Modeling conductive thermal transport in three-dimensional fibrous media with fiber-to-fiber contacts

Understanding heat transfers in fibrous materials, particularly conduction, is a major challenge due to their heterogeneous and multiscale nature, and the unknown contribution of fiber-to-fiber contacts. In most previous modeling studies, the existence of thermal contact resistance is not considered, and the computational complexity limits the size of simulated samples, which often leads to imprecise or inaccurate predictions. The same problem arises when considering electrical conduction through fibrous materials. In this work, we describe a computationally efficient simulation approach based on a multinodal representation to analyze the steady-state heat conduction through the solid structure in numerically generated three-dimensional fibrous networks, including contact resistance. We show that the solid conductivity in these networks is governed by a master curve that depends on a single parameter: a characteristic ratio representing the interplay between the intrinsic fiber conductivity and contact resistance as well as the influence of other geometric parameters, which numerically validates previous theoretical studies. However, we observe a deviation to this established theory for poorly connected networks. We derive an expression for a correction factor, considering the influence of correlations between fiber temperatures, and we then find good agreement with our simulation data. Our results demonstrate that the solid conductivity can be fully predicted based on geometric quantities, regardless of the extent of network connectivity, thus generalizing previous studies on this topic. This work, contributing to improve our understanding of conductive heat transport in fibrous media, may prove useful in the development of accurate predictive models and optimization strategies for fibrous insulation materials.