Gain and Loss of Thermal Conductivity via Geometric Rearrangement in Multiscale Media

The conventional approach to enhancing the thermal performance of a material involves dispersing a more conductive phase within a less conductive matrix, typically leading to an increase in thermal conductivity. However, two-dimensional (2-D) analytical studies have shown that in polydisperse, densely packed media with high volume fractions, the intricate geometry of the microstructure can lead to counterintuitive behavior of the thermal conductivity. This paper addresses this issue by employing a versatile numerical framework that integrates the theory of reiterated homogenization with the finite element method. The distinguished approach enables the systematic analysis of complex three-dimensional geometries, providing numerical evidence for new aspects of heat transfer in multiscale heterogeneous media that were previously only theorized in simpler 2-D systems. Our findings reveal that such geometric rearrangement can significantly modulate effective thermal conductivity, offering a strategy for the thermal optimization of materials in mass-constrained aerospace vehicles.