A Thermal-Electric Cloak via Nonlinear Transformation

A thermal-electric invisibility cloaking is designed by a nonlinear transformation, which can guide both electric current and heat flux around the concealed region and restore their original diffusion directions. Compared with previous thermal-electric cloaks designed by linear transformation, the proposed thermal-electric cloak by nonlinear transformation can introduce some parameters during the coordinate transformations, thus providing more degrees of freedom for subsequent material design and selection. As an example, we further design a 2
N
-layered structure consisting of four isotropic homogeneous materials for implementing the proposed cloak, which shows expected good cloaking effect for both electric current and heat flux by numerical simulations. The simulated results notably shows that the proposed thermal-electric cloak can manipulate the waves without any agitation either the highly conductive material placed in a vacuum or waves can generate from any other direction, which verify the expected thermal-electric invisibility cloaking simultaneously in the steady-state situation.