Reliability of One Dimensional Model of Moisture Diffusion in Wood

A model of the moisture diffusion in wood under isothermal conditions taking into con- sideration coating of the surface of a specimen is presented in a 2-D-in-space formulation. A re- liability of a corresponding 1-D model is investigated for a simulation of moisture movement in 2-D medium. This paper presents a technique to determine the width as well as the degree of edges coating of the specimen making the 1-D model relevant for 2-D medium. This technique bases on the computer simulation of 2-D moisture diffusion to estimate the reliability of the corresponding 1-D model. In the technique, approximate coefficients of the diffusion and surface emission may be employed if accurate values of these coefficients are unknown. Wood drying is a highly energy intensive process of some industrial significance. It is a process whereby the moisture moves from an area of higher moisture content to an area of lower moisture content within the medium. When the surface moisture evaporates from the sides or ends, moisture moves from interior toward these locations. This process continues until the wood reaches its equilibrium moisture content with the ambient air climate (Skaar, 1988; Siau, 1984). Mathematical modelling is gaining an increasing acceptance within the timber dry- ing industry and the use of mathematical simulators, which describe the complex heat and mass transfer phenomena at a fundamental level, can provide important information which could be used in both the design and optimisation of the kiln (Rosen, 1987; Siau, 1984; Turner and Mujumdar, 1997). From a mathematical point of view, the moisture transport process can be treated as a diffusion problem based on the Fick's second law. A model of the wood drying, under ∗ This research was partially supported by Lithuanian State Science and Studies Foundation Grant

[1]  R. Holley,et al.  Diffusion of Acetic and Propionic Acids from Chitosan-based Antimicrobial Packaging Films , 2000 .

[2]  J. Weres,et al.  IDENTIFICATION OF MATHEMATICAL MODEL COEFFICIENTS IN THE ANALYSIS OF THE HEAT AND MASS TRANSPORT IN WOOD , 2000 .

[3]  Edward Hensel,et al.  Inverse theory and applications for engineers , 1991 .

[4]  W. K. Yeung,et al.  Second-order finite difference approximation for inverse determination of thermal conductivity , 1996 .

[5]  C. Skaar.  Wood-Water Relations , 1988, Springer Series in Wood Science.

[6]  Ian Turner,et al.  A 3-D version of TransPore: a comprehensive heat and mass transfer computational model for simulating the drying of porous media , 1999 .

[7]  T. Kudra.  Mathematical Modeling and Numerical Techniques in Drying Technology , 1997 .

[8]  A. Hukka,et al.  The Effective Diffusion Coefficient and Mass Transfer Coefficient of Nordic Softwoods as Calculated from Direct Drying Experiments , 1999 .

[9]  John Finn Siau,et al.  Transport Processes in Wood , 1984, Springer Series in Wood Science.

[10]  Jesper Arfvidsson,et al.  Measurement and Evaluation of Moisture Transport Coefficients During Drying of Wood , 1997 .

[11]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[12]  F. Ivanauskas,et al.  The Influence of Wood Specimen Surface Coating on Moisture Movement during Drying , 2002 .

[13]  M. Maeda,et al.  [Heat conduction]. , 1972, Kango kyoshitsu. [Nursing classroom].

[14]  W. Simpson.  Determination and use of moisture diffusion coefficient to characterize drying of northern red oak (Quercus rubra) , 1993, Wood Science and Technology.

[15]  I. Dincer,et al.  A modelling study for moisture diffusivities and moisture transfer coefficients in drying of solid objects , 1996 .

[16]  J. Salin,et al.  On Determination of Surface Emission Factors in Wood Drying , 1993 .

[17]  W. Simpson,et al.  SOLUTIONS OF DIFFUSION EQUATION WITH CONSTANT DIFFUSION AND SURFACE EMISSION COEFFICIENTS , 1997 .

[18]  M. A. Tung,et al.  Vapor Pressure of Allyl Isothiocyanate and Its Transport in PVDC/PVC Copolymer Packaging Film , 1997 .

[19]  Cheng-Hung Huang,et al.  Numerical algorithm for estimating temperature-dependent thermal conductivity , 1996 .