Two-Dimensional Finite Element Heat Transfer Model of Softwood. Part I. Effective Thermal Conductivity

Abstract

The anisotropy of wood complicates solution of heat and mass transfer problems that require analyses be based on fundamental material properties of the wood structure. Most heat transfer models use average thermal properties across either the radial or tangential direction and do not differentiate the effects of cellular alignment, earlywood/latewood differences, or ring orientation. A model that considers these basic structural characteristics would be more accurate than most models in the literature, which do not consider the anatomical structure of wood. The two-dimensional finite element model described here was developed to determine the effective thermal conductivity as a function of cell alignment and cell porosity by modeling the softwood cell structure in either a pure radial or pure tangential orientation. This paper presents the results predicted from the cellular model, from which a new nonlinear regression equation for radial or tangential effective thermal conductivities is determined as a function of density (porosity). The results will be applied to a two-dimensional softwood board model for transient thermal analysis (Part II). Subsequent papers in this series apply and adapt this model to various lumber orientation and sizes and to wood at various moisture contents (Part III and IV).