The present paper analyzed the mixed convection of (CuO/Water) Nanoliquid in a double lid–driven U-shaped enclosure. The dimensionless equations governing the system were solved using the lattice Boltzmann method. The originality of this study lies in the exploration of mixed convection, generated by two movable lids, and influenced by the application of a periodic horizontal magnetic field. This innovative approach provides valuable insights into the interaction between heat transfer and fluid flow in a complex system. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. The impact of nanoparticles Brownian motion on heat and mass transfer has been studied. Influences of Reynolds number (Re = 1–100), volumetric fraction of nanoparticles ( Φ = 0–0.04), Hartmann number (Ha = 0–80) and period of the periodic magnetic field (λ = 0.25, 0.5, 0.75) on temperature and velocity contours are clarified in details through graphical portraits. In this investigation, it is noted that incorporating the influence of Brownian motion of nanoparticles enhances heat transfer by more than 6%, while the presence of a magnetic field tends to decelerate the flow. Furthermore, the numerical findings indicate an increase in the average Nusselt number with higher values of Reynolds number, and the period of the periodic magnetic field. Also, the results indicate that the higher average rate of heat transport is observed for the non-uniform magnetic effect when λ = 0.75, taking into account the effect of Brownian motion, and that the average Nusselt number for this case increased by 17.94% compared to the case where the applied magnetic field is uniform. Furthermore, the optimal condition for heat transfer is reached when L = 0.2, with the other parameters held constant.
Mliki et al. (2026) studied this question.