Exact thermal invisibility for spherical cloaks with imperfect interfaces

We present new exact results for the design of spherical thermal cloaks with the effect of imperfect interfaces. Thermal metamaterials are of great importance in advanced energy control and management. However, nearly all relevant studies considered that interfaces are ideally perfect. In principle, bonding imperfectness always exists at interfaces, and this effect is particularly important in small-length scales. Here, we will examine in detail the effect of bonding imperfectness on the performance of thermal functionality. The thermal metamaterial is made of a homogeneous spherically anisotropic material with a constant conductivity tensor. Low conductivity- and high conductivity-type interfaces are considered. We show how the anisotropic layer, together with the effect of imperfect bonding interfaces, can be made thermally invisible. An exact condition for thermal invisibility is derived in a simple algebraic form. Conditions for thermal shielding or enhancement are theoretically analyzed and numerically exemplified, in which relevant material and geometric parameters can be tuned to achieve the functionality. In addition, numerical simulations based on finite element calculations are carried out to validate our analytic solutions. The present findings offer a general guideline in the design of spherical thermal metamaterials with imperfect interfaces.