Design of Two-Dimensional Transient Circular Thermal Cloaks with Imperfect Interfaces

In this paper, analytic modeling for the design of a transient thermal invisibility cloak with imperfect interfaces is presented together with numerical simulations. In contrast to steady-state conditions, it is shown that an object can only be made partially invisible under a transient-state condition with either ideal or imperfect interfaces. The thermal visibility of an object to the external region can be optimally suppressed under certain conditions referred to as the "weak invisibility conditions" for the transient response, which are different from the "strong invisibility conditions" that can completely conceal an object in a steady state. In the formulation, a homogeneous metamaterial with constant volumetric heat capacity and constant anisotropic conductivity tensor is employed. It can be demonstrated that the interface's bonding conditions will have a significant effect on the design of metamaterials. Two typical types of imperfect interfaces, referred to as low-conductivity- and high-conductivity-type interfaces, are considered. Conditions, that render an object mostly undetectable, are analytically found and expressed in simple forms under quasi-static approximations. Within the quasi-static limit, the thermal localization in the target region can be tuned with the anisotropy of the conductivity tensor. Thermal shielding or concentrating effects in the target region are exemplified based on finite element simulations to demonstrate the manipulation of heat flux in the target region. The present findings make new advances in theoretical fundamentals and numerical simulations on the effect of the imperfect interface in the transient regime and can serve as guidelines in the design of thermal metamaterials through the entire conduction process.