Abstract
A finite difference solution, based on the “double sweep” method, has been found for solving the non-linear differential equations which describe coupled diffusion of heat and mass (moisture) in hygroscopic textile materials. In addition to the diffusion equations, a rate equation has been introduced describing the rate of exchange of moisture between the solid (textile fibres) and the gas phase (pore space). A numerical application of the theory has been made using wool as an example for the hygroscopic material and it is shown that, similar to forced convective transfer, transfer of moisture from air to the wool and from the wool to air are not symmetrical processes. The magnitude of the error caused by neglecting the rate of transfer of moisture between the solid and gaseous phases as compared to the time scale of the diffusional processes is discussed and shown to depend on the physical dimensions of the slab. Examples are also given of positive and negative temperature and concentration fronts which may be set up in the slab.
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