## 6 Discussion  
The validation of the proposed CFD models was performed by comparing the simulated results with the experimental data in the thermocouple array, the hot surface, and the bottom surface of the container. Figures 7-9 show the differences between the experimental and simulated temperature values for each approach (A, B, and C) analyzed throughout the test and for each of the thermocouple probes in the experimental equipment. The root mean square error (\(RMSD\)) and the coefficient of determination (\(R^{2}\)) parametrical statistics were used for the validation of the simulation of the phase-change process, defined in Equations (12) and (13), and summarized in Table 5:  
\[R^{2}=\frac{\sum_{n=1}^{N}(\hat{y}_{n}-\overline{y})^{2}}{\sum_{n=1}^{N}(y_{n} -\overline{y})^{2}} \tag{12}\]  
\[RMSD=\sqrt{\frac{\sum_{n=1}^{N}(\hat{y}_{n}-y_{n})^{2}}{N}} \tag{13}\]  
where \(\hat{y}_{n}\) is an experimental temperature value, \(y_{n}\) a simulated temperature value, \(\overline{y}\) the average of the experimental temperature values, and \(N\) is the total number of experimental values measured (approach A: 957 values; approach B and C: 210 values). The experimental values of approach B and C were lower than those of approach A as the thermocouple matrix was reduced to a single column. Figure 6: Evolution of the liquid fraction, \(\beta\) (%), estimation in approach A and B.  
Figure 7: Temporal evolution of the differences between experimental and simulated temperatures, \(\mathrm{T_{exp}}-\mathrm{T_{sim}}\) (K), obtained in approach A for each of the thermocouples in the experimental equipment, i(j), i = columns A to F; j = rows 1 to 5. Sub-figures (**a**–**e**) represented rows 1 to 5. Dashed lines show the experimental error of the thermocouple probes. Figure 8: Temporal evolution of the differences between experimental and simulated temperatures, \(\mathrm{T_{exp}-T_{sim}}\) (K), obtained in approach B (EP model) for each row of thermocouples in the experimental equipment. Dashed lines show the experimental error of the thermocouple probes. Figure 9: Temporal evolution of the differences between experimental and simulated temperatures, \(\mathrm{T_{exp}-T_{sim}}\) (K), obtained in approach C (EHC model) for each row of thermocouples in the experimental equipment. Dashed lines show the experimental error of the thermocouple probes. When the models were globally compared, no large deviations were observed, although, at the beginning of the tests, when temperatures were low, all models generated lower temperature values than the experimental ones. Another critical aspect, the melting point temperature, was where greater deviations were also observed. The EP and the EHC models considered a range of temperatures during which the phase change occurred, as shown in Table 6, moving slightly away from the actual behavior of the phase change in a pure substance. All three approaches showed good performance in their simulations of the melting-process temperature profiles, obtaining \(R^{2}\) results higher than 98%. The results of approach A showed the highest deviations in the results, with _RMSD_ in temperatures up to 1 K. The error in the model was greater at the beginning of the test, in the solid phase of the PCM, and the differences between the experimental and simulated temperatures increased in positions furthest from the center of the container; a fact that revealed the existence of horizontal heat flows within the model that did not appear in the experimental test. Approach A was the most complex model under consideration and involved a high number of boundary parameters, which were difficult to evaluate experimentally and were a possible source of error in the simulation. Nevertheless, the results clearly represented the process that occurred in the system. On the other hand, in approaches B and C, which had geometries simplified by vertical symmetries, the results were more accurate, with RMSE in temperatures lower than 1 K. Only the average temperature for each row is included in Figures 8 and 9.