Numerical analysis of free convection in a ternary hybrid nanofluid within a porous enclosure under inclined magnetic field, radiation, and internal heat generation

This research presents a numerical investigation of free convection of a ternary hybrid nanofluid in a permeable enclosure under the impact of an inclined magnetic field, thermal radiation, and internal heat generation. The ternary hybrid nanofluid consists of a base fluid with dispersed nanoparticles of aluminum oxide, copper ( Cu ), and multi-walled carbon nanotubes to increase thermal conductivity. The governing equations for mass, momentum, and energy are formulated in nondimensional form and solved via the Marker-And-Cell (MAC) method on a staggered grid with a finite difference discretization scheme. The effects of key dimensionless parameters including Rayleigh number ( Ra ), Hartmann number ( Ha ), radiation ( Rd ), Darcy number ( Da ), and heat generation/absorption parameter ( Q ) on heat transfer characteristics are analyzed. The results show that increasing Ra from \({10}^{3}to{10}^{6}\) enhances convective heat transfer, leading to a 192% increase in the average Nusselt number (\(N{u}_{a}\)), whereas decreasing Da from 0.1 to 0.0001 suppresses convection and results in a 53% drop in \(N{u}_{a}\). The application of an external magnetic field ( Ha  = 50) reduces energy transfer efficiency by 41%, confirming the suppressive effect of Lorentz forces. Conversely, increasing Rd from 0 to 5 significantly enhances radiative energy transfer, leading to a 229% rise in \(N{u}_{a}\). Internal heat generation ( Q  = 5) weakens convective motion, reducing \(N{u}_{a}\)​ by 12%, while heat absorption enhances convection and increases heat transfer. These findings highlight the strong interplay between buoyancy, magnetic field suppression, porous medium resistance, radiative heat transfer, and internal heat generation, demonstrating that ternary hybrid nanofluids can be optimized for various thermal management applications, including nuclear reactor cooling, MHD power generation, industrial heat exchangers, and electronic cooling systems.