Population balance model for particle-to-particle heat transfer in gas–solid systems

A mathematical model is presented for particle-to-particle heat transfer in gas–solid systems. In developing the model, simple kinetic equations are assumed to describe the inter-particle heat transfer process, and the particle–particle interactions are considered stochastic. A stochastic approach is used to derive the population balance equation describing the variation of the density function of temperature distribution of the particulate phase. The moment equations and numerical solution of the partial integro-differential equation of the population balance model are derived and used to analyse the behaviour of a batch gas–solid system. The results indicate that the population balance approach, used for developing the model describing the inter-particle contact heat conduction during collision capable to take into account a number of parameters affecting the process, can be applied also for predicting heat transfer in gas–solid processing systems.