Pseudocontinuum model

A regime map of Fo versus the solid volume fraction, ap, for various gas-solid flows was presented by Hunt (1989), as shown in Fig. 4.3. Hunt (1989) suggested that except when Fo > 1 and ap > 0.1, use of the pseudocontinuum model is inappropriate. Thus, from Fig. 4.3, it can be seen that the pseudocontinuum model is applicable to packed beds, incipient fluidized beds, and granular flows, whereas it is not applicable to pneumatic transport flows, dilute suspensions, bubbling beds, and slugging fluidized beds [Glicksman and Decker, 1982 Hunt, 1989]. 

Introduction Macroscopic Approximations Allometry Orders of Magnitude and Characteristic Time Constants Time Constant Ratios Systems of Multiple Time Constants Pseudocontinuum Models More Complex Situations References... 

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. 

One of the simplified heat transfer models of two-phase flows is the pseudocontinuum one-phase flow model, in which it is assumed that (1) local thermal equilibrium between the two phases exists (2) particles are evenly distributed (3) flow is uniform and (4) heat conduction is dominant in the cross-stream direction. Therefore, the heat balance leads to a single-phase energy equation which is based on effective gas-solid properties and averaged temperatures and velocities. For an axisymmetric flow heated by a cylindrical heating surface at rw, the heat balance equation can be written as... 

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