Reducing spatial dimensionality in a model of moisture diffusion in a solid material

A model of the moisture movement in solid wood under isothermal conditions taking into consideration coating (insulation) of the surface of the material, is presented in a 2-D-in-space formulation. The validity of using a corresponding 1-D model on a 2-D problem is investigated. A measure of reliability of the 1-D model is introduced. This paper presents a new technique, which adjusts the width of a material as well as the degree of coating of the edges, to ensure the relative error of the problem solution is less than the required, resulting from reducing the model from 2-D to 1-D-in-space. This technique is based on the computer simulation of 2-D diffusion to estimate the reliability of the corresponding 1-D diffusion model.