## 8.4. Discrete Transfer Model

The implementation of the Discrete Transfer model in CFX assumes that the scattering is isotropic; therefore, Equation 8–1 can be simplified as:

| (8–34)

Assuming that the system is reasonably homogeneous, so that:

| (8–35)

the approach is then to solve for the intensity, , along rays leaving from the boundaries using the equation of transfer:

| (8–36)

where:

= Radiation Intensity leaving the boundary

= Mean Radiation Intensity

Then, integrate over solid angle at discrete points to get the spectral incident radiation, and the radiative heat flux, and use the homogeneity assumption to extend the solution to the entire domain. Non-linearities in the system due to scattering, diffuse reflection, or temperature dependency of radiation quantities is overcome by iteration.

Because the objective of thermal radiation modeling is to obtain the total volumetric absorption and emission, additional calculations are still needed. For the Gray spectral model, the calculation is done once for a unique radiation intensity field. For the Multiband and Weighted Sum of Gray Gases, the solution must be computed for each spectral band/ gray gas and a final integration to obtain the total radiation quantities is required. Under the assumption of coherent radiation field, ie., the solution at a given frequency is independent of that at all other frequencies.

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