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Detecting Thermal Cloaks via Transient Effects

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ABSTRACT

Recent research on the development of a thermal cloak has concentrated on engineering an inhomogeneous thermal conductivity and an approximate, homogeneous volumetric heat capacity. While the perfect cloak of inhomogeneous κ and inhomogeneous ρcp is known to be exact (no signals scattering and only mean values penetrating to the cloak’s interior), the sensitivity of diffusive cloaks to defects and approximations has not been analyzed. We analytically demonstrate that these approximate cloaks are detectable. Although they work as perfect cloaks in the steady-state, their transient (time-dependent) response is imperfect and a small amount of heat is scattered. This is sufficient to determine the presence of a cloak and any heat source it contains, but the material composition hidden within the cloak is not detectable in practice. To demonstrate the feasibility of this technique, we constructed a cloak with similar approximation and directly detected its presence using these transient temperature deviations outside the cloak. Due to limitations in the range of experimentally accessible volumetric specific heats, our detection scheme should allow us to find any realizable cloak, assuming a sufficiently large temperature difference.

No MeSH data available.


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Simulated temperature snapshots for mismatched SSC (η = b/(b − a)).Columns correspond to 2.08τD/100, 2.08τD/10, and 2.08τD respectively. Rows correspond to the homogeneous case (no cloak), SSC, and T(SSC) − T(H). Black circles denote the location of the cloak (for reference in the homogeneous case), colored domains are isotherms, and grey lines are constant separation isotherms.
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f2: Simulated temperature snapshots for mismatched SSC (η = b/(b − a)).Columns correspond to 2.08τD/100, 2.08τD/10, and 2.08τD respectively. Rows correspond to the homogeneous case (no cloak), SSC, and T(SSC) − T(H). Black circles denote the location of the cloak (for reference in the homogeneous case), colored domains are isotherms, and grey lines are constant separation isotherms.

Mentions: Since the solution to eq. 5 is not a tabulated function, we use COMSOL multiphysics55 to solve eq. 1 directly for the SSC. Following the most common test of a cloak, we model the cloak in a rectangular region where one pair of ends are held at fixed temperature and the other pair admit no heat (Fig. 1). Given the linearity of eq. 1, one boundary is set to 0 (as is the initial T) and the other to 1 (ΔT ≡ 1). It is helpful to use the natural units of L (the separation of the heat sources) and the diffusion time τD = L2ρ0cp0/κ0 (all parameters values are in the supplement). Figure 2 is the result of these calculations. Each column is a snapshot at a different time. The first row is the homogeneous background that would be observed if there was no cloak, the second is the solution to SSC (with η = b/(b − a) to increase contrast), and the third is the difference . This deviation δT is what must be detected to reveal a cloak. Initially δT is small and mostly localized to where the cloak has been heated (see Fig. 2g). Later (Fig. 2h) δT grows and is clearly observed outside the cloak. Finally in the steady state (Fig. 2i) invisibility is restored, as expected for a SSC (δT ≠ 0 confined to within the cloak).


Detecting Thermal Cloaks via Transient Effects
Simulated temperature snapshots for mismatched SSC (η = b/(b − a)).Columns correspond to 2.08τD/100, 2.08τD/10, and 2.08τD respectively. Rows correspond to the homogeneous case (no cloak), SSC, and T(SSC) − T(H). Black circles denote the location of the cloak (for reference in the homogeneous case), colored domains are isotherms, and grey lines are constant separation isotherms.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5015050&req=5

f2: Simulated temperature snapshots for mismatched SSC (η = b/(b − a)).Columns correspond to 2.08τD/100, 2.08τD/10, and 2.08τD respectively. Rows correspond to the homogeneous case (no cloak), SSC, and T(SSC) − T(H). Black circles denote the location of the cloak (for reference in the homogeneous case), colored domains are isotherms, and grey lines are constant separation isotherms.
Mentions: Since the solution to eq. 5 is not a tabulated function, we use COMSOL multiphysics55 to solve eq. 1 directly for the SSC. Following the most common test of a cloak, we model the cloak in a rectangular region where one pair of ends are held at fixed temperature and the other pair admit no heat (Fig. 1). Given the linearity of eq. 1, one boundary is set to 0 (as is the initial T) and the other to 1 (ΔT ≡ 1). It is helpful to use the natural units of L (the separation of the heat sources) and the diffusion time τD = L2ρ0cp0/κ0 (all parameters values are in the supplement). Figure 2 is the result of these calculations. Each column is a snapshot at a different time. The first row is the homogeneous background that would be observed if there was no cloak, the second is the solution to SSC (with η = b/(b − a) to increase contrast), and the third is the difference . This deviation δT is what must be detected to reveal a cloak. Initially δT is small and mostly localized to where the cloak has been heated (see Fig. 2g). Later (Fig. 2h) δT grows and is clearly observed outside the cloak. Finally in the steady state (Fig. 2i) invisibility is restored, as expected for a SSC (δT ≠ 0 confined to within the cloak).

View Article: PubMed Central - PubMed

ABSTRACT

Recent research on the development of a thermal cloak has concentrated on engineering an inhomogeneous thermal conductivity and an approximate, homogeneous volumetric heat capacity. While the perfect cloak of inhomogeneous κ and inhomogeneous ρcp is known to be exact (no signals scattering and only mean values penetrating to the cloak’s interior), the sensitivity of diffusive cloaks to defects and approximations has not been analyzed. We analytically demonstrate that these approximate cloaks are detectable. Although they work as perfect cloaks in the steady-state, their transient (time-dependent) response is imperfect and a small amount of heat is scattered. This is sufficient to determine the presence of a cloak and any heat source it contains, but the material composition hidden within the cloak is not detectable in practice. To demonstrate the feasibility of this technique, we constructed a cloak with similar approximation and directly detected its presence using these transient temperature deviations outside the cloak. Due to limitations in the range of experimentally accessible volumetric specific heats, our detection scheme should allow us to find any realizable cloak, assuming a sufficiently large temperature difference.

No MeSH data available.


Related in: MedlinePlus