Physics-Guided Machine Learning and Deep Neural Networks for Accurate and Robust Heat Transfer Predictions in Shell and Helical Coil Heat Exchangers

Abstract

This study is the first to develop and benchmark two distinct physics-informed neural networks (PINNs) targeting Nusselt number (Nu) and performance evaluation criterion (PEC) to evaluate twelve real-world shell and helical coil heat exchanger configurations and assess a variety of predictive models. These models include linear regressors (Ridge, Lasso), ensemble learners (AdaBoost), support vector regression, and deep learning models (LSTM, Bi-LSTM, and GRU). As the main novelty, two dedicated PINNs are developed: one for predicting Nu and another for PEC. Both models leverage physical domain knowledge by embedding analytical heat transfer constraints, such as empirical Nu correlations and laminar friction factor formulations directly into the loss function, guiding learning beyond conventional data fitting. Input parameters such as Reynolds number, Dean number, and curvature ratio serve as predictors for both target variables. To improve model reliability, noise-robust data augmentation and grid-based hyperparameter tuning are applied. The results show the proposed PINN delivers unbiased Nu predictions across the full range with markedly lower error than Dittus-Boelter and Gnielinski (RMSE 1.12 vs 4.75 and 3.20; R-2 0.998 vs 0.935-0.962). It also achieves the best PEC accuracy (RMSE 0.044; R-2 0.997) over raw and calibrated empirical correlations (RMSE 1.32 and 0.39). Taylor diagrams show the highest correlation and near-unity normalized variance (r approximate to 0.998-0.999; sigma/sigma(obs)approximate to 1.02-1.03), and MixUp tests confirm robustness (Delta RMSE < 2%) exceeding all other tuned ML/RNN models. These features give the model a reliable capability to predict Nu and PEC with high accuracy and strong generalization for heat exchanger analysis and thermal system design.