Lattice Boltzmann computation of two dimensional differentailly heated cavity of incompressible fluid with different aspect ratios

Lattice Boltzmann Method (LBM) is a novel computational technique to solve fluid flow problem in bounded domain. Continuum based methods are being widely used to solve the natural convection problem, whereas in the last two decades, mesoscopic approach has gained popularity to solve heat transfer and fluid flow problems. In natural convection cavity, density difference caused by heating and cooling of fluid at different locations gives rise to buoyancy force which in turn drives the fluid flow. The right side and left side wall of the cavity is made hot and cold respectively whereas top and bottom walls are made adiabatic. In the present work, natural convection problem of differently heated cavity with constant Prandtl number (Pr = 0.71) and varying Rayleigh number (Ra =10
³
-10
⁶
) is solved employing LBM to study the effect of various aspect ratios (H/L) on both Nusselt number and streamlines. Results are plotted in the form of streamlines and isotherms for different Rayleigh numbers at different aspect ratios. Nusselt numbers are obtained at the hot wall and cold wall to study the rate of heat transfer. Obtained results are compared with the existing results. It is found that with increase of Rayleigh number, there is increase in the Nusselt number. The increment in aspect ratio leads to the significant decrement in the Nusselt number and vice versa.