Combined Effects of Radiation and Natural Convection in a Square Cavity Submitted to Two Combined Modes of Cross Gradients of Temperature

Abstract

The present article reports numerical results of natural convection and surface radiation within a square cavity filled with air and submitted to discrete heating and cooling from all its walls. The thermally active elements are centrally located on the walls of the cavity. Two heating modes are considered: in the first mode, named VB heating mode, the cavity is heated discreetly on the left vertical and bottom horizontal walls, while in the second mode, named VT heating mode, the left vertical and top horizontal walls of the cavity are heated. The remaining portions of the walls, other than those cooled, are considered adiabatic. The parameters governing the problem are the emissivity of the walls (0 ≤ ϵ ≤ 1), the relative lengths of the active elements (), and the Rayleigh number (10⁴ ≤ Ra ≤ 10⁷). The effect of these parameters on heat transfer and fluid flow within the cavity is examined. Results of the study are presented and compared to those of pure natural convection (ϵ = 0) for various typical combinations of the governing parameters in terms of flow and temperature patterns, average convective, radiative and total Nusselt numbers, and heatlines visualization. The heat transfer across the cavity was found to enhance notably with the active wall emissivity, while the effect of the insulated wall emissivity was insignificant. The contribution of radiation to the total heat transfer is generally not negligible for ϵ ≥ 0.5. It was demonstrated that the VB heating mode acts such that the flow circulation is importantly intensified engendering, consequently, high values of the Nusselt number. In contrast, the VT heating mode leads to a slowdown of the fluid flow motion and, therefore, to a weaker convective heat transfer.