Thermal performance of 3D Darcy-forchheimer porous rectangular wavy enclosures containing a water-Fe3O4 ferro-nanofluid under magnetic fields

In the perennial quest for heightened efficiency in heat transfer applications, the inadequacy of water's thermal properties necessitates the exploration of innovative solutions. Nanofluids, particularly those comprising water-Fe3O4 nanoliquid, emerge as promising candidates for aug-menting 3D natural convection and entropy generation within permeable wavy-walled rectan-gular enclosures. The present investigation employs a comprehensive mathematical framework, incorporating the Navier-Stokes equations, magnetic field considerations, and the intricate Darcy-Forchheimer porous media. Utilizing the Galerkin finite element method (GFEM) within the computational domain of COMSOL software, we resolve the system of coupled nonlinear partial differential equations, meticulously derived through non-dimensionalization. Graphical repre-sentations meticulously elucidate the nuanced impacts of Rayleigh and Darcy numbers on flow streamlines, temperature distribution, Nu number, and the proportions of global and local ther-mal entropy generation, frictional entropy generation, and total entropy generation. Our dis-cernments underscore that elevating Rayleigh and Darcy numbers yields a substantial augmentation exceeding 120% in convection flow, particularly prominent for Da = 10-2 vis -`a-vis 10-5 and Ra = 106 in comparison to 103. Intriguingly, the optimal positioning of heating surfaces at the bottom right or left surpasses configurations at the bottom middle by a noteworthy margin of approximately 22%. Moreover, the introduction of the Lorentz force, aligned with gravity, manifests a discernible inhibitory effect on flow dynamics, as evidenced by a notable 15% reduction in irreversibility at a Hartmann number of 100.