0

# 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

## Abstract

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 $d∕λ→0$, 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.

<>

## Figures

Figure 4

Scaled exchange factor as a function of d∕a

Figure 1

Ensemble configuration

Figure 2

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

Figure 3

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

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections