Modeling the radiation of anisotropically scattering media by coupling Mie theory with finite volume method

Abstract

A new mathematical model and code for radiative heat transfer of particulate media with anisotropic scattering for 2-D rectangular enclosure is developed. The model is based on the coupling of (i) finite volume method for the solution of radiative transfer equation with (ii) Mie equations for the evaluation of scattering phase function. It has not been done before to the authors’ best knowledge. The predictions were compared against the only found results, published 15 years ago. For those results the S-N discrete ordinates method for the solution of radiative transfer equation and the Legendre polynomials expansions for the evaluation of scattering phase function were used. The agreement between the results is very good. The advantages of new model and code are in their straight forward application to any given particles parameters without the need for previously designed analytical expression for scattering phase function. In addition, that analytical expression, with generated expansion coefficients, is restricted and can be used only for that particular case of particle parameters. The new model was applied to the solid particles of several various coals and of an ash and the series of 2-D predictions are performed. The effects of particle size parameter and of scattering albedo on radiative heat flux and on incident radiation were analyzed. It was found that the model developed is reliable and very accurate and thus suitable for extension towards: (i) 3-D geometries, (ii) mixtures of non-gray gases with particles as well as for (iii) incorporation in computational fluid dynamics codes.