Due to the high surface energy, aggregation of particles in colloidal dispersions is almost inevitable. In the present study, a comprehensive model was established by coupling a two-phase lattice Boltzmann method (LBM) and population balance equations (PBEs) to describe the dynamic particle aggregations in flowing and heated colloidal suspensions. Typically, the dynamic aggregations in suspensions under natural convection in a rectangular enclosure are investigated. The real-time particle size distribution (PSD) significantly depended on Ra (Rayleigh numbers), concentration, and enclosure geometry, where increasing particle concentrations can inevitably increase the particle size, but the effect of Ra on PSD is different when enclosure geometry changes. The results of average Nusselt number (Nu(ave)) suggested a significant negative impact of particle aggregation on the heat transfer, especially for high concentration and low Ra cases. Our work should be of value when the properties of practical colloidal dispersions are to be predicted and estimated.