Magneto-Hydrodynamic Quadratic Convective TiO2–Cu / Water Hybrid Nanofluid Flow in an Enclosure With Partially Filled Porous Medium

Nanofluid-based fuel cells are emerging as a major development in 21st century energy engineering. A new mathematical model is proposed for the laminar natural convection of a hybrid hydromagnetic nanofluid flow of TiO ₂ -Cu/water in a partially filled porous enclosure with thermal radiation and heat generation/absorption. This model is inspired by recent developments in magnetized hybrid nanofluids, which combine nanoparticles and cupper nanoparticles simultaneously. The numerical investigation is carried out by based Marker-and-Cell (MAC) method is utilized. In order to arrive at a precise numerical solution, we make use of the efficient MAC solver to solve the dimensionless conservative equations of thermal transport, mass, and momentum transport, while ensuring that the appropriate wall conditions. The interplay of magnetic field influence, nanoparticle suspension, thermal radiation, porosity parameter, and internal heat generation/absorption is comprehensively analyzed to understand their collective impact on fluid dynamics and thermal distribution. The impact of magnetic number (0 ≤ Ha ≤ 30), heat generation (-3 ≤ Q ≤ 3), Darcy parameter (10 ^− 4 ≤ Da ≤ 10 ^− 1 ), Rayleigh number (10 ³ ≤ Ra ≤ 10 ⁶ ), Thermal radiation (0 ≤ Rd ≤ 4) and Non-linear temperature parameter (0 ≤ λ ≤ 3) on the fluid flow and thermal transport have been examined. The numerical results have shown that convective thermal transmission in the nanofluid inside the square cavity is described in detail.