This study advances a comprehensive numerical analysis aimed at enhancing thermal transfer within square enclosures filled with water-based oxide nanoparticle suspensions subjected to central sinusoidal heating. Central to this research is the integration of Multi Expression Programming (MEP) for the predictive optimization of thermal efficiency, taking into account the intricate effects of sinusoidal heating geometry, nanoparticles concentration, and an inclined magnetic field. The analysis maintains the initial setup boundary conditions: no-slip at the enclosure walls, isothermal conditions at the left and right walls, and adiabatic conditions at the top and bottom walls, except where sinusoidal heating is applied. Using MEP, these conditions are explored to identify configurations that significantly enhance thermal performance. This method allows for a detailed examination of the impacts of heating element undulation, magnetic field orientation, and nanoparticle dispersion on flow dynamics and thermal transmission. The results emphasize the significant impact of heating element undulation on the heat transfer rate, with MEP predicting optimal undulations that boost thermal efficiency. Furthermore, the strategic application of magnetic fields, as optimized through MEP, facilitates controlled flow distribution and buoyancy effects, with an increased Rayleigh number leading to enhanced convection patterns. The study also delineates the specific boundary conditions under which the Nusselt number, indicative of thermal performance, increases. These MEP-driven insights are invaluable for designing optimized heat transfer systems and energy-efficient applications, establishing a new benchmark for thermal management strategies in practical engineering contexts, firmly rooted in the precision afforded by computational optimization and predictive modeling.
