Natural Convective Behavior and Entropy Generation of a Reacting Nanofluid in a Partially Porous Dome-shaped Cavity with a Fin

This study investigates natural convection, thermal energy transfer, and entropy generation behaviors of ethanol–air mixture containing Al2O3 nanoparticles in a partially porous dome-shaped cavity. The problem is solved using the Galerkin finite element method (GFEM). Results provide that reducing Darcy number (Da) restricts fluid flow and enhances conduction effects in the system. Increasing nanoparticles’ volume fraction (ϕ) improves heat transfer and lowers peak temperature (θmax) by 19%, although the increase in viscosity decreases the maximum stream function (ψmax) by 7%. In contrast, stronger exothermic reactions enhance thermal buoyancy, increasing circulation strength by up to 34% while accelerating species consumption. Entropy generation analysis shows that increasing LP and ϕ reduces global entropy generation (Sglobal) by 26%–46%, leading to lower thermodynamic losses. The Bejan number (Be) decreases to nearly 55%–60% at high Ra, indicating a shift toward friction dominated irreversibility, while the porous structure strongly controls the entropy generation ratio (EGR).