Apparent Radiative Properties of an Isotropically Scattering Medium on a Diffuse Substrate

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Abstract
The apparent directional and hemispherical radiative properties of a finite scattering medium bounded by a diffuse substrate are investigated. The isothermal medium emits, absorbs and isotropically scatters radiation. Specifically, the emittance and reflectance are determined. Using the principle of superposition, exact but simple equations are developed which express the apparent properties in terms of the properties of a medium not bounded by a substrate. Any arbitrary directional distribution of incident radiation can be handled. Integro-differential equations of the initial value type for the radiative properties are developed and solved. In general, when the substrate emittance is less than the emittance of a semi-infinite scattering medium, the scattering layer acts as a source and increases the apparent emittance. Conversely when the substrate emittance is greater, the scattering layer acts as a shield and decreases the apparent emittance.

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