Rosseland Approximation Theory
For The Heat Transfer with Radiation in Participating Media Interface, Rosseland approximation is available as a radiation discretization method. Then for Radiation in Participating Media (Heat Transfer Interface) feature node this theory is applicable.
Rosseland approximation relies on the hypotheses that the participating media is optically thick — that is, τ >>1 — where τ is the optical thickness defined by the integral of absorption coefficient, κ, along a typical optical path:
From a computational point of view this approximation has a limited impact because it does not introduce any extra degree of freedom to the heat equation. Instead it adds nonlinear contribution to the thermal conductivity. This is why this method is popular for some applications where the optical thickness is large. Nevertheless, because it gives a simple approximation of heat transfer by radiation in a participating media, it should be carefully validated.
In this case, the radiative heat flux can be evaluated by (Ref. 20):
For a gray media it leads to
Assuming a constant refractive index, this can be rewritten as qr = − kR ΔT with
and
Notice that the Rosseland approximation does not account at all for the scattering in the participating media.