Investigation of Prandtl number effect on natural convection MHD in an open cavity by lattice Boltzmann method

Magneto hydrodynamic (MHD) flows in fluids is known to have an important effect on heat transfer and fluid flow in various substances while the quality of the substances and the considered shapes can influence the amount of changes. Thus, MHD flows in a different form and widespread alterations in the kind of the material and the power of MHD flow were carried out by lattice Boltzmann method (LBM) in this investigation. The aim of this paper is to identify the ability of LBM for solving MHD flows as the effect of different substances in the presence of the magnetic field changes.

This method was utilized for solving MHD natural convection in an open cavity while Hartmann number varies from 0 to 150 and Rayleigh number is considered at values of Ra=10³, 10⁴ and 10⁵, with the Prandtl number altering in a wide range of Pr=0.025, 0.71 and 6.2. An appropriate validation with previous numerical investigations demonstrated that this attitude is a suitable method for MHD problems.

Results show the alterations of Prandtl numbers influence the isotherms and the streamlines widely at different Rayleigh and Hartmann numbers simultaneously. Moreover, heat transfer declines with the increment of Hartmann number, while this reduction is marginal for Ra=10³ by comparison with other Rayleigh numbers. The effect of the magnetic field on the average Nusselt number at Liquid Gallium (Pr=0.025) is the least among considered materials.

In this method, just the force term at LBM changes in the presence of MHD flow as the added term rises from the classic equations of fluids mechanic. Moreover, all parameters of the added term and the method of their computing are exhibited.