Thermal transparency of tunable thermal metamaterials composed of composite cylinder or sphere with imperfect interface

We present an exact analysis of tunable thermal metamaterials made of composite cylinder or sphere with imperfect interface effects. The composite cylinder or sphere is composed of an isotropic core coated with a layer of curvilinearly anisotropic material. The interface between the core and the anisotropic layer could be imperfectly bonded, either with low-conductivity or high-conductivity type of interface. Based on an effective medium theory of neutral inclusion, we show that it is possible to balance in different ways among the material and geometric parameters, together with bonding parameters, so that the composite cylinder or sphere is thermally transparent to the background medium. We show how these parameters will affect the thermal intensity within our targeted region, either greatly enhanced or shielded. Remarkably, we show that there exists an interesting link between the core conductivity and the imperfect interface parameter for either type of imperfect interface, highlighting how the effect of core conductivity can be correlated exactly to the effect of bonding imperfectness. We also validate our analytic results with numerical simulations based on finite element calculations. Our findings provide insightful guidance towards the understanding of thermal transport mechanism across imperfect interfaces in thermal metamaterials.