# Prediction of Boiling Heat Transfer Coefficient for Micro-Fin Using Mini-Channel
## 5 Results and Discussion  
### Prediction Accuracy Depends on Learning Conditions  
Prediction accuracy was evaluated for each learning condition, and the results were compared. Table 4 shows the prediction results for each learning condition. Additionally, Figure 10 illustrates the relationship between predicted values \(a_{i}^{cal}\) and training values \(a_{i}^{exp}\) for each learning condition. R20 and R30 represent the ratios of the number of data points within \(\pm 20\%\) and \(\pm 30\%\) deviation, respectively, from each predicted value \(a_{i}^{cal}\) to the total number of data points. The prediction results confirmed that those of fine-tuning (Case 3) exhibited the highest accuracy in terms of \(SD\), \(R20\), \(R30\), and \(MSE\). Additionally, fine-tuning allowed for accurate prediction of HFO refrigerants, which are relatively new, indicating that high-accuracy prediction can be achieved regardless of the refrigerant type. The improved prediction accuracy with fine-tuning is attributed to its ability to utilize the weights of the pre-trained model as initial values and retrain the entire model, effectively incorporating the feature of micro-fins. Using the weights of mini-channels as initial values in Case 3, the features of micro-fin heat transfer coefficients were more effectively captured than learning from micro-fin data. Furthermore, to evaluate accuracy in predicting under operating conditions, we assessed predictive accuracy using heat flux and mass flux conditions. Table 5 shows the prediction results under heat flux conditions. Table 6 shows the results under mass flux conditions. From the results, it is confirmed that high accuracy in prediction is achieved regardless of the operating conditions. Furthermore, Figure 11 illustrates the relationship \begin{table}
\begin{tabular}{c c c c} \hline  & **DNN, Case 1** & **DNN + GPR, Case 2** &
\begin{tabular}{c} **Fine-Tuning and Consideration of Physical** \\ **Mechanisms, Case 3 (Present)** \\ \end{tabular} \\ \hline \(SD\) & 21.9 & 19.8 & 18.7 \\ \hline \(R20\) & 88.2 & 93.0 & 93.5 \\ \hline \(R30\) & 94.5 & 96.2 & 96.7 \\ \hline \(MSE\) & 5.1 & 2.4 & 2.3 \\ \hline \end{tabular}
\end{table} 
Table 4: MSE and percentages of SD, R20, and R30 per prediction condition. between MSE and variance by the proposed method. The variances can be considered as uncertainties, and it is observed that as variance increases, MSE also increases. In the proposed method, prediction accuracy is improved by minimizing both the predicted error and its uncertainties in each prediction phase. Figure 10: Comparison of predictions and experimental data: (**a**) Results of DNN (Case 1); (**b**) Results of DNN + GPR (Case 2); (**c**) Results of fine-tuning and consideration of physical mechanisms (Case 3). To visualize the contribution of each feature to the prediction accuracy for each model, SHAP (SHapley Additive exPlanations) was utilized to evaluate the importance of features, representing the impact of each feature on the model's predictions for the training data [54]. Figure 12 illustrates the differences in feature importance attributed to the training data. It compares the SHAP results for Case 3 (which utilized pre-training with mini-channel data) and Case 2 (which used micro-fin data). Figure 12 shows that the importance of a feature depends on the training data. When mini-channel data is used as training data, features such as surface tension, heat flux, latent heat, and liquid thermal conductivity are highly important. Conversely, when micro-fin data is used, features such as mass flux, quality, \(Fr\) number, Re number, and fin height are more important. Mini-channels exhibit slug flow, primarily in regions characterized by low flow rate and low quality, where the effect of surface tension becomes significant. This results in a thinner liquid film surrounding the gas plug, which enhances evaporative heat transfer coefficients due to heat conduction. Also, micro-fins show high importance in groove shape features, mass flux, quality, and \(Fr\) number.