Research Papers: Conduction

Cylindrical Thermal Cloak Based on the Path Design of Heat Flux

[+] Author and Article Information
Linzhi Wu

Center for Composite Materials,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: wlz@hit.edu.cn

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 22, 2014; final manuscript received October 18, 2014; published online November 18, 2014. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 137(2), 021301 (Feb 01, 2015) (9 pages) Paper No: HT-14-1337; doi: 10.1115/1.4028920 History: Received May 22, 2014; Revised October 18, 2014; Online November 18, 2014

When heat flux flows in a given medium, its path will solely be determined. This implies that material parameters determined by the predesigned path of heat flux will guide heat to flow along the designed path. Based on this idea, we develop a new method for the design of the cylindrical thermal cloak which can make heat flux detour the cloaked object. For the inhomogeneous anisotropic medium, we derive the relation between the path trajectory of heat flux and material parameters and obtain two differential equations and one boundary condition which are used to determine material parameters in the cylindrical cloak. The transient behavior on the flow of heat flux is simulated by Comsol Multiphysics and the transient thermal protection of the cylindrical cloak for the cloaked object is examined. The effect of the product of density and specific heat on the dynamic diffusion process of heat flux is analyzed. Since one can flexibly design the path of heat flux in the cloak, it has the large degree of freedom to construct thermal cloaks with the specific distributions of material parameters. The present method provides a new blue print for the transient thermal protection of a specific target.

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Grahic Jump Location
Fig. 1

Path trajectory of heat flux in the cylindrical cloak

Grahic Jump Location
Fig. 2

Simulated temperature distributions. The first to fourth columns demonstrate the snapshots captured at t = 10, 30, 80, and 160 s, respectively. The first, second, and third rows correspond to cases 1–3 illustrated in Eqs. (41)–(43). The arrows in Fig. 2(l) denote the pathway of heat flux. Here, η = 1.

Grahic Jump Location
Fig. 3

Simulated temperature distributions. The first to fourth columns demonstrate the snapshots captured at t = 10, 30, 80, and 160 s, respectively. The first, second, and third rows correspond to cases 1–3 illustrated in Eqs. (41)–(43). The arrows in Fig. 3(l) denote the pathway of heat flux. Here, η = 2.

Grahic Jump Location
Fig. 4

Variation of temperature at the center of cylinder with time. The lines with symbols ▪, ●, and ▲ correspond to cases 1–3, respectively, at η = 1; the lines with symbols ▼, ◆, and ◂ do to cases 1–3, respectively, at η = 2.

Grahic Jump Location
Fig. 5

Variations of material parameters of the cylindrical cloak with the radial coordinate. The lines with symbols ▪, ●, and ▲ correspond to normalized material parameters κr, κθ, and ρc, respectively. Here, the cylindrical thermal cloak corresponds to case 2 and η = 2.



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