Simulation of magnetic field effect on natural convection of non-Newtonian power-law fluids in a sinusoidal heated cavity using FDLBM

In this paper, the effect of a magnetic field on natural convection of non-Newtonian power-law fluids in a cavity with a sinusoidal heated wall has been analyzed by finite difference Lattice Boltzmann method (FDLBM). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra=10⁴ and 10⁵), Prandtl number (Pr=10), Hartmann number (Ha=0-60) and power-law index (n=0.5-1.5) as the magnetic field is applied at different inclinations of γ=0° and 90°. Results indicate that the augmentation of the power-law index in the absence of the magnetic field causes heat transfer to drop. The magnetic field decreases heat transfer in different power-law indexes generally. The increment of the magnetic field power decreases the effect of the power-law index on heat transfer. The magnetic field for various Hartmann numbers at Ra=10⁴ has different effects on heat transfer against the enhancement of power-law index. At Ra=10⁵ and in the presence of the magnetic field, the heat transfer falls with the rise of the power-law index as the effect is weakened by the increase of Hartmann number significantly. The amount of the magnetic field influence on the heat transfer and the fluid flow is different in the vertical and horizontal ones.