Influence of Prandtl number on the instability of natural convection flows within a square enclosure containing an embedded heated cylinder at moderate Rayleigh number

Abstract

Influence of Prandtl number (0.07 ≤ Pr ≤ 7) on the buoyancy induced flow within a square domain containing an embedded heated cylinder is investigated numerically at moderate Rayleigh number (2 × 105 2 × 106). In general, reduction of Prandtl number thickens the thermal boundary layer, and hence, the decrease of predicted Nusselt number is observed. However, the dynamic boundary layer becomes thin and this leads to the increase of internal counter rotating vortex pairs and further to the breakdown of vortex symmetry and hence the eventual instability. In the unsteady regime, the Nusselt number oscillation frequency is as expected twice of other flow variables and increases with the reduction of Prandtl number. For the Rayleigh number investigated, the unsteady-regime is dominated by the growth of thermal boundary layer and hence the averaged Nusselt number decreases accordingly. Also, different scaling laws for the Nusselt number exist due to the change of vortex structures in the steady and unsteady regions. Rayleigh number and Boussinesq number are the proper scaling parameters in the respective steady and unsteady regions with higher and lower Prandtl numbers.