Scaling laws for radiation-convection coupling in a two-dimensional model of a glass tank

Free convection, due to the coupling between radiation and convection in shallow two-dimensional differentially heated cavity, considered as a model of a glass tank, is studied. All physical properties except the density of the fluid are considered to be independent of temperature. Convection in the cavity is controlled by two parameters only: Ra'(R)A(2), the product of an appropriately-defined 'radiative' Rayleigh number and the square of the cavity's aspect ratio, and the optical thickness, tau. For a given value of c, as the value of Ra'(R)A(2) increases, convection in the cavity transitions from the 'radiative' (radiation dominates, motion occurs in the bulk of the cavity) to the 'convective' (convection dominates, motion occurs in the vicinity of the walls) regime. AS T decreases, the transition from the radiative to the convective regime occurs at smaller Ra'(R)A(2) values.