Research Papers: Radiative Heat Transfer

Prediction of Thermal Emission and Exchange Among Neighboring Wavelength-Sized Spheres

[+] Author and Article Information
Daniel W. Mackowski

Department of Mechanical Engineering,  Auburn University, Auburn, AL 36849mackodw@auburn.edu

Michael I. Mishchenko

 NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025

J. Heat Transfer 130(11), 112702 (Sep 03, 2008) (7 pages) doi:10.1115/1.2957596 History: Received August 22, 2007; Revised January 11, 2008; Published September 03, 2008

An analysis of radiative emission and radiative exchange among an ensemble of closely spaced, wavelength-sized spheres, in which each sphere in the ensemble is at a distinct and uniform temperature, is presented. We show that the rate of spectral emission from a specific sphere in the ensemble and the rate at which emission is exchanged between a pair of spheres can be deduced from the application of reciprocity and energy conservation principles to the solution of Maxwell’s time harmonic wave equations for a sphere ensemble that is exposed to a plane wave incident field of wavelength λ. We show that in the limit of dλ0, the emissive exchange between a pair of spheres becomes inversely proportional to the gap thickness d. We also show that when the spheres are in the mutual far-field zones of each other, the emissive exchange between the spheres can be well approximated by geometric configuration factors, with an effective area correction to account for finite wavelength effects.

Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 4

Scaled exchange factor as a function of d∕a

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Figure 1

Ensemble configuration

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Figure 2

Emission∕absorption ratio for a sphere in a two-sphere cluster as a function of gap thickness kd

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Figure 3

Exchange cross section, scaled with a limiting value, as a function of gap thickness kd



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