.643 \\ Cross Validation 2 & 2553 & 851 & 0.0007 & 0.0022 \\  & & 0.904 & 0.853 \\ Cross Validation 3 & 2553 & 851 & 0.0011 & 0.0026 \\  & & 0.354 & 0.932 \\  & & 0.0004 & 0.0032 \\ Cross Validation 4 & 2553 & 851 & 0.417 & 1.087 \\  & & 0.0005 & 0.0032 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of the ANN using a 4-fold cross-validation procedure. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Fluid Name**} & \multirow{2}{*}{**N. of Points**} & \multicolumn{3}{c}{**This Work**} & \multicolumn{2}{c}{**Equation (1)**} & \multicolumn{2}{c}{**REFPROP 10.0**} \\ \cline{3-8}  & & **AARD\%** & **MARD\%** & **AARD\%** & **MARD\%** & **AARD\%** & **MARD\%** \\ \hline R1224 yd(Z) & 53 & 0.451 & 1.299 & 3.041 & 5.896 & 6.365 & 8.861 \\ R1233 zd(E) & 1132 & 0.260 & 1.545 & 1.155 & 3.930 & 0.337 & 1.584 \\ R1234 yf & 267 & 0.290 & 1.163 & 1.446 & 7.242 & 0.303 & 1.557 \\ R1234 ze(E) & 494 & 0.251 & 2.235 & 1.634 & 5.941 & 0.336 & 2.041 \\ R1234 ze(Z) & 61 & 0.560 & 1.574 & 1.771 & 5.080 & 1.775 & 5.705 \\ R1336 mzz(E) & 118 & 1.223 & 5.499 & 6.456 & 13.197 & - & - \\ R1336 mzz(Z) & 1279 & 0.490 & 6.074 & 4.120 & 19.018 & 9.390 & 13.84 \\ \hline Overall & 3404 & 0.389 & - & 2.585 & - & 3.82 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average absolute relative and maximum absolute relative deviations between the experimental \(\lambda_{L}\) data of the studied refrigerants and the calculations provided by the proposed neural network, Equation (1) and REFPROP 10.0.  
results. As expected, this correlation gave higher deviations for R1336 mmz(E) since its \(\lambda_{\rm L}\) data were not used in the regression of the coefficients. Figure 3: Behavior of R1336 mmz(E) and absolute relative average percent deviation related to experimental temperature. (a) corresponds to Ref. [40] and (b) corresponds to Ref. [39].