Analytical equations for predicting effective thermal conductivity in laminated wood composites

This paper presents an analytical modeling approach to predict the effective in-plane and out-of-plane thermal conductivities of laminated wood composite products such as Cross-Laminated Timber (CLT). Considering wood’s orthotropic nature, having models that could be used to estimate the effective thermal conductivity properties of laminated wood products in various directions becomes essential for understanding the coupling between mechanical and thermal properties, as well as predicting the dimensional stability of large wood composite panels. For this purpose, analytical thermal conductivity equations were derived in three orthogonal directions, considering different properties of wood along its orthotropic directions, following Fourier’s Law. The derived equations were then applied to different CLT panel products and results were compared to assess their accuracy. As CLT panels may be produced without edge gluing, two scenarios were investigated to understand the effect of edge gluing on thermal conductivity of such panels. First, the presence of adhesive between timber layers was ignored (i.e. not edge-glued panels); second, adhesive and its thickness were included. Results demonstrated the reasonable accuracy of the proposed approach in predicting the thermal conductivity of CLT panels made with different gluing methods. The modeling of imperfect bonds and air gaps is also briefly discussed.