A Heuristic Physics-Informed Neural Network for Unsteady Magnetohydrodynamic Squeezing Flow through a Darcy-Forchheimer Porous Channel with Brownian Motion, Thermophoresis, Thermal Radiation, and Heat Generation

Abstract

The unsteady two-dimensional magnetohydrodynamic squeezing flow of an electrically conducting hybrid nanofluid through a Darcy-Forchheimer porous channel is studied under the Buongiorno Brownian and thermophoretic fluxes, nonlinear Rosseland radiation, and a temperature-dependent heat source or sink. A symbolically confirmed similarity transformation reduces the governing partial differential equations to a coupled nonlinear ordinary differential system, which is recast as a fixed point problem through explicit Green functions. Existence, uniqueness, and an a posteriori error certificate are established. The fields are then obtained by a heuristic physics-informed neural network trained by a hybrid particle swarm and neural network algorithm with a trust-region refinement. The influence of every physical parameter on the velocity, temperature, and concentration is analysed.