Optimum Average Diffusion Coefficient: An Objective Index in Description of Wood Drying Data
Keywords:Drying, diffusion-coefficient, optimization, Fourier series, golden section search
AbstractIn the existing schemes for estimating average diffusion coefficients, the equations are approximate because of the use of only the first term in an infinite series and the subjective nature of the methods. The method described here takes into account all data points, and provides a systematic and objective way of analyzing wood drying data. Using the formula of the theoretical Fourier series solution, a series of theoretical Ē values, representing the fractional amounts of water in wood during drying, were coupled with experimental data, and the sum of squares minimized. The method sets up upper and lower expected bounds for diffusion coefficients, and then locates the optimum average diffusion coefficient by using a FORTRAN program based on the golden section search principle. Using data from a previous drying study on six hardwoods, it was found that the theoretical curves in the longitudinal direction fitted the data points satisfactorily. This suggests that diffusion coefficients in the longitudinal direction are virtually constant. This method, however, depends upon the assumption that the value of Ē at the surface drops immediately to zero as drying starts.
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