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Research Papers: Radiative Heat Transfer

Direct and Indirect Methods for Calculating Thermal Emission From Layered Structures With Nonuniform Temperatures

[+] Author and Article Information
L. P. Wang

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

S. Basu1

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

Z. M. Zhang2

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

1

Present address: Assembly Technology Department, Intel Corporation, Chandler, AZ 85226.

2

Corresponding author.

J. Heat Transfer 133(7), 072701 (Apr 01, 2011) (7 pages) doi:10.1115/1.4003543 History: Received May 19, 2010; Revised January 14, 2011; Published April 01, 2011; Online April 01, 2011

The determination of emissivity of layered structures is critical in many applications, such as radiation thermometry, microelectronics, radiative cooling, and energy harvesting. Two different approaches, i.e., the “indirect” and “direct” methods, are commonly used for computing the emissivity of an object. For an opaque surface at a uniform temperature, the indirect method involves calculating the spectral directional-hemispherical reflectance to deduce the spectral directional emissivity based on Kirchhoff’s law. On the other hand, a few studies have used a combination of Maxwell’s equations with the fluctuation-dissipation theorem to directly calculate the emissivity. The present study aims at unifying the direct and indirect methods for calculating the far-field thermal emission from layered structures with a nonuniform temperature distribution. Formulations for both methods are given to illustrate the equivalence between the indirect and the direct methods. Thermal emission from an asymmetric Fabry–Pérot resonance cavity with a nonuniform temperature distribution is taken as an example to show how to predict the intensity, emissivity, and the brightness temperature. The local density of states, however, can only be calculated using the direct method.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation of a multilayered structure with a nonuniform temperature distribution for the study of thermal emission based on (a) the direct method and (b) the indirect method

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Figure 2

Schematic of an asymmetric Fabry–Pérot resonance cavity with temperature nonuniformity for demonstration of the direct and indirect methods

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Figure 3

Calculated normal spectral intensity emitted by the Fabry–Pérot structure shown in Fig. 2 from the direct method. Note that df=21nm, dc=622nm, T1=800K, and T2=1000K.

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Figure 4

(a) The spectral normal absorptivity from the indirect method (or emissivity from the direct method) of each Au film in the Fabry–Pérot structure and that of a freestanding Au film. (b) The spectral directional absorptivity (or emissivity) as a function of emission angles for both polarizations at a wavelength of 900 nm.

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Figure 5

Calculated LDOS inside the SiO2 cavity at θ=0 deg for contributions from the top Au film and bottom Au layer

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Figure 6

The brightness temperature calculated for the Fabry–Pérot structure: (a) as a function of wavenumbers at θ=0 deg and (b) as a function of emission angles for both polarizations at a wavelength of 900 nm

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