Application of Lattice Boltzmann Method for Simulation of Natural Convection Nanofluid Flow inside a Parallelogram Shaped Cavity with Two Triangular Obstacles in the Presence of Magnetic Field

In this paper, for the first time, natural convection heat transfer of a nanofluid in the presence of a uniform magnetic field inside a parallelogram shaped cavity with two triangular obstacles with different boundary conditions is simulated by using lattice Boltzmann method. The right vertical wall of the cavity is assumed to be adiabatic and the inclined walls are kept at constant cold temperature, while the left vertical walls are kept at constant hot temperature. The flow and temperature field is calculated by solving lattice Boltzmann equations for velocity and temperature distribution functions simultaneously. D2Q9 lattice arrangement for each distribution function is used. The results have been validated with available results in the literature. The effects of different parameters such as Rayleigh number (103-105), Hartmann number (0-90), nanoparticle volume fraction (0-0.05) and different boundary conditions at triangular obstacles on natural heat convective heat transfer are investigated. The results show that, at a constant Rayleigh and Hartmann number, the average Nusselt number takes its maximum and minimum value when the triangular obstacles are kept at constant cold and hot temperatures, respectively. For all cases, it is found that the average Nusselt number increases with enhancement of Rayleigh number. Also, increasing of Hartman number decreases the flow velocity and heat transfer rate. Furthermore, increase of volume fraction of nano particles enhances heat transfer rate, however its changes for different Rayleigh and Hartman numbers are not the same.