Simulation of three dimensional MHD natural convection using double MRT Lattice Boltzmann method

In this study, a three-dimensional mesoscopic simulation of magneto hydrodynamics (MHD) natural convection in a cubic cavity has been studied by new means of the Lattice Boltzmann method with double Multi-Relaxation-Time (MRT) model. In order to solve the momentum and energy equations, two different populations with various lattices have been used. This paper has been conducted for specific values of the Grashof number ( Gr = 2 × 1 0 3 _ 2 × 1 0 5 ) and Hartmann number (Ha=0–100), while the Prandtl number is fixed at Pr = 0 . 73 . The results are presented in the form of average and local Nusselt number and contours of temperature and velocity at different planes of the cavity. It was found that the double MRT-LBM method is an appropriate approach to solve the studied case. The present results also show that the increase of the Hartmann number causes the heat transfer to drop considerably. Also, the effect of Hartmann number increases by enhancing the Grashof number, as the reduction of average Nusselt number is 12% for Gr = 2 × 1 0 3 and 71% for Gr = 2 × 1 0 5 when Hartmann number increases from 0 to 100. In contrast with Hartmann number, increasing of Grashof number raises heat transfer rate and the average Nusselt number increases by more than three times by enhancing the Grashof number from 2 × 1 0 3 to 2 × 1 0 5 .