Breaking efficiency limit of thermal concentrators by conductivity couplings

The concentrating efficiency of a thermal concentrator can be reflected in the ratio of its interior to exterior temperature gradients, which, however, has an upper limit in existing schemes. Here, we manage to break this upper limit by considering the couplings of thermal conductivities and improve the concentrating efficiency of thermal concentrators. For this purpose, we first discuss a monolayer scheme with an isotropic thermal conductivity, which can break the upper limit but is still restricted by its geometric configuration. To go further, we explore another degree of freedom by considering the monolayer scheme with an anisotropic thermal conductivity or by adding the second shell with an isotropic thermal conductivity, thereby making the concentrating efficiency completely free from the geometric configuration. Nevertheless, apparent negative thermal conductivities are required, and we resort to external heat sources realizing the same effect without violating the second law of thermodynamics. Finite-element simulations are performed to confirm the theoretical predictions, and experimental suggestions are also provided to improve feasibility. These results may have potential applications for thermal camouflage and provide guidance to other diffusive systems such as static magnetic fields and dc current fields for achieving similar behaviors.