Spectral effectiveness of engineered thermal cloaks in the frequency regime

Abstract

We analyse basic thermal cloaks designed via different geometric transforms applied to thermal cloaking. We evaluate quantitatively the effectiveness of these heterogeneous anisotropic thermal cloaks through the calculation of the standard deviation of the isotherms. The study addresses the frequency regime and we point out the cloak's spectral effectiveness. We find that all these cloaks have comparable effectiveness irrespective of whether or not they have singular conductivity at their inner boundary. However, approximate cloaking with multi-layered cloak critically depends upon the homogenization algorithm and it is shown that the standard deviation varies linearly with the inverse of the number of layers.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

“…In section IV, we propose a multilayered spherical device which approximates the functionality of a diffusion cloak in the homogenization regime. 13,29 In section V, we look at so-called diffusion carpet cloaks and we conclude the paper in section VI.…”

“…There is currently a keen interest in the control of heat flux using thermal metamaterials in steady, 1-7 transient [8][9][10][11][12] and periodic 13 regimes. In the present paper, we discuss the functionality of diffusion cloaks for heat and mass, as well as concentrators and rotators, 14 via transformed Fourier 8,15 and Fick [16][17][18] equations.…”

Analogies between optical propagation and heat diffusion: applications to microcavities, gratings and cloaks

“…A novel association of optics and heat has been proposed recently [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. It is based on an analogy between the governing equations of propagation for optics and diffusion for heat.…”

“…Under these conditions, electromagnetic fields decay exponentially fast away from a metal-dielectric interface so that their behaviour is somewhat reminiscent of a temperature field undergoing a fast decay away from a heat source. Such an analogy has been first used in the design of thermal cloaks, heat concentrators and rotators [16][17][18][19][20][21][22][23][24][25][26][27][28][29], using geometric transformation methods previously applied to electromagnetics [30][31]. A series of papers subsequently emerged and confirmed tools of transformation optics can be applied to control other diffusion processes [32][33].…”

Achieving bifunctional cloak via combination of passive and active schemes

“…but also other fields like dc electric field, 14,15 static magnetic field, [16][17][18] thermal field, [19][20][21][22][23][24][25] mass diffusion [26][27][28] and electrostatic field. 29 Recently, increasing attention has been paid to the manipulation of multi-physic field.…”