Advanced multi-layer deep learning model for accurate estimation of heat transfer and flow designing parameters across diverse dataset configurations

Abstract

This study introduces a hybrid deep learning (DL) model for accurately predicting key parameters of Advanced plate heat exchanger (APHE) performance, including the Nusselt number (Nu), friction factor (f), and thermal performance parameter (P). The hybrid deep learning (DL) model integrates multiple deep learning (DL) models—Feedforward Neural Network (FNN), Cascade Forward Neural Network (CFNN), and Fitting Network (FN)—in a multi-layered design to optimize predictive accuracy. Evaluations were conducted using five diverse datasets, each divided into three scenarios targeting Nu, f, and P, respectively, thereby capturing a broad range of thermal system behaviors. The experimental analysis reveals that the proposed hybrid DL model delivers outstanding predictive accuracy, as reflected in the following results. For Nu prediction, the Root Mean Square Error (RMSE) of the top models in the second layer ranged from 0.0003 to 0.00305 across various datasets. In the case of predicting f, the RMSE spanned from 0.0002 to 0.0041, while for predicting P, it varied between 0.0001 and 0.0004. Notably, the third layer retained CFNN as the most effective architecture, achieving remarkably low RMSE values of 8.1 × 10−6, 4.8 × 10−6, and 4.86 × 10−6 for Nu, f, and P, respectively. Mean Absolute Error (MAE) and Nash-Sutcliffe Efficiency (NSE) metrics further validated the model's robustness, consistently yielding NSE scores near 0.9999. These models effectively minimized errors, particularly in high-variability regions. In the third layer, the hybrid DL framework selected CFNN as the optimal DL model for final predictions across all scenarios. This refinement achieved near-perfect accuracy, with Coefficient of Determination (R2) values surpassing 0.9999 and RMSE values reduced to less than 0.00003, showcasing exceptional generalization and reliability. The hybrid DL model consistently outperformed standalone DL models by combining their strengths and leveraging a hierarchical architecture. These results highlight the potential of hybrid DL approaches in addressing complex regression tasks and advancing predictive modeling in engineering applications. This study provides a significant contribution to optimizing heat exchanger performance and demonstrates the utility of hybrid DL models in real-world thermal system challenges.