Enhanced predictive modeling of Nusselt number in boiler tubes: numerical simulations and machine learning for water and SiO2/water

This research investigates the complex phenomenon of nanofluid flow boiling and its associated heat transfer characteristics. Employing advanced numerical simulations and machine learning techniques, we explore the behavior of dimensionless heat transfer correlations in subcooled flow boiling scenarios using water and SiO 2 /water nanofluids. The study begins with an adaptive design of experiment, yielding a comprehensive dataset of nearly 250 simulations. In the numerical simulation phase, the extracted data are examined, and the grid independence of the modeling process is confirmed, ensuring robustness and reliability. The data, validated against experimental results, provides critical insights into the intricate interplay of dimensionless numbers influencing Nusselt number behavior. Subsequently, the extracted dataset from the numerical simulations underwent a two-stage feature selection process, incorporating Pearson correlation and iterative techniques, to identify the most influential dimensionless parameters for the calculation of the Nusselt number. Later, the data are randomly split into training and testing sets (70–30%), and predictive models are developed using Python, leveraging libraries such as Pandas, NumPy, scikit-learn, and Keras. A tenfold cross-validation approach is employed to ensure model stability and accuracy. Through response surface methodology (RSM), we establish regression equations for average and local Nusselt numbers, achieving minimal mean absolute error (MAE) and high R -squared ( R 2 ) values, demonstrating the effectiveness of our approach. Further enhancing predictive capabilities, we explore random forest, support vector machine, and artificial neural network (ANN) models. The ANN model emerges as the top performer, offering exceptional accuracy with MAE below 2.21% and R 2 above 0.95 for both average and local Nusselt numbers. Notably, the machine learning algorithms, from data preprocessing to the final model evaluation, required only about 10% of the time invested in the numerical simulations.