Continuum approach based on radiation distribution function for radiative heat transfer in densely packed particulate system

Radiative transfer equation (RTE) is the commonly accepted continuum scale governing equation for radiative heat transfer in particulate system. However, its applicability is questionable for non-random, densely and regularly packed particulate systems, due to dependent scattering and strong correlation of particle locations that may largely violate the basic assumptions of the RTE. In this work, a new continuum approach is proposed for radiative heat transfer in densely packed particulate system composed of optically large particles, which does not rely explicitly on the RTE. The new approach is based on an introduced concept of radiation distribution function (RDF), which is an extension of the concept of radiation distribution factor (RD) at discrete scale (particle scale) to continuum scale. The governing equations are in integral form of spatial coordinates, in which the RDF is the key continuum scale physical parameter that characterizes the radiative heat transfer in the system. The continuum approach is verified through heat transfer simulation at particle scale, and demonstrated to have excellent performance in predicting the temperature distribution in dense particulate system. This work provides an alternative continuum theory for the analysis and understanding of radiative heat transfer in densely packed particulate and porous materials.