Numerical Study of Natural Convection-Surface Radiation Coupling in Air-Filled Square Cavity Using the Gauss’s Theorem on Triangular Meshes

Abstract

In this paper a numerical Study of natural convection-Surface radiation coupling in a differentially heated 2D square cavity, while the horizontal walls are insulated and all walls have the same emissivity filled with air is presented. The governing equations are formulated in Helmholtz variables (ψ, ω).The study has been investigated by a numerical method; the basic principle of this method is the Gauss’s theorem (integrals over a closed line around an area). The current method was developed for being used on triangular meshes. The paper presents the main convective and radiative Nusselt numbers distributions for various Rayleigh number and for various emissivity values, the isothermal and streamlines are also presented. The effect of emissivity on the net radiative flux, temperature and velocity profiles has been analyzed. The increasing of emissivity increases the net radiative flux at the top horizontal wall (the top wall loses the heat depending the emissivity's value) and decreases the net radiative flux at the bottom horizontal wall (the bottom wall receives the heat depending the emissivity's value).
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