This work aims to improve heat transmission a fundamental component of engineering and industrial processes, by examining entropy formation in magnetohydrodynamic natural convection inside an enclosure containing a saturated porous material under circumstances of local thermal non-equilibrium. The study utilizes an Al2O3–Cu/water hybrid nanofluid, with a cross-shaped obstacle and thermally elevated corners. The model employs a two-phase nanofluid methodology, the local thermal non-equilib rium approximation, and Darcy’s law to characterize the behavior of the porous medium. Numerical solutions to the governing partial differential equations are derived using the finite difference technique, with validation against prior work demonstrating strong concordance. The research investigates heat transfer rates and micropolar hybrid nanofluid flow by illustrating contours of nanofluid flow, isotherms for both fluid and solid phases, and distributions of stream function, temperature, and nanoparticle volume percent. Results demonstrate that positive heat sources (Q = 5) augment convective currents, whereas negative heat sinks (Q = − 15) diminish buoyancy effects and decrease efficiency. Moreover, elevating nanoparticle concentration (ϕ) enhances ther mal conductivity, markedly augmenting heat transfer efficiency in convection-dominated environments. The Cu-based hybrid nanoparticles demonstrated superior efficacy compared to Al2O3 by providing increased thermal conductivity, improved heat transfer, and less entropy production. The results underscore the need of optimizing heat transfer processes to reduce entropy generation and fluid friction irreversibility, thereby improving the efficiency of thermal systems.