The present study investigates magnetohydrodynamic (MHD) natural convection of Al 2 O 3 -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 ( T c ), while the bottom wall and semicircular obstacle are heated to a higher temperature ( T h ), with the vertical walls kept thermally insulated. Parametric analysis is carried out for Rayleigh numbers in the range of 10 3 ≤ Ra ≤ 10 5 , 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 Nu av 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.
KeywordsFree ConvectionNanofluidMagnetic FieldWavy CavityFinite Element Method
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