Four Hidden Layers based Causal cPINNs Guided Thermal Engineering Study of Ternary Nanofluid with PDFP Optimizer: Multifactorial Aspects

Importance of the study: This study contributes to the implementation of the Physics-Informed Neural Network (PINNs) approach for fluid models and ensures physically consistent solutions for temperature and velocity fields. Aim of the study: This paper aims to implement the Physics-Informed Neural Network (PINNs) for an established fluid model to explore the nature of natural convection and heat transfer of a ternary nanofluid in a rectangular cavity under complex thermal boundary conditions. This study examines the interaction of heat sources, sinks, viscous dissipation, and magnetic fields on thermal performance. Physical parameters are used to assess their impact on streamline patterns, isotherm contours, and the average Nusselt number. Causal Physics-Informed Neural Networks (cPINNs) Methodology: The authors employ the model using four hidden layers and 32 neurons in the Causal Physics-Informed Neural Network (cPINNs) approach to solve the thermal engineering model problem involving the ternary nanofluid. The authors employ the preconditioned optimizer PDFP to implement the cPINNs. Vital key outcomes: Vital Key Outcomes: The results are significant in the cooling of electronic devices, energy storage devices, and solar power, where the regulation of temperature and the efficiency of heat transfer are important. As shown in Fig. 1, the graphical abstract summarizes the integrated workflow of the proposed PINN-based thermal engineering study, highlighting the connection between mathematical modeling, physics-informed learning, and numerical validation. It provides a concise visual overview of the methodology and multifactorial analysis employed in this work.