A symbolic regression-based correlation for the heat transfer coefficient of saturated flow boiling in mini/micro-channels

The demand for high-performance thermal management has increased interest in saturated flow boiling in mini/micro-channels, while accurate prediction of the heat transfer coefficient remains challenging due to the complex nature of two-phase flow. Existing empirical correlations rely on predefined variables and functional forms selected based on prior knowledge and empirical judgment and are often developed from limited databases, which can restrict their applicability beyond the development range. Black-box machine learning models, despite their superior predictive capability, lack physical interpretability and may exhibit reduced predictive accuracy under unseen conditions. To address these limitations, this study utilizes symbolic regression as an interpretable machine learning approach to develop a data-driven explicit correlation that combines high predictive accuracy with physical interpretability. A consolidated pre-dryout database of 12,406 data points was constructed from 41 independent sources, covering 20 working fluids and a wide range of channel geometries and operating conditions. The derived correlation adopts an additive form comprising nucleate- and convective-boiling terms, consistent with the underlying flow boiling mechanisms, and achieves a mean absolute percentage error (MAPE) of 19.4% across the consolidated database. The generalization capability was further assessed using an independent unseen dataset of 2138 data points from 8 sources. While existing empirical correlations showed limited accuracy and black-box models, including XGBoost, Random Forest, and Artificial Neural Networks, exhibited less consistent predictive performance, particularly for extrapolative cases, the proposed model maintained robust predictive accuracy with a MAPE of 13.6%. This explicit, closed-form correlation enables intuitive physical interpretation and demonstrates reliable predictive performance for independent unseen data, offering a practical tool for thermal system design.