The current paper studied the behavior of a triangular cavity occupied with Ag-MgO/water nanofluid under MHD natural convection and provided with a rotating circular barrier, while the right-angled corner is equipped with quarter-circle porous medium and maintained at a fixed hot temperature T h . Several parameters are tested such as Rayleigh number (10 3 ≤ Ra ≤ 10 6 ), Hartmann number (0 ≤ Ha ≤ 80) and Darcy number (10 −5 ≤ Da ≤ 0.15). The obtained results depict the enhancing effect of Ra and the controlling role of the magnetic parameter on heat transport. Increasing the characteristics of the porous media such as the porosity and the permeability showed a substantial impact on the heat transport efficiency within the enclosure. Moreover, the novelty findings in this paper are principally illustrated in the boosting impact of raising the porous medium thickness when it is associated with the growing up of the heated parts of the geometry by increasing the dimension of the radius (r p ). Also, the rotational velocity (ω) and the radius (r ob ) of the circular obstacle are tested and showed an important influence on the energy transport within the cavity. Moreover, the obtained results by modifying the length (a) prove its pertinent influence on the heat transfer performance.

The current article aims to discuss the natural convection heat transfer of Ag/Al2O3-water hybrid filled in an enclosure subjected to a uniform magnetic field and provided with a rotating cylinder and an inner undulated porous layer. The various thermo-physical parameters are investigated such as Rayleigh number ($$100 \le Ra \le 100000$$ 100 ≤ R a ≤ 100000 ), Hartmann number ($$0 \le Ha \le 100$$ 0 ≤ H a ≤ 100 ), and the nanoparticles concentration ($$0.02 \le \phi \le 0.08$$ 0.02 ≤ ϕ ≤ 0.08 ). Likewise, the rotational speed of the cylinder ($$- 4000 \le \omega \le + 4000$$ - 4000 ≤ ω ≤ + 4000 ), as well as several characteristics related to the porous layer, are examined li its porosity ($$0.2 \le \varepsilon \le 0.8$$ 0.2 ≤ ε ≤ 0.8 ), Darcy number ($$- 100000 \le Da \le - 100$$ - 100000 ≤ D a ≤ - 100 ) which indicates the porous medium permeability and the number of undulations ($$0 \le N \le 4$$ 0 ≤ N ≤ 4 ). The calculations are carried out based on the Galerkin Finite element method (GFEM) to present the streamlines, isotherms, entropy generation, and average Nusselt numbers in details. The main results proved that increment of Rayleigh number and Darcy number enhances heat transfer convection within the enclosure. Whilst, the porosity presents a minimal impact. Also, the rotational speed in a positive direction has a favorable influence on the heat transfer dispersion across the cavity.