A graph-theory based directed network feature for thermal anisotropy

Abstract

The effective thermal conductivity of a granular material varies with the predominant heat transfers direction. The anisotropic effective thermal conductivity is known to be dominated by the microstructure in a dry material. However, no microstructural parameters that are well related to thermal anisotropy have been proposed. After analysing the heat transfer mechanisms at the particle scale, this work constructs new directed weighted thermal networks for both lattice and randomly distributed sphere packings, by considering particles as nodes and local heat transfer paths with thermal resistance as directed edges. With the implementation of graph theory to the directed weighted thermal networks, the shortest preferential heat transfer paths between nodes paired at opposite faces of a sample across the driving temperature gradient direction are identified. Based on the shortest heat transfer paths, a new sample-scale feature named “directed network thermal resistance” is computed for each sample. This new parameter accounts for particle connectivity, interparticle contact orientation and contact quality simultaneously. After computing the effective thermal conductivity of each sample in different directions using a weighted thermal network model, it is found that directed network thermal resistance is inversely proportional to anisotropic effective thermal conductivity.