FEM-ANN-GNN modeling of MHD Darcy–Forchheimer Boger nanofluid flow with coupled heat–mass transfer in a Y-shaped hourglass cavity

Purpose This study aims to numerically investigate steady two-dimensional MHD Darcy–Forchheimer mixed convection flow of a Boger nanofluid (Cu/H2O) with coupled heat and mass transfer inside a Y-shaped hourglass cavity containing a cylindrical obstacle, incorporating thermal radiation, Cattaneo–Christov heat flux, Soret effects and chemical reaction to capture non-Fourier conduction and thermo-solutal transport. Methodology The coupled nonlinear partial differential equations are solved using a combined FEM–ANN–GNN strategy: the finite element method (FEM) generates accurate solutions, the artificial neural network (ANN) learns nonlinear input–output relationships and the graph neural network (GNN) preserves spatial interactions and mesh connectivity. Parametric studies span solvent fraction, relaxation, Forchheimer, Darcy, Hartmann, Richardson, radiation, thermal relaxation, nanolayer thickness, nanoparticle radius, Lewis, Soret and chemical reaction parameters. Findings Flow circulation and transport are governed by the interplay of porous resistance, magnetic effects and buoyancy. Increasing permeability and solutal buoyancy enhance fluid motion and transport, whereas inertial resistance and thermal buoyancy suppress flow. Thermal radiation and nanolayer effects improve heat transfer, while larger nanoparticle size reduces thermal efficiency. The ANN yields rapid predictions with major computational savings and the GNN attains superior accuracy by preserving mesh connectivity, agreeing closely with FEM results. Originality/value This work introduces a novel FEM–ANN–GNN framework for coupled thermo-fluidic transport in MHD Darcy–Forchheimer Boger nanofluids within a complex Y-shaped hourglass geometry. By integrating graph-based spatial learning with numerical and neural approaches, it delivers high efficiency and accuracy, enabling fast parametric analysis and real-time prediction of complex thermo-fluidic systems.