Nonlocal thermal Willis coupling in laminated conductors

TL;DR

This paper demonstrates nonlocal thermal Willis coupling in laminated conductors through homogenization, revealing macroscopic thermal bianisotropy with direction-dependent impedance, advancing understanding of thermal metamaterials.

Contribution

First explicit demonstration of spatial nonlocality in thermal Willis coupling using multiple homogenization methods in laminated conductors.

Findings

Consistent nonlocal cross-coupling terms from three homogenization approaches

Direction-dependent thermal impedance as a signature of thermal bianisotropy

Clarification of the roles of spatial asymmetry and averaging in nonlocal effects

Abstract

Building on Willis' homogenization framework, recent work has revealed that heterogeneous conductors exhibit macroscopic thermal bianisotropy, in which the macroscopic heat flux and entropy are nonlocally coupled to both temperature and temperature gradient. Existing numerical examples, however, are limited to the subwavelength regime. Here, we provide the first explicit demonstration of this spatial nonlocality by computing the effective kernels of a periodic laminate using three independent homogenization methods. The three approaches yield consistent nonlocal cross-coupling terms, clarifying the roles of spatial asymmetry and averaging choice. We also calculate the corresponding thermal impedance and show that it is direction-dependent, highlighting a physical signature of thermal bianisotropy relevant to thermal metamaterials.