A theoretical expression for drying time of thin lumber

An analytical expression for the drying time of thin lumber is derived, based on a method presented in this study. The laws of moisture content change in wood as function of mass transfer are used for the theoretical approach. The diffusion equation for moisture content is set up for a three-dimensional block of lumber based on the assumption of uniform initial distribution of moisture throughout the specimen. The boundary condition stipulates that the moisture gradient at the boundary is proportional to the deviation of the moisture content of the slab from the equilibrium value at that temperature. These conditions are used to derive an analytical expression for the time required to get from an initial moisture distribution to a desired final moisture content of thin lumber. For a sample calculation, the result of drying time agrees within 10% with the prediction of previously published analytical formulas for the drying curve.