# Mathematical formulation

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## MATHEMATICAL FORMULATION

Following from: Discrete ordinates and finite volume methods

The radiative transfer equation (RTE) for an emitting-absorbing-scattering medium may be written as follows (Modest, 2003):

 (1)

where subscript ν denotes the wave number. In this equation, I(s) is the radiation intensity in direction s, r is the position vector, Ib is the blackbody radiation intensity, κ, β, and σs are the absorption, extinction, and scattering coefficients of the medium, respectively, and Φ(s′, s) is the scattering phase function. Although the discrete ordinates method (DOM) and the finite volume method (FVM) may be applied to nongray media (see article “Application to nongray media”), the present analysis is restricted to gray media, so that the subscript ν will be dropped from now on. The directio ...

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