Lattice Boltzmann Simulation of Natural Convection in a Square Cavity with Linearly Heated Wall(s)

In this study, the lattice Boltzmann method is used in order to investigate the natural convection in a cavity with linearly heated wall(s). The bottom wall is heated uniformly and the vertical wall(s) are heated linearly, whereas the top wall is insulated. Investigation has been conducted for Rayleigh numbers of 103to 105, while Prandtl number is varied from 0.7 to 10. The effects of an increase in Rayleigh number and Prandtl number on streamlines, isotherm counters, local Nusselt number and average Nusselt number are depicted. It has been observed that the average Nusselt number at the bottom wall augments with an increase in Prandtl number.