In the formation of nano-particles during coal char combustion, the vaporization of inorganic components in char and the subsequent homogeneous particle nucleation, heterogeneous condensation, coagulation, and coalescence play decisive roles. However, conventional measurements cannot provide detailed information on the dynamics of nano-particle formation and evolution. In this work, a sophisticated intrinsic char kinetics model that considers ash effects (including ash film formation, ash dilution, and ash vaporization acting in tandem), both oxidation and gasification by CO2 and H2O, homogeneous particle nucleation, heterogeneous vapor condensation, coagulation, and coalescence mechanisms is developed and used to compare the temporal evolution of the number and size of nano-particles during coal char particle combustion as a function of char particle size, ash content, and oxygen content in O-2/N-2 and O-2/CO2 atmospheres. Based on comparisons with measurements of char particle temperature, carbon conversion, mineral vaporization, and mean size of nano-particles at various residence times, the model can accurately predict the transient combustion of pulverized coal char particles and nano-particle formation and growth. Model results show that in either O-2/N-2 or O-2/CO2 atmospheres, the char combustion temperature has a dominant effect on the formation and growth of nano-particles. High char burning temperatures result in a high mineral vaporization rate within the char particle, and subsequent high nucleation and condensation rate, and consequently more and larger nano-particles. As a result, high oxygen content, low ash content, and small sized char particles, all of which promotes high local char burning temperatures, yield more nano-particles and shift the nano-particle size distribution to larger sizes. In comparison to combustion in O-2/N-2, both the number density and size of the nano-particles formed in O-2/CO2 are lower. Unlike condensation, which contributes to particle growth until the vapor molecules are fully consumed, nucleation ceases during the last stage of char combustion. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.