Thermal Optimization of Magneto-Nanofluid Convection in Wavy Circular Enclosure Using Response Surface Method

This study investigates the thermal optimization of unsteady nanofluid natural convection within a quarter-circular domain with an inner wavy boundary under inclined periodic magnetic forcing. A combined finite-element method (FEM) and central composite design-based response surface methodology (RSM) is employed for optimizing both the geometric configuration and the parametric setting. For the geometric optimization, we find that the wavy-wall amplitude is the key parameter to determine the optimal configuration, followed by the inner radius and undulation number. The parametric analysis shows that strong magnetic effects suppress convection, while increasing the Rayleigh number and the nanoparticle volume fraction significantly enhances heat transport. Additionally, rising magnetic field wavelength and/or inclination angle result in a reduction in heat transmission under strong magnetic intensity. A statistical quadratic correlation equation with the help of the RSM method between Rayleigh number, Hartmann number, and nanoparticle volume fraction, and the mean Nusselt number is formulated, which gives a good match with numerical FEM analysis results in which about 99% of the variation in the response variable is predicted (R2 = 0.9975). The results obtained in this study offer valuable information along with computational efficiency in predicting the behavior of such advanced thermal systems.