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Mackowski, D.W., and M.I. Mishchenko, 2008: Prediction of thermal emission and exchange among neighboring wavelength-sized spheres. J. Heat Transfer, 130, 112702, doi:10.1115/1.2957596.
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.
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