Isothermal Rectangular Roughness Elements in a Rectangular Cavity Heated at Bottom

The purpose of the present research was to explore the role of rectangular roughness elements during natural convection in a two-dimensional rectangular cavity. The computational algorithm was developed based on the single relaxation time Bhatnagr-Gross and Krook (BGK) model of lattice Boltzmann method (LBM). Rectangular roughness elements were located on the horizontal walls. The computational algorithm was validated against benchmark studies using different numerical techniques, and a good agreement was found to exist. The range of the Rayleigh (Ra) number was explored from 10³ to 10⁶ for a Newtonian fluid of Prandtl number equal to 1.0. The dimensionless amplitude (h/H) of roughness elements was fixed to 0.1, while the spacing between these elements was equal to twice their height. The maximum reduction in the average heat transfer was calculated to be 27 percent at Ra number 1×10⁶.