Investigating the effect of magnetic field, slope variations and wall temperature boundary conditions on the natural convection in the cavity with obstacle filled with water

In this article, the magnetic field effect on the natural convection heat transfer is simulated via LBM. The vertical wall of the left side of the cavity is at a constant hot temperature, while the vertical wall of the right side of the cavity has three different temperature boundary conditions, 1) constant cold temperature, 2) linear temperature and 3) constant hot temperature. A lozenge-shaped obstacle located in the center of the cavity is examined in four different modes, 1) cold, 2) conducting, 3) adiabatic, and 4) hot. The bottom wall of the cavity is also evaluated in three different slopes. The results show that increasing the slope of the wall and the Rayleigh number by unchanged all the parameters leads to an increase in heat transfer. Also, changing the boundary temperature of the walls and the obstacle can affect the amount of heat transfer. In addition, increasing the strength of the magnetic field reduces the average Nusselt number, which differs in different conditions.