Modeling of Coupled Moisture and Heat Transfer During Wood Drying

Development of an accurate mathematical model of sufficient generality to evaluate drying processes in materials having diverse moisture transport properties is proposed. The process of wood drying is interpreted as simultaneous heat and moisture transfer with local thermodynamic equilibrium at each point within the timber. The model is a mathematical one treating wood as a continuous and homogenous medium not trying to explain the several parallel physical mechanisms of moisture transport actually taking place in the internal structure of wood. The transfer of moisture from a wooden surface and the corresponding mass transfer coefficient in relation to the heat transfer coefficient is considered. The Finite Element Method is used for numerical approach in the paper. The predicted values by the theoretical model are compared with experimental data taken under actual drying conditions to demonstrate the efficiency of the predictive model. INTRODUCTION In hygroscopic porous material like wood, mathematical models describing moisture and heat movements may be used to facilitate experimental testing and to explain the physical mechanisms underlying such mass transfer processes. A number of theoretical models have been suggested in wood drying (e.g. Chen and Pei 1989) but they are not completely applicative to simulate real drying processes as seen in industry. The process of wood drying can be interpreted as simultaneous heat and moisture transfer with local thermodynamic equilibrium at each point within the timber. Drying of wood is in its nature a unsteady-state non-isothermal diffusion of heat and moisture, where temperature gradients may counteract with the moisture gradient. For a theoretical description of these phenomena, thermodynamic models seem to be most suitable. Although unsteady-state non-isothermal experiments have been conducted (e.g. Avramidis et al. 1994), we are convinced that practical solutions of mathematical models that couple moisture and heat transfer with inhomogeneous material, combined with an experimental verification is still lacking (Irudayaraj et al. 1990). A considerable volume of research has been carried out regarding modeling moisture and heat transfer in materials like polymers, wood, or agricultural products (e.g. Parrauffe and Mujumdar 1988, Salin 1991, Kamke and Vanek 1994). For wood, model developments have been based on either a mechanistic approach with the transfer phenomena derived from Fick’s and Fourier’s laws, or on the principles of thermodynamics and entropy production. These models may be divided into three categories: (a) diffusion models (Rosen 1987), (b) models based on transport properties (Plumb et al. 1985, Stanish et al. 1986) and (c) models based on both the transport properties and the physiological properties of wood related to drying (Pang 1996, 1997). The modeling of moisture fluxes under unsteadystate non-isothermal conditions has been noticeably absent in literature (Avramidis et al. 1994), although the theory behind it was proposed twenty years ago (Siau 1983). Heat and moisture transfer should be considering as coupled processes; the thermally induced mass transfer, Soret effect (Avramidis et al. 1994, Siau 1984) and the heat flux resulting from moisture diffusion, the Duffour effect (Siau 1992), should be taken into account. Luikov (1966) and in much details Whitaker (1977) developed a unique approach that describes the simultaneously heat and moisture transfer in drying 8 International IUFRO Wood Drying Conference 2003 373 processes, based on irreversible thermodynamic processes. The difficulty with the mathematical formulation is the number of combined transfer mechanisms, the interdependencies among these mechanisms, and the different variables controlling them. MATERIAL AND METHOD Diffusion equations are used to describe moisture and heat transport phenomena in wood. Moisture content and temperature gradient are set as driving forces, since all the other possible factors related to moisture content are applicable only in the hygroscopic region. Thus, the model is purely mathematic treating wood as a continuous and homogenous medium, without explaining those physical mechanisms associated with the moisture transport that take place simultaneously inside wood. The three-dimensional transfer of heat and moisture is generally described as follows: dt(w)=div(D grad(w)) dt(T)=1/cρ div(λ grad(T)), where ρ is wood density, c specific heat, T temperature, t time, λ thermal conductivity and D moisture diffusion coefficient. Non-isothermal diffusion is analysed by using a thermodynamic model with the gradients of both water potential and temperature considered. The proposed equations are inspired by Siau and Avramidis (1992), who found with these equations the best agreement between the experimental fluxes and thermodynamic model. The differentiated unsteady-state equations for twodimensional cross-section are