Population balance model of heat transfer in gas–solid particulate systems

A population balance model is derived for heat transfer processes in gas–solid systems with intensive motion of particles in order to describe the temperature distribution of particulate phase. The model involves collisional particle–particle and particle–wall heat transfers, and continuous gas–particle, gas–wall and wall–liquid environment heat transfer processes. Collisional heat transfers are characterised by collision frequencies and random heat exchange parameters with general probability distributions with support [0, 1], describing the heat transfer efficiency between the colliding solid bodies. An infinite hierarchy of moment equations, describing the time evolution of moments of the temperature of particle population is derived from the population balance equation, which can be closed at any order of moments. The properties of the model and the effects of parameters are examined by numerical experiments using the second order moment equation model of a spatially homogeneous fluidized bed.