Coupling Theory for Temperature-Independent Thermal Conductivities: Thermal Correlated Self-Fixing

Abstract

It is a challenge to design intelligent thermal metamaterials due to the lack of suitable theories. Here we propose a kind of intelligent thermal metamaterials by investigating a core-shell structure, where both the core and shell have an anisotropic thermal conductivity. We solve Laplace’s equation for deriving the equivalent thermal conductivity of the core-shell structure. Amazingly, the solution gives two coupling relations of conductivity tensors between the core and shell, which cause the whole core-shell structure to counter-intuitively self-fix a constant isotropic conductivity even when the area or volume fraction of core changes within the full range in two or three dimensions. The theoretical findings on fraction-independent properties are in sharp contrast to those predicted by the well-known effective medium theories, and they are further confirmed with our laboratory experiments and computer simulations. This chapter offers two coupling relations for designing intelligent thermal metamaterials, and they are not only helpful for thermal stabilization or camouflage/illusion, but also offer hints on how to achieve similar metamaterials in other fields.