Encyclopaedia Index

6. Rosseland Diffusion Model

A medium is said to be optically thick if the reciprocal of the absorption/extinction coefficient is very small compared with a characteristic dimension of the medium.

When the medium is optically thick, the radiation can be approximated as an isotropic "diffusion" process by use of the well-known Rosseland approximation for radiative heat transfer ( see for example Deissler [1964], Ozisik [1973] and Siegel and Howell [1992]).

This was shown in Section 3 and 4 above.

In PHOENICS, the radiosity model can conveniently be used as the vehicle for invoking Rosseland's model.

All that is needed is to set the scattering coefficient s to zero and the absorption coefficient a to a relatively large value so as to force radiative equilibrium.

The diffusion model implies a radiative conductivity in the energy equation defined by:

lamda_rad = 16 * S * T**3 / {3 * (a+s)} (6.1)

and so the medium behaves like a conductor with a temperature-dependent conductivity.

It should be noted that, as conventionally formulated, the diffusion approximation is not valid near a boundary solid-fluid boundary ( see for example Deissler [1964] and Viskanta [1966] ).

However, this is difficulty is overcome in the PHOENICS implementation, because the wall boundary condition (5.7) for the radiosity allows for a temperature jump at the wall.