Experimental Demonstration of

A Bilayer Thermal Cloak

Tiancheng HanXue Bai

Dongliang GaoJohn T.L. Thong

Browen LiCheng-Wei Qiu

Paper Source:PRL 112,054302 (2014)

preprocessing ：前處理

solution ：運算求解

Postprocessing ：後處理

Simulation for 3D thermal cloak a finite element method (FEM)

(a)A bare object with radius of 6 mm. (b)A single layer of polystyrene with thickness of 4.2 mm. (c)A single layer of alloy with thickness of 4.2 mm. (d)A bilayer cloak. with a=6 mm, b=9 mm, c=10.2mm

Inner layer ： a<r<b Outer layer ： b<r<cK ： thermal conductivity ( W/(m ． K) )Kb ： thermal conductivity of background

K ： thermal conductivity ( W/(m ． K) )▽T ： temperature gradient ( K ． m-1 )Q ： the inner heat-generation rate per unit volumeT ： temperatureTi ： temperature in different regionsAi

m ， Bim ： constants (determined by the boundary conditions)

(For steady state situation)

(Q=0)

(For Fourier-Legendre series)

i=1 for (r<a) ， i=2 for the(a<r<b) ， i=3 for (b<r<c) ， i=4 for (r>c).

(For Laplace ‘s equation)

(Spherical coordinates of partial differential equations)

Simulation for 3D thermal cloak

(b) The bilayer cloaka= 6mm b= 9mm c=10.2mm

(a) A single layer of polystyrenethickness =4.2mm

a=6mm ， b=9.5mm ， c=12mmCloaked object ： an aluminum cylinder (r=6mm)Inner layer ： expanded polystyrene (K=0.03 W/mK)Outer layer ： Inconel 625 alloy (K=9.8 W/mK)sealant ： (ACC SILICONES—AS1802) (K=2.3 W/mK)Host block ： 45mm(width) ， 45mm(depth) ， 35mm(height)

hot ： 60℃cold ： 0 ℃(water)IR-camera ： Flir i60

(a),(b) The bare perturbation (aluminum cylinder)without bilayer cloak(c),(d) The single layer of expanded polystyrene(e),(f ) The bilayer thermal cloak (a=6mm, b=9.5mm, c=12 mm)

For quantitative comparison

(g),(h) The bilayer thermal cloak in the presence of a point heat source ,emitting cylindrical heat fronts.

Prove ：The effectiveness of the bilayer thermal cloak in non-uniform thermal field.

To examine the transient performance of the bilayer cloak

Temperature ： 80 ℃

(a)The bare perturbation (aluminum cylinder)without bilayer cloak (b)The single layer of expanded polystyrene (c)The bilayer thermal cloak

Simulated time-dependent temperature distributions

Temperature distributions for different thermal cloaking schemes

(a) A pure background (b) The bilayer thermal cloak (c) AI thermal cloak with m=0.2 (d) AH thermal cloak with n=3

AI thermal cloak

AH thermal cloak

r ： the radius in the physical spacer' ： the radius in the virtual spacer1 ： the inner radiusr2 ： the outer radiusr0 ： the radius of a finite small region Kb ： the conductivity of the backgroundKr ： the radial coefficientKθ ： the azimuthal coefficient

AH thermal cloak

a circular region (r<=b) in original space (r, θ, z) is compressed into an annular region (a<=r’<=b) in physical space (r’, θ’, z’).

(e) Temperature gradient at (0,0) for AI thermal cloak with different m(f ) Temperature gradient at (0,0) for the AH thermal cloak with different n

(a) Oblique incidence with 30 ° (b) (b) Oblique incidence with 45 °

1. Not rely on transformation optics2. Use the regular materials3. Excellent performance

Summary ：The bilayer thermal cloak is suitable for real engineering applications.