Double MRT Lattice Boltzmann simulation of 3-D MHD natural convection in a cubic cavity with sinusoidal temperature distribution utilizing nanofluid

In this work numerical simulation of magneto hydrodynamics (MHD) natural convection in a three-dimensional cubic cavity with sinusoidal temperature distribution on one side wall has been considered. New means of the Lattice Boltzmann method with double Multi-Relaxation-Time (MRT) model has been applied utilizing cu/water nanofluid. D3Q19 and D3Q7 models have been used to solve the momentum and energy equations, respectively. Different Rayleigh numbers (Ra = 103_105) and various Hartmann numbers (Ha = 0-100) for volumetric fraction of the nanoparticles (Ø) between Ø = 0 and 12% have been investigated. Also, phase deviation varied from θ = 0 to π with interval π/2. The magnetic field is considered horizontally and the results have been shown at different planes and lines of the 3-D enclosure. Based on the results, the double MRT-LBM method is a proper method for simulating the 3-D flows with complex boundary conditions. The results show that augmentation of the Hartmann number decreases the heat transfer rate whereas the increase of the Rayleigh number and nanoparticles' volumetric fraction enhance the heat transfer rate. The highest effect of magnetic field is obtained at Ra = 104 and the lowest effect is seen at Ra = 103. Also, the greatest effect of Rayleigh number is captured at Ha = 0 for all volumetric fraction of the nanoparticles.