The Rosseland approximation is a simplification of the Radiative Transport Equation (RTE) for the case of optically thick media. It introduces a new diffusion term into the original energy transport equation with a strongly temperature-dependent diffusion coefficient.

A good source for the simplification of the Radiation Transport Equation for the optically thick limit can be seen in Siegel and Howe [23]. The total radiative heat flux in an optically thick, and linearly anisotropic scattering medium can be written as:

(8–24)

where is the extinction coefficient (that is, absorption plus scattering).

When the Rosseland Approximation is introduced into the energy transport equation, the conduction and radiative heat flux can be combined as:

(8–25)

(8–26)

(8–27)

where is the thermal conductivity and is the "total radiative conductivity." Equation 8–25 is called upon to calculate the temperature field in the energy equation.