Entropy Generation Analysis in MHD Nanofluid Flow Using the Brinkman–Forchheimer Model in a Quadrantal Porous Enclosure

This study presents a detailed numerical investigation of natural convection heat and mass transfer within a fluid-saturated porous quadrantal enclosure containing a heated circular cylinder and filled with TiO2–H2O nanoliquid. Emphasis is placed on the effects of internal heat generation and entropy production, using the finite element method (FEM) to explore the influence of key dimensionless parameters: Darcy number (Da), Hartmann number (Ha), Rayleigh number (Ra), porosity (ɛ), and heat generation parameter (λ). The findings reveal that increasing the Darcy number improves the average Nusselt number by 2.498% and total entropy by 9.48%, but significantly reduces the Sherwood number by 314.19%. An increase in Hartmann number suppresses heat and mass transfer, decreasing Nusselt number by 621.05%, Sherwood number by 7.404%, and Bejan number by 10.59%, while slightly increasing total entropy by 1.8%. Higher values of λ intensify entropy generation by 84.16%, increase Sherwood number by 149.175%, and Bejan number by 8.81%, but reduce Nusselt number by 105.178%. Enhancing porosity (ɛ) leads to a 2.88% rise in Nusselt number and a 13.72% increase in entropy, while causing substantial decreases in Sherwood number (438.54%) and Bejan number (16.65%). Similarly, rising Rayleigh number enhances heat transfer by 2.498%, increases entropy by 9.58%, and decreases Sherwood number and Bejan number by 332.419% and 10.96%, respectively. This research contributes to the optimization of heat and mass transfer performance in complex enclosures, offering practical insights for thermal management in advanced energy systems, electronics cooling, and aerospace applications.