Abstract: Numerical studies were conducted using Lattice
Boltzmann Method (LBM) to study the natural convection in a square
cavity in the presence of roughness. An algorithm based on a single
relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice
Boltzmann Method (LBM) was developed. Roughness was
introduced on both the hot and cold walls in the form of sinusoidal
roughness elements. The study was conducted for a Newtonian fluid
of Prandtl number (Pr) 1.0. The range of Ra number was explored
from 10^3 to 10^6 in a laminar region. Thermal and hydrodynamic
behavior of fluid was analyzed using a differentially heated square
cavity with roughness elements present on both the hot and cold wall.
Neumann boundary conditions were introduced on horizontal walls
with vertical walls as isothermal. The roughness elements were at the
same boundary condition as corresponding walls. Computational
algorithm was validated against previous benchmark studies
performed with different numerical methods, and a good agreement
was found to exist. Results indicate that the maximum reduction in
the average heat transfer was 16.66 percent at Ra number 10^5.