Population Balance Model of Heat Transfer in Gas-Solid Processing Systems

In modeling heat transfer in gas-solid processing systems, five interphase thermal processes are to be considered: gas-particle, gas-wall, particle-particle, particle-wall and wall-environment. In systems with intensive motion of particles, the particle-particle and particle-wall heat transfers occur through inter-particle and particle-wall collisions so that both experimental and modeling study of these collision processes is of primary interest. For modeling and simulation of collisional heat transfer processes in gas-solid systems, an Eulerian-Lagrangian approach, with Lagrangian tracking for the particle phase (Boulet et al., 2000, Mansoori et al., 2002, 2005, Chagras et al., 2005), population balance models (Mihálykó et al., 2004, Lakatos et al., 2006, 2008), and CFD simulation in the framework of EulerianEulerian approach (Chang and Yang, 2010) have been applied. The population balance equation is a widely used tool in modeling the disperse systems of process engineering (Ramkrishna, 2000) describing a number of fluid-particle and particleparticle interactions. This equation was extended by Lakatos et al. (2006) with terms describing also the direct exchange processes of extensive quantities, such as mass and heat between the disperse elements as well as between the disperse elements and solid surfaces by collisional interactions (Lakatos et al., 2008). The population balance model for describing the collisional particle-particle and particlesurface heat transfers was developed on the basis of a spatially homogeneous perfectly mixed system (Lakatos et al., 2008). In order to take into consideration also the spatial inhomogeneities of particles in a processing system a compartment/population balance model was introduced (Süle et al., 2006) which has proved applicable to model turbulent fluidization and the gas-solid fluidized bed heat exchangers (Süle et al., 2008). However, the spatial transport of gas and particles in turbulent fluidized beds usually is modeled by continuous dispersion models (Bi et al., 2000) thus, in order to achieve easier correlations of the constitutive variables, it has appeared reasonable to formulate the population balance combining it with the axial dispersion model (Süle et al., 2009 2010). Particle-particle and particle-wall heat transfers may result from three mechanisms: heat transfers by radiation, heat conduction through the contact surface between the collided bodies, and heat transfers through the gas lens at the interfaces between the particles, as well as between the wall and particles collided with that. Heat conduction through the contact surface was modeled by Schlünder (1984), Martin (1984) and Sun and Chen (1988) developing analytical expressions for particle-particle and particle-wall contacts. Often, however, the conductive heat exchange can hardly be isolated from the mechanism