Natural Air Convection Using LBM in a Cavity Heated Linearly

The numerical study of natural convection of confined air flow within a closed square cavity was conducted using the lattice Boltzmann Method (LBM) employing the BGK model. In this setup, the right side of the enclosure is maintained at a cooling temperature, while the left side exhibits a linear decreasing temperature profile from the heated bottom wall to the adiabatic top one. The effect of buoyancy, induced by gravitational acceleration and influencing the convection force, was assessed through the Rayleigh number, varied between (laminar regime). The analysis of heat transfer was conducted using the Nusselt number for different Rayleigh values. The results are represented by streamlines, isotherms, as well as velocity and temperature profiles. By analyzing these results, it can be concluded that an increase in the Rayleigh number leads to an increase in natural convection heat exchange inside the cavity.