Transfer Phenomena During the Drying of a Shrinkable Product: Modeling and Simulation

Drying is an essential step in many production and treatment processes. The control of dry product quality is more and more required in order to insure a good using or handling of the material. Then new mathematical models should integer these requirements and consider the phenomena of shrinkage. This work gives a mathematical formulation of the different transfer phenomena (heat, mass, and momentum) which describe the process. The model tries to be relatively simple but sufficiently complete in order to predict and analyze the distribution of the temperature, the moisture, the strain, and the stress during the process. The product is considered as a two-phase, homogeneous, hygroscopic, isotropic, and highly shrinkable medium. The thickness of the sample is sufficiently small in order to consider the fluxes of heat and mass unidirectional. The principal equations of the model are written in a Lagrangian formulation because of the shrinkage behavior. The model is solved numerically by a finite difference method. A validation of the results is achieved by the comparison of the numerical and experimental data. The simulation allows the derivation of the time and space evolution of several parameters: temperature, moisture, strain, and stress.