This study presents a comprehensive numerical investigation of transient natural convection and entropy generation in a tilted square enclosure filled with a binary hybrid nanofluid (Ag/GO-water) and subjected to localized cold sources and internal heat generation/absorption. The thermal and hydrodynamic behavior is analyzed under the simultaneous effects of buoyancy-driven flow, enclosure inclination, and an externally applied magnetic field. A localized heat source, modeled as two superposed elliptic cylinders, induces convective motion, while the enclosure is maintained at mixed thermal boundary conditions. The governing Navier–Stokes and energy equations are solved using a finite volume method with an implicit time-stepping scheme to capture transient evolution and flow periodicity. Results reveal that higher Rayleigh numbers induce intensified convective currents, leading to enhanced heat transfer and the emergence of oscillatory flow regimes. Moreover, it has been found that the best heat transfer conditions occur at ϕ = 8%, Q > 0, and Ha = 0. Phase-space analysis of velocity components demonstrates a transition from steady-state to periodic convection at higher Rayleigh numbers. Entropy generation analysis highlights the competing effects of viscous dissipation, thermal gradients, and magnetic field interactions, offering insight into optimizing thermal management systems. The findings underscore the critical interplay among hybrid nanofluid properties, internal sources, and magnetic field strength in controlling unsteady convection. These results contribute to the advancement of magnetohydrodynamic-assisted energy systems, cooling technologies, and heat transfer optimization in enclosures.
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