Development of mathematical model of fluidization of particles in presence of internal heat sources

Devices for heat treatment of bulk media due to the supply of high-temperature agent from an external source are widely used. In this case using the fluidization technique, the thermal agent also performs the function of a fluidizing medium. The ohmic heating of particles directly in the fluidized bed can be considered as an alternative and preferred technology in some cases. However, to organize such processes effectively we need reliable models to predict the structure of the fluidized bed itself, since it largely determines the conductivity, and, hence, the intensity of heating. The fluidized bed is an inhomogeneous heterogeneous system, therefore, mathematical models assuming its spatial discretization are necessary for its adequate description. Thus, the development of such models is an urgent task. The mathematical apparatus of the Markov chain theory is used as a mathematical basis to model the structure of a bulk medium in a fluidized bed. Parametric identification of the model is performed using the dependencies known from the literature. The transition matrices have been aligned with the physical parameters of the mass flows, which makes the proposed model nonlinear. The electrothermal process in the fluidized bed is described at a qualitative level with an assumption that the heating intensity of the representative volume of the bed is inversely proportional to the volume concentration of particles in it. The gas-particle heat and mass transfer process is a limiting factor that determine the asymptotic temperature in the bed. The authors have studied numerically the influence of the structure and expansion of the fluidized bed on the heating intensity of its phases in case we have internal heat sources, the intensity of which is inversely related to the concentration of the solid phase. The influence of various parameters of the model on the formation of the thermal regime in the apparatus is estimated. It is shown that for an appropriate description of processes in the apparatus, its analysis as an object with distributed spatial parameters is necessary. The paper shows that the methodology of the Markov chain approach is an acceptable tool to describe the structure of such particle systems as a fluidized bed. The obtained results of numerical experiments are in good qualitative agreement with the fluidized bed theory. They can be considered as a reliable scientific basis to calculate the system of ohmic heating of media in a fluidized bed.