Accurate prediction of the coefficient of heat transfer (HTC) under extremely high parameter conditions in nuclear reactors is crucial for the design and operation of reactors, but the HTC is influenced by many factors, and there are issues such as unclear physical model and lack of experimental data. Traditional empirical relations often struggle to meet the demands of high-precision numerical calculations. Machine learning algorithms can effectively address the complex nonlinear problems, but some results do not conform to physical laws.

This study aims to propose a physical information machine learning (PIML) algorithm model that can calculate thermal parameters more accurately.

Firstly, HTC experimental data were collected from a circular tube and subjected to preprocessing. Then, the HTC model was developed by combining the Jens-Lottes formula and the Thom formula with Multi-layer Perceptron (MLP), Backpropagation Neural Network (BPNN), and Random Forest (RF). Following this, the preprocessed data were partitioned into training and testing sets, with the training set utilized for model training and the testing set employed for model validation. Finally, six algorithms in the HTC models were evaluated and compared against empirical correlations.

Evaluation results show that the calculation accuracy of Jens-Lottes formula combined with RF in the HTC model is the highest, with average relative error of predicting experimental data of 3.17%. The expandable range of the model accounts for 63.6% of the total applicable range, demonstrating good extrapolation capabilities. At the same time, using the PIML algorithm significantly enhances the computational accuracy of the physical model. The model based on the Jens-Lottes relationship combined with RF reduces the relative error of evaluation by 24.5% compared to the empirical relationship.

The PIML algorithm proposed in this study provides a framework for a high precision calculation model for HTC. It also provides a reference for expanding the scope of application.