Entropy reduction in magnetohydrodynamic radiative hybrid nanofluid flow in a porous pile-cap enclosure containing pairs of heated cylinders

Maximizing thermal efficiency while minimizing entropy generation is essential for advanced energy systems such as heat exchangers, thermal storage units, and electronic cooling devices. This study numerically investigates magnetohydrodynamic natural convection and entropy generation of an Ag–MgO/water hybrid nanofluid inside a pile-cap-shaped enclosure containing two symmetrically heated circular cylinders. The model incorporates porous media resistance, thermal radiation, and complex enclosure geometry within a unified framework. The side walls are maintained at a constant cold temperature, while the top and bottom walls are adiabatic, producing strong coupling between buoyancy-driven flow and magnetic forces. The steady incompressible governing equations are formulated under the Boussinesq approximation, nondimensionalized, and solved using the Galerkin finite element method implemented in COMSOL Multiphysics. Grid independence analysis is performed to ensure numerical accuracy. Results indicate that increasing the Rayleigh number (Ra) significantly strengthens buoyancy-driven circulation, compresses thermal boundary layers, and increases the average Nusselt number by up to 71.6% within the investigated parameter range. In contrast, stronger magnetic fields introduce Lorentz damping, reducing heat transfer by 36%–52%. Decreasing permeability from (Da)=10−2 to 10−4 suppresses convective transport and promotes conduction-dominated heat transfer, resulting in a 60%–65% reduction in convective performance under strong magnetic effects. Increasing nanoparticle volume fraction enhances effective thermal conductivity but also increases viscosity, weakening circulation and raising entropy generation by 8%–22%. Higher thermal radiation parameter (R) enhances radiative diffusion, smooths temperature gradients, and modifies the irreversibility characteristics of the system.