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 augmenting 3D natural convection and entropy generation within permeable wavy-walled rectangular 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 representations meticulously elucidate the nuanced impacts of Rayleigh and Darcy numbers on flow streamlines, temperature distribution, Nu number, and the proportions of global and local thermal entropy generation, frictional entropy generation, and total entropy generation. Our discernments underscore that elevating Rayleigh and Darcy numbers yields a substantial augmentation exceeding 120% in convection flow, particularly prominent for Da = 10⁻² vis-à-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.