Natural Convection Heat Transfer in a Square Cavity with Sinusoidal Roughness Elements

Natural convection in a two-dimensional square cavity in the presence of roughness on vertical walls was studied numerically. A single relaxation time Bhatnagar-Gross and Krook (BGK) model of Lattice Boltzmann method (LBM) was utilized to solve coupled momentum and energy equations. Validation of computational algorithm was performed against benchmark solutions, and a good agreement was found. Numerical study was performed for a range of the Rayleigh number from 103 to 106 for a Newtonian fluid of the Prandtl number 1.0. The sinusoidal roughness elements were located on a hot, and both the hot and cold walls simultaneously with varying number of elements and the dimensionless amplitude. Hydrodynamic and thermal behavior of fluid in the presence of roughness was analyzed in form of isotherms, velocity streamlines, and the average heat transfer. Results based on this numerical study showed that the sinusoidal roughness considerably affect the hydrodynamic and thermal behavior of fluid in a square cavity. A dimensionless amplitude of sinusoidal roughness elements approximately equal to 0.025 has no significant effects on the average heat transfer. The maximum reduction in the average heat transfer was calculated to be 28% when the sinusoidal roughness elements were located on both the hot and cold walls simultaneously