Our objective for this work is to study natural convection in a cavity differentially heated in 3D. The equations which govern our problem are expressed in a dimensionless form with a calculation procedure based on the finite element method implemented in the COMSOL Multiphysics calculation code. The flow is unsteady turbulent flow. Several numerical studies have been carried out in parallelepiped cavities using the Boltzmann lattice method. In our case, the cavity is heated by the ceiling and the left, right walls and the floor are maintained at the same imposed temperature, while the side walls (front and rear) are assumed to be adiabatic. A validation study of the calculation code was carried out, taking into account the studies carried out by (Hong Wang, 2006). The study on some cavities encountered in the literature was carried out to change the position of the hot temperature and noted the effect of convection in the middle of the cavities, to see the convergence time and the most important convergence time step. We carry out thermal and dynamic studies of natural convection in the cavity K_d. The flow results will be studied in terms of isotherms, flow velocity vectors, streamlines, velocity and temperature isovalues. The effect of thermal radiation from the walls is negligible. The boussinesq approximation is applied. The fluid is Newtonian P_r=0,71. The Rayleigh number is R_abased on the height of the cavity so it is fixed equal toR_aH=3,349〖10〗^10.
