The methods so far applied to determine the bound water diffusion coefficient in wood do not provide credible results on this coefficient as well as on the boundary condition. An alternative approach based on the concept of solving the inverse transfer problems was recently applied. Two European species were investigated in the present study. A series of sorption experiments was performed and followed by the numerical identification of the coefficients. Several case studies were carried out for the constant and bound water content dependent diffusion coefficients. The obtained results were validated by comparison to a set of experimental data.
In this work, a relaxation term was added to the convective boundary condition to increase the accuracy of the transient bound water diffusion modeling in wood. The implemented term accounts for a relaxation time constant in the equilibrium moisture content. The inverse finite element analysis approach was used to determine the values of all coefficients of the modified diffusion model. This procedure was performed for beech wood (Fagus sylvatica L.) in the radial and longitudinal directions. The experimental data obtained by Perré et al. (2007) for transient diffusion configurations were used here. The accurate control of moist air parameters and the improved procedure for mass measurements of a sample during sorption experiments were used. The influence of the modification of the boundary condition on accuracy of diffusion modeling was analyzed. Weight function
List of symbolsGreek symbols C Points located at the two boundary sides of the domain (two points in the onedimensional model) r Surface emission coefficient (m/s) s Relaxation time (s) X Geometric domain of the R 1 space X Geometric domain of the R 1 space with the boundary
The hygroscopic properties of thermally modified wood have been studied in terms of adsorption and desorption processes. Poplar ( Populus spp.) and European beech ( Fagus sylvatica L.) were in focus. The obtained isotherms were parameterized with the models of HailwoodHorrobin, Guggenheim-Anderson-deBoer, generalized D ' Arcy and Watt, and Yanniotis and Blahovec. The changes in equilibrium moisture content (EMC) were quantified, and the accessibility of water vapor to the sorption sites was determined. The monolayer and multilayer sorption was studied and the sorption isotherms were classified. All sorption isotherms were type II, and the type was not changed after the modification. The monolayer sorption was found to be responsible for the reduction in EMC after thermal modification. The observed increase in the hystere sis coefficient was explained by the reorganization of the wood ultrastructure.
An alternative approach to determining the bound water diffusion coefficient is proposed. It comprises a method for solving the inverse diffusion problem, an improved algorithm for the bound-constrained optimization as well as an alternative submodel for the diffusion coefficient's dependency on the bound water content. Identification of the diffusion coefficient for Scots pine wood (Pinus sylvestris L.) using the proposed inverse approach is presented. The accuracy of predicting the diffusion process with the use of the coefficient values determined by traditional sorption methods as well as by the inverse modeling approach is quantified. The similarity approach is used and the local and global relative errors are calculated. The results show that the inverse method provides valuable data on the bound water diffusion coefficient as well as on the boundary condition. The results of the identification can significantly improve the accuracy of mass transfer modeling as studied for drying processes in wood. Local relative error (%) e 2 Global relative error (%) E Reduced bound water content (−) lHalf-thickness (m) M Water content (kg/kg dry base ) M ∞ Equilibrium water content (kg/kg dry base ) M 0 Initial water content (kg/kg dry base ) M(t)Global water content in selected time instants (kg/kg dry base ) M exp (t) Experimental water content (kg/kg dry base ) M pred (t) Predicted water content (kg/kg dry base ) NT Number of time intervals in computation NT exp Number of time intervals in experiment S Objective function t Time (s) t F Final time (s) w i Weight function x Space dimension (m)Greek symbols Points located at the two boundary sides of the domain (two points in the one-dimensional model) σ Surface emission coefficient (m/s) Geometric domain of the R 1 space Geometric domain of the R 1 space with the boundary
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.