Nonlinear ciliary flagellar flow dynamics and energy transport in a curved porous channel: An optimization via...

Physics-informed neural networks have vital importance due to mesh-free simulations for capturing the nonlinear dynamics of peristaltic transport by unifying learning with governing physical phenomena of fluid mechanics. In this study, magnetize non-Newtonian Carreau-Yasuda viscoelastic fluid is modelled in a wavy curved channel with ciliary wall motion. The study has demonstrated the potential of PINNs as a numerical technique to handle Multiphysics problems, such as magnetohydrodynamics and porous media on non-Newtonian fluid flow, for solving nonlinear transport equations. It is observed that the numerical results agree with the Physics-Informed Neural Network (PINN) findings. There are numerous cutting-edge biomedical, physiological, and engineering uses for a wavy curved porous channel with peristaltic transport of a Carreau-Yasuda viscoelastic fluid that contains ciliary movement of the wall. This model explains the non-Newtonian fluid behavior, wall pumping, curvature, porosity, and cilia propulsion. This type of model incorporates all these complicated phenomena into a single framework, making it relevant and useful to study the natural and engineering process of fluid transport. The developed algorithm is specifically applicable to various industrial and engineering applications, i.e. polymer extrusion, electrochemical reactors, geothermal energy recovery, and innovative thermal management. A combined Adam and L-BFGS optimization strategy provides stability and quick convergence. Parametric analysis indicates that velocity decreases with increasing Hartmann number because of magnetic damping. When the value of the Darcy number is increased, flow penetration and streamline coherence increase. The convergence and comparison of fully developed PINN prediction with numerical results are shown graphically to ensure the accuracy and validity of the scheme.