Implementation of a relaxation equilibrium term in the convective boundary condition for a better representation of the transient bound water diffusion in wood

Abstract

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

Integration of experimental and computational methods for identifying geometric, thermal and diffusive properties of biomaterials

“…In the case of traditional methods for determination of the coefficient of water diffusion for wood, based on the boundary condition of the first kind, the local relative error values were reaching 60%. In the case of traditional methods based on the convective boundary condition, the global relative error values approached 20% (Olek and Weres, 2007;Olek et al, 2011).…”

“…In the case of water sorption and desorption another setup was built to obtain data (Olek et al, , 2011Olek and Weres, 2007). In this setup, air of controlled temperature and relative humidity flows around a sample of a product of known and uniform initial moisture content.…”

“…Uncertainty of such modelling depends on the adequacy and reliability of data used to represent the geometric, thermal and diffusive properties of biomaterials in mathematical structures. In the case of heating, cooling, drying, and rewetting it has generally been accepted that the 3D geometry, thermal conductivity, specific heat, coefficient of water diffusion, equilibrium water content and convective heat and water transfer coefficients in the boundary layer are the most important quantities affecting the accuracy of modelling (Chen et al, 2009;Fanta et al, 2014;Olek et al, 2011;Nowakowski et al, 2013;Perré and Turner, 2007;Weres and Jayas, 1994;Weres and Olek, 2005;Wu et al, 2004). Experimental approaches to determine the physical properties listed above have not been effective.…”

“…Inverse and direct finite element analysis based on the algorithms of identification of thermal and diffusive properties of investigated products and prediction of the product behaviour during heat and water transport processes (Nguyen and Boyce, 2011;Olek et al, 2005Olek et al, , 2011Ruggiero et al, 2011;Siatkowski et al, 2010a;Weres and Olek, 2005;Weres et al, 2009). Problems of estimation of unknown or unreliable property values were discussed in the papers, and further research is needed to improve the algorithms for reducing the uncertainty of mathematical modelling.…”

Computer-aided identification of the water diffusion coefficient for maize kernels dried in a thin layer

“…Computer simulation is helpful in designing such operations -it enables users to quickly assess various options of the drying and storing processes. However, satisfactory simulation results can only be achieved when based on a mathematical model supplemented by appropriate, adequate and reliable values of physical properties of the investigated system (Erbay and Icier, 2010;Olek et al, 2011). In analysing the maize kernel drying processes the falling-rate period is often assumed as the only period, and the internal diffusion of water plays a dominant role in the drying process.…”