MHD Natural convection and entropy generation of Fe3O4–MgO/water hybrid nanofluid in an inclined enclosure with flower-shaped heated fins

Controlling both the heat removal and the associated irreversibility is a central requirement in compact energy-storage and electronic-cooling systems containing multiple localized heat sources. This study presents a comprehensive numerical investigation of magnetohydrodynamic (MHD) natural convection and entropy generation in an inclined enclosure filled with a binary hybrid nanofluid composed of magnetite (Fe 3 O 4 )) and magnesium oxide (MgO) dispersed in water. The dimensionless governing equations for continuity, momentum, and energy are solved using the finite volume method (FVM) implemented in a FORTRAN-based computational code. The simulation is conducted for a wide range of controlling parameters, including Rayleigh number (Ra=10³–10 6 ), Hartmann number (Ha=0–75), enclosure inclination angle (γ = 0°–120°), and nanoparticle volume fraction (φ = 0–4%). In addition to the governing parameters, four geometric configurations (C1–C4) of heated flower-shaped internal fins are examined to assess the impact of heat source placement on flow circulation. The results show that increasing Ra and φ intensifies buoyancy-driven circulation and enhances the average Nusselt number, while higher Ha values suppress convection due to the Lorentz force. At Ra=10⁶ and φ = 0.04, raising Ha from 0 to 75 reduces the Nusselt number by 21.9% at γ = 0° but only 12.7% at γ = 60°, so tilting lowers the sensitivity to the field. Without a field the vertical enclosure performs best, whereas under a field the tilted one becomes superior by 5–7.2%. Further noteworthy findings and comprehensive discussions are provided throughout the remainder of this study. These findings provide important guidance for the optimal design of MHD thermal systems incorporating complex internal heat sources.