Three-dimensional numerical analysis of water transfer in wood: determination of an expression for the effective mass diffusivity

Abstract

The objective of this article is to determine an expression for the effective mass diffusivity related to the description of wood drying using a diffusion model and experimental data. With this objective, a three-dimensional numerical solution of diffusion equation for the parallelepiped, with convective boundary condition, was used to describe the drying process. For the adopted diffusion model, the convective mass transfer coefficient h was considered constant. The effective mass diffusivity D was considered as a function of the local moisture content, and several expressions were tested to describe the process. To this end, the numerical solution was coupled to an optimizer based on the inverse method, which determines the process parameters D and h using an experimental dataset. For both temperatures of the drying air studied in this article (40 and 80°C), the results obtained by considering the variable effective mass diffusivity are better than those obtained when considering such parameter with a value constant. In addition, with the results for D and h obtained by optimization, the drying kinetics was simulated with success. List of symbols A, BCoefficients of the discretized diffusion equation (dimensionless) DEffective mass diffusivity (m 2 s -1 ) hConvective mass transfer coefficient (m s -1 ) MLocal moisture content at instant t (db, kg kg -1 ) MAverage moisture content at instant t (db, kg kg -1 ) M 0 Initial moisture content (db, kg kg -1 ) M 1 Equilibrium moisture content (db, kg kg -1 )

Inverse Estimation of Effective Moisture Diffusivity in Lumber during Drying Using Genetic Algorithms

“…The multiple coefficient of correlations (R 2 ) value of 0.9 to 1.0 is considered a good regression fit to the experimental data for estimating the diffusivity values obtained in this work. This observation is in agreement with the results of Silva et al (2013), and indicated that Eq. 8 represented the relationship between moisture diffusivity and moisture content as rational.…”

“…This figure reveals an expected result, i.e., effective moisture diffusivity increased with increasing temperature and with increasing moisture content. This trend of diffusivity was also noticed by Zhou et al (2011) and Silva et al (2013).…”

“…According to Silva et al (2013), the drying process, in many occasions, is considered isothermal because the thermal diffusivity is greater than the effective moisture diffusivity. This assumption was used in the present work.…”

“…Although the empirical models (Zhan et al 2007) and permeation models (Salin 2008) provide an approach in modeling, diffusion models (Dincer and Dost 1996;Silva et al 2011Silva et al , 2013Zhao et al 2016a) have been used frequently to describe the drying process. To consider liquid diffusion as the only mechanism of water mass transfer inside the lumber is a simplification of the model.…”

“…Alternatively, Olek et al (2005) optimized the inverse procedure to identify the diffusion coefficient. Eriksson et al (2006) and Silva et al (2011Silva et al ( , 2013 successfully used this technique to determine effective moisture diffusivity in wood. Thus, the optimization of algorithms applied in the solving process may be crucial.…”