Data-Driven Machine learning prediction of Nusselt number in Fin-Enhanced natural convection within square cavities

• Developed a validated numerical model of fin-assisted natural convection in square cavities. • Generated a large dataset (40,590 cases) spanning wide geometric and thermal parameter ranges. • Compared five ML regression models for predicting average Nusselt numbers on hot and cold walls. • Decision Tree and Ensemble models achieved R 2 > 0.999 with minimal error (MAE < 0.027). • Shapley analysis revealed Rayleigh number as the dominant driver and fin length as a key secondary parameter. • Demonstrated that physics-informed ML can replace full-scale simulations for real-time prediction and design optimization. This study presents a machine-learning (ML) framework for accurately predicting convective heat transfer in square enclosures with a horizontal fin mounted on the heated vertical wall. A dataset of 40,590 COMSOL simulations was generated by systematically varying Rayleigh number ( Ra ), Prandtl number ( Pr ), fin length, thickness, vertical position, and the fin-to-fluid thermal conductivity ratio. Five supervised ML models, Decision Tree, Artificial Neural Network, Support Vector Machine, Kernel Learning, and Random Forest Ensemble, were trained to predict the average Nusselt number on both hot and cold walls. All models achieved high accuracy ( R 2 > 0.94), with the Decision Tree and Ensemble methods outperforming the others across all datasets. Specifically, the cold wall models achieved R 2 > 0.999, RMSE < 0.05, and MAE < 0.027, whereas the hot wall models achieved RMSE ≈ 0.023 and MAE < 0.0145. Feature importance analysis revealed Ra as the most influential parameter in both regimes, with fin length having a significant impact on hot-wall heat transfer. The ML-based models effectively captured nonlinear interactions between geometric and thermal parameters, surpassing traditional empirical methods in both accuracy and efficiency. These results demonstrate the suitability of ML-based models for real-time prediction, thermal design optimization, and control of convection-dominated systems.