Energy flux and kinetic energy analysis of MHD natural convection of Ag–MgO/water hybrid nanofluid in a porous trapezoidal enclosure with an internal heated obstacle

Efficient thermal management in porous enclosures is important for energy systems, thermal storage unit, fuel cells and electronic cooling applications. The combined use of hybrid nanofluids and magnetic-field control offers a promising approach for regulating convective heat transfer in such systems. In this study, magnetohydrodynamic natural convection of an Ag–MgO/water hybrid nanofluid in a porous trapezoidal enclosure containing an internally heated triangular obstacle is numerically investigated under the influence of an inclined magnetic field. The flow is assumed to be two-dimensional, steady, laminar, and incompressible, while the porous medium is modeled using the Darcy–Brinkman formulation. The governing equations are transformed into dimensionless form and solved using a finite-difference method. Grid independence and validation with previous studies are included. The effects of Rayleigh number, Hartmann number, Darcy number, magnetic-field inclination angle, heat generation/absorption parameter, and nanoparticle volume fraction on flow structure and heat-transfer performance are analysed. The results show that increasing the Rayleigh number from 10 ³ to 10⁶ enhances the average Nusselt number by approximately 90.8%, whereas increasing the Hartmann number from 0 to 50 reduces heat transfer by about 4.9% due to magnetic damping. Increasing the Darcy number from 10⁻⁵ to 10⁻² improves heat transfer by approximately 12.5% owing to reduced porous-medium resistance. The heat generation/absorption parameter exhibits the strongest influence, causing a 73.1% reduction in the average Nusselt number as Q varies from −50 to 50. Furthermore, increasing the nanoparticle volume fraction from 0.01 to 0.05 decreases the average Nusselt number by approximately 34.9%, indicating that viscosity-induced flow suppression can outweigh thermal-conductivity enhancement under the present conditions. The thermal performance of the system is governed by the interaction among buoyancy forces, magnetic damping, porous-medium permeability, and nanoparticle concentration. The obtained results provide useful guidance for the design and optimization of porous thermal-management systems employing hybrid nanofluids under magnetic-field control.