Physics-informed neural networks with combination optimizers ADAM and L-BFGS for modeling unsteady two-phase nanofluid flow with time-dependent MHD: A novel framework for heat transfer and energy system

This paper presents an innovative approach using Physics-Informed Neural Networks (PINNs) to tackle the challenging problem of two-phase nanofluid flow and unsteady heat transfer. The coupled governing equations present a nonlinear transport problem. PINNs, by incorporating physical laws into the training loss function, are employed to approximate solutions of the similarity-reduced governing equations. In particular, the study sheds light on the impact of key parameters on both flow characteristics and heat transfer characteristics. The results reveal how changes in these parameters significantly affect temperature and concentration profiles, skin friction, and the Nusselt number. Moreover, the research demonstrates close agreement between PINN predictions and reference numerical solutions for velocity, temperature, concentration, skin friction coefficient, and Nusselt number. The comparison with numerical solutions shows good agreement for the investigated parameter settings. These findings demonstrate the applicability of PINNs to the considered similarity-reduced nanofluid transport model while highlighting the need for further computational benchmarking to assess efficiency and broader applicability.