Numerical Investigation of Natural Convection and Entropy Generation in a Square Enclosure Filled with Cu-Fe₃O₄/Water Hybrid Nanofluid under the Impact of Discrete Heat Sources

This study investigates magnetohydrodynamic (MHD) natural convection and total entropy generation of a Cu-Fe₃O₄/water hybrid nanofluid in a two-dimensional square enclosure equipped with a discrete bottom heat source. The left and right vertical walls are maintained at a cold temperature Tc, the top horizontal boundary is thermally insulated, and the bottom horizontal wall features a centrally positioned localized heat source kept at a high temperature Th. The non-dimensional governing conservation equations—mass, momentum, and thermal energy—are solved numerically using the Finite Volume Method (FVM) coupled with the SIMPLE algorithm. The investigation evaluates a parametric domain: Rayleigh number (10³ ≤ Ra ≤ 10⁶), Hartmann number (0 ≤ Ha ≤ 60), solid volume fraction of hybrid nanoparticles (0 ≤ φ ≤ 0.04), and heat source length (0.2 ≤ ε ≤ 0.8). Results show that increasing the Rayleigh number and expanding the heat source length enhance natural convection strength, local/average Nusselt numbers (Nu), and total entropy generation. Conversely, applying a magnetic field (Ha > 0) induces opposing Lorentz forces that suppress fluid circulation, dampening convective heat transfer and overall irreversibility. The addition of Cu-Fe₃O₄ hybrid nanoparticles yields superior heat transfer rates compared to single-nanoparticle suspensions and pure water. Bejan number (Be) analysis demonstrates a transition from thermal-irreversibility domination at low Ha to viscous and magnetic irreversibility domination at higher magnetic field strengths.