Modeling of Coupled Radiative and Convective Heat Transfer through Three-Dimensional Packed Beds with Random Arrangement

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Radiative energy transmittance is studied through three-dimensional packed spheres with random arrangement by using a Monte Carlo method. The sphere diameter is far greater than the wave length of the radiative energy. The following results are obtained.1. A computer program is developed to produce three-dimensional randomly-arranged packed spheres with arbitrary packing density.2. Analytical and experimental studies through two-dimensional packed columns show that the main mechanisms of the radiative transmittance through the packed spheres are a collimation effect and a streaming effect of radiative energy passing through the spheres and the multiple reflection on the surfaces of the spheres.3. Analytical studies through three-dimensional packed spheres show that:(1) the radiative energy transmittance through regularly arranged packed spheres is generally lower than the one through randomly arranged packed spheres;(2) radiative energy transmittance obtained by a conventional continuous model approximation is far greater than the actual value especially for the packed spheres with higher packing density;(3) the regularity of the arrangement has little effect on the radiative energy transmittance through packed spheres, when the packing density is less than 0.3;(4) the radiative energy reflectance of the packed spheres is not affected by the packing density for random arrangement. For regular arrangement, it is increased by the increase in the packing density;(5) when the packed spheres have side walls, the radiative energy transmittance is increased due to the existence of the lower local packing density layer near the walls;(6) the radiative energy transmittance through the packed spheres with specular surfaces is higher than the one with diffuse surfaces.