Particulate flow model governing equations

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

The two-fluid granular flow model is formulated applying the classical Eulerian continuum concept for the continuous phase, while the governing equations of the particle phase are developed in accordance with the principles of kinetic theory. In this theory it is postulated that the particulate system can be represented considering a collection of identical, smooth, rigid spheres, adapting a Boltzmann type of equation. This microscopic balance describes the rate of change of the distribution function with respect to position and time. 

---