Modeling Hall current-induced electrified flow in rotating cylinders via physics-informed neural networks with sensitivity analysis

Physics-informed neural networks (PINNs) have gained popularity in fluid mechanics for solving various types flows, including supersonic, temporal, high-speed, Reynolds-averaged turbulent flows, and so forth with certain limitations. The architecture of PINNs consists of a deep neural network that serves as a solution function for the flow quantities, along with a set of governing equations that describe the physics of the problem. We apply PINNs to solve the incompressible Navier–Stokes equations for magnetohydrodynamic laminar, viscous Newtonian fluid flow (10≤Re≤150) in the annular region between concentric electrified rotating cylinders, with an aspect ratio of R*=0.5. The flow is also influenced by Hall current, viscous dissipation, and Joule heating resulting from the applied radial magnetic field. Moreover, a face-centered central composite design technique is employed within the framework of response surface methodology to compute the quadratic relationships between the response variables (skin friction and Nusselt number) and the flow parameters. The analysis of variance for these outputs is presented in tabular form, followed by a sensitivity analysis of the response variables, which is illustrated using both tables and bar charts.