Modeling radiation in particle clouds: On the importance of   inter-particle radiation for pulverized solid fuel combustion
  The importance of inter-particle radiation for clusters of gray and diffuse particles is investigated. The radiative cooling of each individual particle is found to vary strongly with its position in the cluster, and a mean radiative particle cooling term is proposed for single particle simulations of particle clusters or for high detail simulation, like Direct Numerical Simulations of small sub-volumes of large clusters of particles. Radiative cooling is shown to be important both for furnaces for coal gasification and coal combustion. Broadening the particle size distribution is found to have just a minor effect on the radiative particle cooling. This is particularly the case for large and dense particle clusters where there is essentially no effect of size distribution broadening at all. For smaller and more dilute particle clusters, the effect of distribution broadening is clear but still not dominant. 
Nils Erland L. Haugen and Reginald E. Mitchell
physics.optics