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
(4-92)
Equation 4-91 is the blackbody radiation intensity and nr is the refractive index
ε is the surface emissivity, which is in the range [0, 1]
1 − ε is the diffusive reflectivity
  n is the outward normal vector
qr,out is the heat flux striking the wall:
For black walls ε = 1. Thus I(Ω) = Ib(T).