This study presents a high-fidelity numerical analysis of magnetohydrodynamic (MHD) convective heat transfer and entropy generation in a copper-based nanofluid within a porous enclosure embedded with multiscale fractal barriers. The Darcy–Forchheimer model captures nonlinear drag in the porous matrix, while the applied magnetic field influences buoyancy-driven flow. Simulations are performed using the finite element method (FEM) in COMSOL Multiphysics with the PARDISO solver. The objective is to evaluate how fractal barrier geometry, Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), and porosity influence heat transfer and thermodynamic behavior. Results reveal that fractal barriers enhance convective mixing, break flow symmetry, and increase Nusselt number while reducing thermal stratification. Higher Ra significantly improves heat transfer (Nu avg up to 16.4%) but increases entropy generation, indicating a trade-off in thermal efficiency. Increasing Ha suppresses convection and reduces Nu avg , S Total , and Be avg by up to 0.166%, 0.154%, and 0.095%, respectively. A higher Darcy number improves convective strength, while increased porosity raises Nu avg by 2.31% and S Total by 2.79%, but lowers Be avg by 0.98%. These insights support the application of fractal-structured porous systems for advanced thermal management in energy, electronics, and biomedical engineering.
Khan et al. (2026) studied this question.