Directional Emissivities From a Two-Dimensional, Absorbing-Scattering Medium: The Semi-Infinite Slab

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Abstract
A closed-form solution is presented for the directional emissivity at any location on the surface of a semi-infinite slab of an absorbing-scattering medium. The medium is assumed to be a gray, isothermal dispersion which emits, absorbs, and scatters isotropically, and is confined by free boundaries. The solution to this two-dimensional problem is found by the approximate technique based on an iteration of the solution to the diffusion equation. Polar plots of directional emissivity are presented which show the influence of optical thickness, surface location, and scattering strength (albedo).

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