## 5 Results and Discussion
### Parameter Sensitivity Analysis  
To understand the contribution of different features to predictions, feature importance analysis can be conducted using SHAP values [67]. SHAP values quantify the contribution of each feature by considering all possible combinations of features and computing the difference in the model prediction when the feature is included versus when it is not. In this study, the SHAP values are used to show the importance and contribution of each feature to the thermal conductivity of EG-Al\({}_{2}\)O\({}_{3}\) nanofluids. Figure 12 presents the feature importance values obtained using SHAP. The bar plot indicates the mean absolute SHAP value for each feature, which represents the importance of features on the output magnitude. The results show that the feature T obtained the highest importance value (0.163) among all features, suggesting it has the most significant influence on the model predictions. After \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{3}{c}{**Input Features**} & \multicolumn{2}{c}{**Thermal Conductivity (W/(m-K))**} & \multirow{2}{*}{**Absolute**} \\ \cline{2-2} \cline{4-5}  & **D (nm)** & **T (K)** & **VF (vol\%)** & **Actual** & **Predicted** & **Error** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 7: The results of model validation using a new dataset. Figure 11: Regression graphs of the optimal models using four subsets: (**a**) [43]; (**b**) [44]; (**c**) [45]; (**d**) [46]. this feature, VF also obtained a higher importance value (0.057) than D (0.023) for predicting the thermal conductivity of EG-Al2O3 nanofluid. Figure 13 provides a detailed SHAP summary plot, depicting the SHAP value for each feature and its impact on the output, with blue indicating low values and red indicating high values. It can be seen that the feature T shows a significant positive contribution to thermal conductivity. This indicates that high temperatures lead to an increase in the thermal conductivity values. Similarly, most SHAP values of VF are positive, which means that this feature has a globally positive impact on the output. As the VF increases, the SHAP values rise, suggesting that high VF enhances the thermal conductivity of the EG-Al2O3 nanofluids. In contrast, the feature D exhibits a predominantly negative impact on the output. The SHAP values of D are clustered around negative values, indicating that this feature has a negative impact on the output. In general, this trend demonstrates that while T and VF significantly boost thermal conductivity, D has a minor negative effect on it. To further analyze the interaction between features and their contribution to the predictions, SHAP dependence plots are employed. These plots illustrate how the SHAP value for each feature varies with the feature value and reveal interactions between features. As shown in Figure 14, the principal feature is represented on the x-axis, while the color indicates the value of the most interacted feature among all features. The y-axis displays the SHAP values calculated for the principal feature. Figure 14a demonstrates the relationship between T and its SHAP values, with the color representing the VF (vol%). It can be observed that all values of T have positive SHAP values, indicating a positive contribution to thermal conductivity. This observation aligns with findings from various studies, suggesting that the enhancement of thermal conductivity with increasing temperature can be attributed to enhanced microconvection driven by Brownian motion [20, 68, 69]. Figure 14b depicts the SHAP values of VF (vol%) with the color representing D. It is observed that most points have positive SHAP values, indicating a globally positive contribution to the output. However, when VF is less than 0.4% and D equals 13 nm, the SHAP values become negative, indicating a negative contribution to the prediction. For the red points  
Figure 12: Importance values of features through SHAP analysis. Figure 13: SHAP diagram of features through SHAP analysis.