LBM Study of MHD Natural Convection of Nanofluid in an Open Wavy Enclosure with a Linear Temperature Profile

This work presents a numerical investigation of magnetohydrodynamic (MHD) natural convection in an open cavity with a sinusoidal wall, where the heated boundary is subjected to a linearly varying temperature profile. A water-based nanofluid containing different nanoparticles (SWCNT, Cu, and TiO ₂ ) is considered, and the lattice Boltzmann method (LBM) is employed to resolve the coupled flow and thermal fields. A second-order boundary treatment is applied to accurately represent the wavy wall condition. The effects of Rayleigh number (Ra), Hartmann number (Ha), nanoparticle volume fraction ( φ ), wall geometry parameters, including the number and amplitude of undulations, and nanoparticle type are systematically explored. The results indicate that increasing the Hartmann number suppresses convection, causing the average Nusselt number to decrease by up to 66.08% at Ra = 10 ⁵ . Increasing the wall amplitude from 0 to 0.12 decreases the average Nusselt number by approximately 19.3% at high Rayleigh numbers. An even greater reduction is observed with increasing wall undulations, where increasing the number of wall undulations from 0 to 4 reduces heat transfer by up to 45.31% at Ra = 10 ⁶ . Under non-magnetic conditions, Cu nanoparticles increase the average Nusselt number by up to 5.24%, whereas under strong magnetic fields, SWCNT nanofluid exhibits the best thermal performance, with a maximum enhancement of 12.66% at low Ra and the smallest reduction of 5.34% at high Ra. These results demonstrate that the combined effects of nonuniform heating and wall geometry significantly influence thermal behavior in applications such as solar receivers and electronic cooling systems.