Mathematical Modeling of the Diffusion of Water in Wood During Drying
Keywords:Kiln drying, diffusion, air velocity, humidity, solar power
The drying of lumber was modeled by the diffusion of water in wood, according to Fick's second law. In the model the following assumptions were made: (1) Moisture content is the driving force; (2) the diffusion coefficient is a constant value above the fiber saturation point and one-fourth that value below the fiber saturation point; (3) equilibrium exists between the moisture content at the wood surface and the film of air adjacent to the surface; (4) moisture movement from the film to the bulk air stream occurs by film mass transfer. Five independent variables—half thickness of the board, species factor (density-diffusivity), temperature, relative humidity, and air velocity—were found to influence the drying process. This study reveals that variable interactions are important considerations when one wishes to predict drying times.
Using red oak and constant values for lumber thickness and kiln air velocity, three cases were modeled to illustrate the potential for improved operation. The first case follows temperature and humidity schedules typical of current kiln operations, forming a basis for comparison. In the second case, a solar-powered kiln produces harmonic variations in temperature and relative humidity. The most favorable drying conditions occur in the late afternoon, the least favorable before dawn. Slower drying with nightly relaxation of the moisture profile may produce a board with few defects. In the final study, temperature and maximum permissible drying rate are specified, with relative humidity chosen according to the model. This case produced the most rapid drying, yet has milder moisture gradients than the base case. The results of these studies show the possibility of producing a high-quality product at low cost in a solar-powered dryer, or optimizing drying schedules to reduce drying time and increase product quality.
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