Uncertainty-aware physics-informed machine learning for non-equilibrium heat transport in casson fluid

Abstract

The current study provides a comprehensive analysis of heat transfer in porous media within the framework of local thermal non-equilibrium (LTNE). It takes into account the combined effects of non-Newtonian Casson fluid behavior, spatially varying Biot number, and temperature-dependent thermal conductivities. The simultaneous consideration of these interacting factors poses significant analytical and numerical complexities, particularly when extending the formulation to more complex geometries or thermal behavior. To effectively solve the resulting nonlinear and coupled system of differential equations, we employ Physics-Informed Neural Networks (PINNs), ensuring high accuracy and efficiency. The PINN framework integrates the governing equations and associated boundary conditions directly into the neural network training process, enabling effective handling of nonlinearities and spatial variations. The accuracy of the PINN approach is validated through comparison with solutions obtained from MATLAB’s bvp4c solver, especially for cases where the spatially varying Biot number profiles presented significant training difficulties. Parametric studies demonstrate the significant influence of fluid rheology, spatially varying Biot number, and nonlinear thermal conductivity on heat transfer characteristics within the porous media. Additionally, to quantify epistemic uncertainty in predictions, arising from model formulation, numerical approximation, and learning dynamics, Monte Carlo dropout is employed during inference, enabling estimation of a 95% confidence interval and thereby enhancing the reliability of our results. The outcomes highlight the potential of PINNs as powerful computational tools for tackling complex multiphysics problems involving LTNE models.