Neural-network modeling of magnetohydrodynamic non-Darcy Jeffrey-fluid flow with thermosolutal cross-diffusion over a vertical porous plate

This study presents a numerical and machine-learning investigation of magnetohydrodynamic flow with coupled heat and mass transfer for a Jeffrey fluid over a vertical porous plate embedded in a non-Darcy Forchheimer medium under nonuniform boundary conditions. The model incorporates thermal radiation, Soret–Dufour cross-diffusion, viscous dissipation, internal heat generation or absorption, and a first-order chemical reaction. Similarity transformations reduce the governing partial differential equations to a coupled nonlinear system of ordinary differential equations, which is solved using an adaptive Runge–Kutta–Fehlberg shooting algorithm. A Levenberg–Marquardt artificial neural network is subsequently trained as a surrogate for the numerical solver. The results indicate that the Jeffrey relaxation parameter enhances the velocity within the boundary layer, whereas magnetic damping and Forchheimer inertia suppress the flow. Thermal radiation, viscous dissipation, heat generation, and the Dufour effect raise the fluid temperature, while the Soret effect increases species concentration. The neural-network predictions closely reproduce the numerical solutions, demonstrating the suitability of the proposed hybrid framework for rapid prediction of nonlinear magnetohydrodynamic transport.