Effect of surface radiation on the breakdown of steady natural convection flows in a square, air-filled cavity containing a centered inner body

The physical model considered in the present numerical work is a square air-filled cavity cooled from below and above, with a heated square body located at the cavity center. The aim is to establish the effects of radiation interchanges amongst surfaces on the transition from steady, symmetric flows about the cavity centerline to complex periodic flows. Owing to the low temperature differences involved (1 K ≤ ΔT ≤ 5 K), the two-dimensional model is based on the Boussinesq approximation and constant thermophysical fluid properties at room temperature. The cavity walls are assumed gray and diffuse. The flow structure is investigated for various Rayleigh numbers, emissivities of the wall surfaces and sizes of the inner body. The results clearly establish the influence of surface radiation, both for steady and unsteady flows. For the geometry and thermal boundary conditions considered, the Rayleigh number for the transition to unsteady flows is considerably increased under the influence of radiation. This work underlines the difficulties in comparing experimental data and numerical solutions for gas-filled cavities partly subjected to wall heat flux boundary conditions.