The purpose of the present study was to numerically investigate the effects of the roughness elements on the heat transfer during natural convection. A computational algorithm was developed based on the Lattice Boltzmann method to conduct numerical study in two-dimensional rectangular cavities and Rayleigh-Bénard cell. A single relaxation time Bhatnagar-Gross-Krook model of Lattice Boltzmann method was used to solve the coupled momentum and energy equations in two-dimensional lattices. Computational model was validated against previous benchmark solutions, and a good agreement was found to exist. A Newtonian fluid of Prandtl (Pr) number 1.0 was considered for this numerical study. The range of Ra numbers was investigated from 103 to 106. The roughness was introduced in the form of sinusoidal elements on a hot, cold, and both the hot and cold walls of the cavities and Rayleigh-Bénard cell. The frequency or number of the roughness elements and the dimensionless amplitude (h/H) were varied from 2 to 10 and 0.015 to 0.15 respectively. Numerical results showed that thermal and hydrodynamic behaviors of the fluid were considerably affected in the presence of the roughness elements. A dimensionless amplitude of approximately 0.025 has no significant effects on the average heat transfer. In contrast, a dimensionless amplitude of ≥ 0.05 cause a degradation in the average heat transfer and delay in the onset of natural convection. The maximum reduction in the average heat transfer was calculated to be approximately 51 percent in the Rayleigh-Bénard convection when the roughness was present on both the hot and cold walls with a dimensionless amplitude of 0.15 and the number of roughness elements equal to 10 --Abstract, page iv
