TITLE:
Optimization of MHD Natural Convection in a Wavy Square Enclosure with Semicircular Heater Using RSM and Al-Water Nanofluid
AUTHORS:
Mohammad Mahfuzul Islam, Md. Yousuf Ali, Md. Abdul Alim, Md. Mahmud Alam
KEYWORDS:
Free Convection, Nanofluid, Magnetic Field, Wavy Cavity, Finite Element Method
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.15 No.4,
December
22,
2025
ABSTRACT: The present study investigates magnetohydrodynamic (MHD) natural convection of Al2O3-water nanofluid in a wavy square cavity containing a heated semicircular obstacle using the Finite Element Method (FEM). The top wavy wall of the cavity is maintained at a cold temperature (Tc), while the bottom wall and semicircular obstacle are heated to a higher temperature (Th), with the vertical walls kept thermally insulated. Parametric analysis is carried out for Rayleigh numbers in the range of 103 ≤ Ra ≤ 105, nanoparticle volume fractions 0 ≤ φ ≤ 0.05, and Hartmann numbers 0 ≤ Ha ≤ 100. Flow structures and heat transport are illustrated through streamlines, isotherms, velocity, and temperature profiles, along with the average Nusselt number. Results show that increasing Ra enhances buoyancy-driven convection and improves heat transfer, while higher nanoparticle volume fractions (φ) further augment the thermal performance due to enhanced conductivity of the nanofluid. In contrast, stronger magnetic fields (higher Ha) suppress convective circulation and reduce heat transfer rates. A maximum enhancement of approximately 19.8% in Nuav is observed at φ = 0.05 compared with the base fluid, whereas heat transfer decreases noticeably with increasing Ha. The combined effects of cavity geometry, nanoparticle loading, and magnetic field highlight the complex interplay between buoyancy and Lorentz forces, offering valuable insights for the design of thermally efficient nanofluid-based systems.