An Improved Mathematical Simulation of the Coupled Diffusion of Moisture and Heat in Wool Fabric

An improved mathematical model that takes into account the water vapor sorption mechanisms of wool fiber is developed to describe and predict the coupled heat and moisture transport in wool fabrics. The two-stage moisture sorption of wool is handled by a diffusion equation with two sets of variable water vapor diffusion coefficients in the fibers. The improved model is solved numerically by the finite difference method. Predictions from the new model are compared with those from the Nordon-David model and the previous two-stage model, and with experimental observations. Processes of moisture transfer in the air and in fibers and their interaction with heat transfer under humidity transient conditions are illustrated by a series of 3D diagrams.