Application of the 2D diamond scheme to predict the macroscopic thermal conductivity of a three-phase composite with local anisotropy directions

Abstract

In this contribution, we are interested in the prediction of the macroscopic thermal conductivity of three-phasic composite materials such as wood fibers. The main idea is to make use of up-scaling such as homogenization to link the pore scale and the sample scale. The studied wood species incorporates three phases: the air, the lumen or matrix and the fibers. Image processing is preformed on a tomographic acquisition with high resolution of some micrometers. It serves to identify the present phases and generates the morphology mesh. The 2D diamond scheme is employed to discretize Fourier's model posed on the segmented morphology. The resulting algorithm is validated using an exact solution. Optimal numerical convergence rates of second order are recorded. The thermal conductivity is therefore estimated following the 2D orthotropic directions. An emphasis is set on the impact of the orientation of fibers on this thermal property.