Thermal conductivity of wood at angles to the principal anatomical directions

For an orthotropic material, the thermal conductivity in arbitrary directions follows from the conductivities in the principal material directions by rotation of the thermal conductivity tensor. Thus, in case of orthotropy, three analytical relations describe the thermal conductivity of wood between the principal anatomical directions depending on the rotation angle. Experiments were made to prove if these functions hold for wood. Thermal conductivity measurements were performed in the principal anatomical directions of European oak (Quercus sp.), European beech (Fagus sylvatica) and Norway spruce (Picea abies) and at angles to the grain in the longitudinal-radial plane. Test instrument was a single-specimen guarded hot plate apparatus. Experimental data for thermal conductivity at angles to the grain were compared with values predicted from the conductivities in the principal anatomical directions using the relations for rotation of the thermal conductivity tensor. Excellent agreement between the experimental data and the theoretical curve in the longitudinal-radial plane was obtained. It is concluded that thermal conductivity of wood at angles to the principal anatomical directions can be described by transformation equations derived by the respective rotation of the thermal conductivity tensor. This shows that wood exhibits orthotropic symmetry of the thermal conduction behaviour.