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.

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