## 3 Results and Discussion
### Second Set of 30 Possible \(n\)-Tuples to Match the Experimental Results (2 nd Dataset)  
Thanks to the internal numerical optimization routine of the RSM software, it has been possible to generate other 30 \(n\)-tuples of values for the unknown parameters to make the FVM model match the experimental results. Even in this case, only the first 30 \(n\)-tuples (i.e., with the highest value of desirability) have been selected and subsequently inquired via the FVM software. Table 11 shows the simulated \(n\)-tuples, together with the numerical estimates for the three temperatures, calculated with the RSM models illustrated above in Table 10. The results coming from the simulation have been collected in Table 12, together with the percentage errors (related to the experimental target values) and the aforementioned metrics, based on these errors, to evaluate each \(n\)-tuple. It is worth noting that also in this case there are two \(n\)-tuples (nr. 10, 12) that correspond to a physically impossible situation; the same considerations as above apply.  
The positioning of the points corresponding to the 30 \(n\)-tuples of Table 12 in the Cartesian plane (Figure 11 left) shows a better situation than in the previous iteration under many aspects. First of all, the points are generally closer to the bisector of the quadrant, and their distance to the bisector decreases approximating to the origin (the slope of the interpolation line is greater than unitary), thus indicating a lower dispersion of the three temperature differences. Then, there are up to 15 points below the threshold of 14.14 of the merit function (i.e., under the red arc of Figure 11 left; previously, they were only 6), and 12 have both coordinates below the threshold of 5% (previously they were only 4). The histogram of the merit function (Figure 11 right) shows higher bars than in the previous case, indicating a closer matching of the CFD-FVM software to the reality. The four highest bars in the represented graphic correspond to \(n\)-tuples 3, 4, 5, and 7 (all with a value for \(M_{f}\) above 30). The best-ever combination of this set of 30 combinations of factors (and also of the previous set of combinations) is the \(n\)-tuple number 4, achieving a value for \(M_{f}\) of 50.7, a mean of absolute errors of 1.1% (\(-0.7\) percentage points with respect to the previous iteration) and a maximum absolute error of 1.6% (\(-1.0\) percentage points than the previous iteration); the three temperatures from the CFD-FVM model are, respectively: 453, 534, and 669 \({}^{\circ}\)C (i.e., +3, \(-6\), and \(-11\)\({}^{\circ}\)C with respect to case P\({}_{0}\)). According to these evidences, is therefore possible to state that the values of the factors associated with \(n\)-tuple number 4 allow having a tuned CFD-FVM model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**R\({}^{2}\)**} & **Adj R\({}^{2}\)** \\ \hline \(T_{1}\) = +194.80036 + 0.46497.7 + 11,898.19656.\(\dot{m}_{xx}\) - 2.14856-\(H_{h}\) - 1.23564-\(H_{xx}\) - 26.35972-\(e_{xx}\) + 0.32078-\(C_{h}\) & 0.9798 & 0.9776 \\ \hline \(T_{2}\) = +212.17727 + 0.48821.7 + 10,843.33590.\(\dot{m}_{xx}\) - 0.31434-\(H_{h}\) - 2.18245-\(H_{xx}\) - 50.42908-\(e_{xx}\) & 0.9864 & 0.9851 \\ \hline \(T_{3}\) = +61.55935 + 0.71766.T + 17,518.39820.\(\dot{m}_{xx}\) - 0.81363-\(H_{xx}\) & 0.9476 & 0.9449 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Multilinear regression models for the three temperatures using the second dataset of 61 cases.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{10}{c}{**Factors (Unknown Independent Parameters)**} & \multicolumn{10}{c}{**RSM Optimization**} \\ \cline{2-13} \multicolumn{1}{c}{**Nr.**} & \multicolumn{1}{c}{\(T\)} & \(\hat{m}_{ex}\) & \(H_{h}\) & \(H_{ex}\) & \(e_{h}\) & \(e_{ex}\) & \(C_{h}\) & \(C_{r}\) & **Desirability** & \(T_{1