Boundary Condition for the Radiative Transfer Equation
For gray walls, corresponding to opaque surfaces reflecting diffusively and emitting, the radiative intensity I(Ω) entering participating media along the Ω direction is
where
(4-117) 
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Equation 4-117 is the blackbody radiation intensity and nr is the refractive index
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 ε is the surface emissivity, which is in the range [0, 1]
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 1 − ε is the diffusive reflectivity
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  n is the outward normal vector
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 qr,out is the heat flux coming from the domain and striking the wall:
For black walls ε = 1. Thus I(Ω) = Ib(T).
The net heat flux corresponding to the balance between the energy received by the surface and emitted by the surface is defined by
This net heat flux accounts for the radiation coming from the domain where the RTE is solved for, the radiation coming from the exterior is not modeled and hence not accounted for.
If the surface is semitransparent, the radiative intensity transmitted diffusively or specularly. For an external boundary the external intensity, Iext, is transmitted in the domain. The radiative intensity entering participating media along the Ω direction is
for all Ω such that ,
where
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ρd is the surface diffuse reflectivity, 
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τd is the surface diffuse transmissivity,
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 τs is the surface specular transmissivity,
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 Iext is the external radiation intensity,
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 qr,in is the heat flux striking the wall from exterior:
The emissivity, diffuse reflectivity, diffuse transmissivity, and specular transmissivity satisfy the following relation:
The net heat flux corresponding to the balance between the energy received by the surface and emitted by the surface is defined by
For semitransparent surfaces, the net heat flux accounts for the radiation coming from the domain and from the exterior.
The definition of the radiative intensity on internal boundaries is similar to the definition for external boundaries except that the external radiation is replaced by the radiation exiting the adjacent domain.