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The importance of inter-particle radiation for clusters of gray and diffuseparticles is investigated. The radiative cooling of each individual particle isfound to vary strongly with its position in the cluster, and a mean radiativeparticle cooling term is proposed for single particle simulations of particleclusters or for high detail simulation, like Direct Numerical Simulations ofsmall sub-volumes of large clusters of particles. Radiative cooling is shown tobe important both for furnaces for coal gasification and coal combustion.Broadening the particle size distribution is found to have just a minor effecton the radiative particle cooling. This is particularly the case for large anddense particle clusters where there is essentially no effect of sizedistribution broadening at all. For smaller and more dilute particle clusters,the effect of distribution broadening is clear but still not dominant.

Modeling radiation in particle clouds: On the importance of inter-particle radiation for pulverized solid fuel combustion