Mathematical analysis and numerical simulation of convection diffusion reaction equations in fluidized beds

Abstract

Fluidization is a significant process in many industries. In this process, solid particles newlineare interacted with a liquid or gas to convert it into a fluid state. During fluid bed newlinegranulation, a powder is fluidized with air so that individual particles are easily newlineaccessible. Using spray nozzles, a liquid is sprayed on top of the fluidized powder newlineand the particles stick together forming granules. Through fluid bed granulation, newlinecritical characteristics of the particle can be exactly defined. The humidity in the newlinefluidized bed, temperatures of the particle, sprayed liquid and air inside the fluidized newlinebed play an important role in the quality of the final product. The resulting granules newlinefind applications as pharmaceuticals, catalysts, cleaning agents, etc. newlineThe mathematical model describing the heat and mass transfer inside a fluidized newlinebed form a system of five coupled semilinear convection-diffusion-reaction equations. newlineThese equations arise as a result of mass and energy balances of the air, liquid newlineand solid particles in the fluidized bed. The primary variables in these equations newlineare air humidity, temperature of air, degree of wetting, temperature of liquid and newlinetemperature of particle. The reaction part in all the five equations are highly nonlinear newlineand coupled. This work examines in detail the intricacies in both the theoretical newlineand computational aspects of the model. The theoretical part mainly concerns the newlineexistence and uniqueness of weak solution, a priori error estimates in the context newlineof both finite elements and discontinuous Galerkin and a posteriori error estimates. newlineThe computational part is devoted to finding the numerical solution of these model newlineequations using discontinuous Galerkin schemes and adaptive numerical solution newlineusing finite element schemes. The existence and uniqueness of weak solution of newlinethese equations have been proved using classical results in functional analysis and the newlineSchauder fixed point theorem. newline