Mathematical Modeling of the Process of Convective Drying of Materials Taking into Account their Shrinkage

Abstract

The authors have discussed the physical regularities of internal mass transfer in drying colloidal capillary-porous materials, which is characterized by the fact that in addition to the phenomenon of mass conductivity (diffusion of moisture) in a fixed coordinate system, the transfer of moisture by the matrix of the material due to its shrinkage is observed. As applied to this case, for a body in the shape of an unbounded plate dried symmetrically from both surfaces, a mathematical model has been written that describes mass conductivity and convective transfer of moisture in the body. The convective transfer of moisture depends on the normal coordinate to the plate’s surface: it is maximum at the surface of the plate and is equal to zero in its central plane. The authors have formulated the problem describing the process of symmetric drying of an unbounded plate on the basis of the convective-diffusion equation with a uniform initial distribution of the concentration and a boundary condition of mass transfer of the third kind. It has been noted that the formulated problem can be solved by numerical methods. For analysis of the degree of influence of the convective component on internal mass transfer, an analytical solution to the problem at constant parameters of the process has been obtained. According to the obtained solution, calculations of the change in the volume mean relative concentration as a function of the Fom number have been performed for the internal problem (Fom = 100) and the mixed diffusion problem (Fom = 10). It has been shown that the maximum effect of the influence of the convective component is observed for the intradiffusion problem.