Investigation of 3-D Nanofluid Natural Convection in Presence of Magnetic Field using Double MRT Lattice Boltzmann method

In this work numerical simulation of magneto hydrodynamics (MHD) natural convection in a three dimensional square cavity has been considered by new means of the Lattice Boltzmann method with double Multi-Relaxation-Time (MRT) model utilizing cu/water nanofluids. D3Q19 and D3Q7 models have been used to solve the momentum and energy equations, respectively and the effect of different Grashof numbers (Gr=1e3 _1e5) and various Hartmann numbers (Ha=0-100) for volumetric fraction of the nanoparticles between 0 and 12% have been investigated. The results have been shown at different planes and lines of the 3-D enclosure and based on the results the double MRT-LBM method is a proper method for simulating the complex 3-D flows. Also, the results show that augmentation of the Hartmann number decreases the heat transfer for base fluid and the maximum reduction of Nusselt number with increasing Hartmann number from 0 to 100 has been observed as 71% for Gr=1e4. While increasing the Grashof number and volumetric fraction of the nanoparticles enhance the heat transfer rate for all Hartmann number. The highest effect of nanoparticle is obtained at Gr=1e4 and Ha=50 as with increasing 12% of volumetric fraction of the nanoparticles Nusselt number enhances 43% .