The significance of fluid flow under hydrothermal conditions within a hexagonal enclosure spans across numerous fields, underlining its broad applicability. However, our understanding of the free convection flow in these geometries is still limited despite its potential importance in science and technology. Therefore, this study numerically examines the heat convection and entropy generation within a porous hexagonal cavity containing a heated obstacle while subjected to a static magnetic field of intensity B ₀ . Micropolar hybrid nanofluid, composed of TiO ₂ and graphene oxide nanoparticles, was used to fill the hexagonal cavity with water as the base fluid. The finite difference method is associated with successive over-relaxation, successive relaxation, and Gauss–Seidel techniques, which are used to solve the dimensionless governing partial differential equations. The desired outcomes are computed using in-house developed MATLAB codes. A specific result from prior research findings is used to validate the accuracy of these MATLAB codes. The outcomes demonstrate that an upsurge in Ra from 10 ⁴ to 10 ⁶ and ϕ hnf {\phi }_{{\rm{hnf}}} from 0 to 4% leads to an enhancement in Nu _ABW to 53.05 and 3.14%, respectively. However, Nu _ABW diminishes by approximately 0.797 and 4.135% as Ha increases from 0 to 20 and K ₀ increases from 2 to 7.5, respectively. The average Bejan number (Be _avg ) consistently decreases as Ra increases, but Be _avg improves as Ha, vortex viscosity parameter ( K ₀ ), and ϕ hnf {\phi }_{{\rm{hnf}}} increase. The most important finding of the work is that the position of the heated obstacle significantly influences both the heat convection and entropy generation processes.