A numerical model is developed to simulate combined natural convection and radiation heat transfer of various anisotropic absorbing-emitting-scattering media in a 2D square cavity based on the discrete ordinate (DO) method and Boussinesq assumption. The effects of Rayleigh number, optical thickness, scattering ratio, scattering phase function, and aspect ratio of square cavity on the behaviors of heat transfer are studied. The results show that the heat transfer of absorbing-emitting-scattering media is the combined results of radiation and natural convection, which depends on the physical properties and the aspect ratio of the cavity. When the natural convection becomes significant, the convection heat transfer is enhanced, and the distributions of and along the walls are obviously distorted. As the optical thickness increases, along the hot wall decreases. As the scattering ratio decreases, the along the walls decreases. At the higher aspect ratio, the more intensive thermal radiation and natural convection are formed, which increase the radiation and convection heat fluxes. This paper provides the theoretical research for the optimal thermal design and practical operation of the high temperature industrial equipments. 1. Introduction The combined heat transfer of the radiation and natural convection in the participating (absorbing-emitting-scattering) media is an important problem in the many fields of building and industry, including the boiler, furnace, building thermal comfort, and solar reactor. In the recent decades, the combined natural convection and radiation heat transfer has received the prominent interest and wide-spread research due to the wide industrial applications. Research on the numerical solution of heat transfer and fluid flow phenomena, where radiative heat transfer has an essential contribution, becomes a key aspect for the employment of CFD simulation, which always involve the solution of the Navier-Stokes equations (NSE) and the radiative transfer equation (RTE). Saravanan and Sivaraj [1] made a fundamental theoretical study to understand the interaction of surface radiation and natural convection in an air-filled cavity with a centrally placed thin heated plate. Sun et al. [2] studied the effects of radiation interchanges amongst surfaces on the transition from steady, symmetric flows about the cavity centerline to complex periodic flows. Mondal and Li [3] theoretically studied the effect of volumetric radiation on natural convection in a square cavity by using lattice Boltzmann method (LBM) with nonuniform lattices. Hou and
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