Numerical and supervised neural-network analysis of magnetoconvective williamson blood-based Fe₃O₄–Cu hybrid ferrofluid over a moving flat plate

This study examines the momentum and thermal behavior of a blood-based Williamson hybrid ferrofluid containing magnetite and copper nanoparticles flowing over a moving flat plate in the presence of a transverse magnetic field and viscous dissipation. A steady two-dimensional laminar boundary-layer formulation is considered, together with effective hybrid-fluid properties. The transformed equations are investigated numerically, and a supervised artificial neural network is evaluated as a data-driven surrogate for reference numerical profiles. Unlike a physics-informed neural network, the documented neural loss does not impose differential-equation residuals and boundary conditions. The reported numerical profiles show that increasing the wall-to-free-stream velocity ratio and magnetic parameter increases the plotted velocity, whereas increasing the Williamson parameter decreases it for the chosen cases; temperature increases with the Williamson and Eckert parameters and decreases with the magnetic parameter. The originally reported profile comparisons yield small pointwise differences (typically near 10⁻⁶ in the displayed tables), although these errors are measured against the numerical training reference and are not independent physics validation. The analysis identifies the potential of data-driven prediction for parametric flow studies, while highlighting the need for a consistency-checked non-similar formulation, independent benchmarking, and physically constrained training before PINN performance can be claimed.