Modeling of Heat- and Mass-Transfer Processes during Convective Drying of Cotton Fabrics

A mathematical model of heat and mass transfer in the process of convective drying of fabric in chemical technology of its finishing is presented. The equations are written for thermophysical variables averaged over the sample volume. The model controls the state of water in a capillary-porous system and takes into account the flow of the liquid phase in a bound state. Free water is motionless. Changes in the concentration of free water can occur due to phase transitions at the boundaries of the liquid and gaseous phases. The mathematical model can be considered as a variant of the well-known model of diffusion heat and mass transfer by A.V. Lykova with certain additions. In addition to the equations of moisture conductivity, thermal conductivity, and total pressure, the model includes an equation for the concentration of the vapor component of the gaseous phase. For local values of the diffusion coefficient of the liquid phase and the phase transition criterion, analytical dependences of these values on moisture content and temperature are used. The mathematical model was investigated numerically using the finite difference method. The model was validated using laboratory experiment data for cotton fabric samples of different densities, thicknesses, and weaving methods. Calculations of drying curves using the proposed model showed satisfactory agreement with experimental dependences. The contribution of two mass-transfer mechanisms associated with phase transitions and capillary flows of the liquid phase to the tissue drying process was investigated.