The Application of Multiple Relaxation Time Lattice Boltzmann Method to Simulate the Newtonian and Non-Newtonian MHD Natural Convection in Cavity with Lozenge Barrier

The purpose of this work is to investigate the effect of magnetic field direction on heat transfer of Newtonian and non-Newtonian fluids in both uniform and non-uniform forms, with the power-law model by using the multiple relaxation time lattice Boltzmann method (MRT-LBM) with written computer code by Fortran language. The natural convection is created in the two-dimensional cavity with lozenge barrier and is examined in three different temperature boundary conditions. The cold wall of the cavity is investigated in three modes: smooth, curved and diagonal. The results show that increasing the Rayleigh number and decreasing the power-law index and the Hatmann number increase the strength of fluid flow and heat transfer. The smooth design of the wall increases the average Nusselt number by about 30%. Placing the barrier at a constant cold temperature increases the average Nusselt number by 20% on average. The effect of the magnetic field is highest for the smooth wall and lowest for the diagonal wall and this effect decreases with increasing the power-law index. In general, an applied non-uniform magnetic field increases the average Nusselt number by about 10% and increases the flow strength. The effect of wall shape and type of magnetic field applied on shear thickening fluid is negligible. Further reduction of flow strength and average Nusselt number is observed by applying a magnetic field horizontally.