Computation of the effective conductivity of unidirectional fibrous composites with an interfacial thermal resistance

We present numerical calculations of the effective thermal conductivity of unidirectional fibrous composite materials with an interfacial thermal resistance between the continuous and dispersed components. We first develop a continuous variational formulation of the heat conduction problem and then apply the method of homogenization to derive the appropriate cell problem. Next, we solve the latter using the finite element method and present and validate effective conductivity results for ordered composites. Finally, to highlight the wide applicability of our approach, we also present a posteriori contact conductance results for a disordered composite whose microstructure is based on a real optical micrograph.