Natural convective flow of CuO–water nanofluid with variable thermophysical properties in a square-shaped cavity embedded in a porous medium

The study investigates the effects of magnetohydrodynamic (MHD) forces, nonlinear thermal radiation, and variable thermophysical properties on natural convection within a square enclosure containing an inner corrugated circular cylinder. Understanding these effects is crucial for optimizing thermal management in engineering applications such as electronic cooling and energy storage. A numerical simulation using the finite element method is performed, considering CuO-water nanofluid diffusion within a porous medium. The results reveal that increasing the Rayleigh number ( Ra ) enhances the average Nusselt number ( Nu avg ) by approximately 32%, while a higher Hartmann number ( Ha ) suppresses convection, reducing Nu avg by nearly 17%. The addition of CuO nanoparticles ( ϕ = 9%) leads to a 47% decrease in heat transfer performance under strong buoyancy forces, illustrating the complex interaction between nanoparticle concentration and convection. However, introducing a porous medium significantly reduces the heat transfer rate, showing a clear inverse relationship between the Darcy number ( Da ) and Nu avg . These findings provide valuable insights into optimizing heat transfer in MHD-driven porous media systems, aiding in the design of efficient thermal management strategies.