Mathematical modelling of heat and mass transfer processes in the treatment of polidispersed materials in fluidized beds
M. Stynes (Department of Mathematics, National University of Ireland, Cork, Ireland), G. I. Shishkin (Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Russia), K. Cronin (Department of Process and Chemical Engineering, National University of Ireland, Cork, Ireland) and M. Viscor (Department of Mathematics, National University of Ireland, Cork, Ireland)
The thermal behaviour of spherical particles in fluidized beds is considered. In our mathematical model, the heat and mass transfer processes are considered separately inside and at the surface of each particle---the inner and boundary problems. The solution of the boundary problem has a singularity: its first derivative in the radial direction (which controls the heat and mass fluxes) tends to infinity on the particle surface when the particle diameter becomes small. This singularity induces unacceptably large errors in standard numerical methods. Our computational approach combines accurate models of the transfer processes with robust numerical techniques for singularly perturbed differential equations.