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Research Papers: Radiative Heat Transfer

Application Conditions of Effective Medium Theory in Near-Field Radiative Heat Transfer Between Multilayered Metamaterials

[+] Author and Article Information
X. L. Liu, T. J. Bright

George W. Woodruff
School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Z. M. Zhang

George W. Woodruff
School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: zhuomin.zhang@me.gatech.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 20, 2014; final manuscript received May 14, 2014; published online June 27, 2014. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 136(9), 092703 (Jun 27, 2014) (8 pages) Paper No: HT-14-1143; doi: 10.1115/1.4027802 History: Received March 20, 2014; Revised May 14, 2014

This work addresses the validity of the local effective medium theory (EMT) in predicting the near-field radiative heat transfer between multilayered metamaterials, separated by a vacuum gap. Doped silicon and germanium are used to form the metallodielectric superlattice. Different configurations are considered by setting the layers adjacent to the vacuum spacer as metal–metal (MM), metal–dielectric (MD), or dielectric–dielectric (DD) (where M refers to metallic doped silicon and D refers to dielectric germanium). The calculation is based on fluctuational electrodynamics using the Green's function formulation. The cutoff wave vectors for surface plasmon polaritons (SPPs) and hyperbolic modes are evaluated. Combining the Bloch theory with the cutoff wave vector, the application condition of EMT in predicting near-field radiative heat transfer is presented quantitatively and is verified by exact calculations based on the multilayer formulation.

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Figures

Grahic Jump Location
Fig. 1

Illustration of radiative heat transfer between two multilayered metamaterials (at temperatures T1 and T2, respectively) separated by a vacuum gap of distance d. Note that tm and td are the thicknesses of D-Si (metallic behavior) and Ge (dielectric), respectively. The resulting period is P = tm + td.

Grahic Jump Location
Fig. 2

Effective dielectric function components for (a) f = 0.5 and (b) f = 0.8. Shaded regions denote hyperbolic dispersion (type I or type II).

Grahic Jump Location
Fig. 3

Total near-field radiative heat flux for different configurations as a function of gap distance: (a) s-polarization, f = 0.5; (b) s-polarization, f = 0.8; (c) p-polarization, f = 0.5 and (d) p-polarization, f = 0.8. The frequency region covering most of thermal radiation is chosen from 2 × 1012 rad/s to 4 × 1014 rad/s.

Grahic Jump Location
Fig. 4

Spectral near-field radiative heat flux for different configurations at gap distance d = 10 nm for f = 0.5: (a) s-polarization and (b) p-polarization

Grahic Jump Location
Fig. 5

Spectral heat flux at different distances for p-polarization with f = 0.5: (a) d = 100 nm; (b) d = 200 nm; and (c) d = 300 nm

Grahic Jump Location
Fig. 6

Transmission coefficient contours ξp(ω,β) for (a) effective medium, different hyperbolic region are delineated; (b) MM; (c) MD; and (d) DD

Grahic Jump Location
Fig. 7

Loss-dependent cutoff wave vector at the surface resonance frequency. The numerically calculated values are based on Eq. (10). The fitted curve given in Eq. (11) and that from Biehs et al. [55] are also shown.

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