Radiative Transfer Equation
The balance of the radiative intensity including all contributions (propagation, emission, absorption, and scattering) can now be formulated. The general radiative transfer equation can be written as (see Ref. 23):
(4-115)
where
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 I(Ω) is the radiative intensity at a given position following the Ω direction (SI unit: W/(m2·sr))
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Ib(T) is the blackbody radiative intensity (SI unit: W/(m2·sr)), defined as
(4-116) 
The quantity Ib(T) is available as a predefined function, ht.fIb(T), in heat transfer interfaces.
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nr is the refractive index (SI unit: 1)
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σ is the Stefan-Boltzmann constant (SI unit: W/(m2·K4))
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κ, β, σs are absorption, extinction, and scattering coefficients, respectively (SI unit: 1/m) and are related by:
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is the scattering phase function (SI unit: 1)
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T is the temperature (SI unit: K)
Scattering Phase Function
The phase function, , gives the probability that a ray from the Ω′ direction is scattered into the Ω direction. The phase function’s definition is material dependent and its definition can be complicated. It is common to use approximate scattering phase functions that are defined using the cosine of the scattering angle, μ0. The current implementation handles:
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Isotropic phase functions:
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Linear anisotropic phase functions:
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Polynomial anisotropic up to the 12th order:
where Pn are the nth order Legendre polynomials.
Legendre polynomials can be defined by the Rodriguez formula:
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Henyey–Greenstein phase function:
where is the anisotropy parameter and K is defined as follows to produce a normalized phase function:
Incident Radiation
A quantity of interest is the incident radiation, denoted G (SI unit: W/m2), and defined by