## 8.1. Radiation Transport

The goal of radiation modeling is to solve the radiation transport equation, obtain the source term, S, for the energy equation, and the radiative heat flux at walls, among others quantities of interest. You should restrict yourself to coherent time-independent radiation processes. This is normally a very good approximation of situations likely to be met in industrial applications because the time scale for radiation to come into local equilibrium is very short and the temperatures are relatively low.

The spectral radiative transfer equation (RTE) can be written as:

| (8–1)

where:

- = frequency

- = position vector

- = direction vector

- = path length

- = absorption coefficient

- = scattering coefficient

- = Blackbody emission intensity

- = Spectral radiation intensity which depends on position (r) and direction (s)

- = local absolute temperature

- = solid angle

- = in-scattering phase function

- = radiation intensity source term, or particle-radiation interactions

The RTE is a first order integro-differential equation for I v in a fixed direction, s. To solve this equation within a domain, a boundary condition for I v is required. The following are the boundary conditions currently supported in CFX:

- Diffusely emitting and reflecting opaque boundaries

  | (8–2)

where =spectral emissivity.

- Diffusely emitting and specularly reflecting boundaries

  | (8–3)

where:

- =diffuse reflectivity=*diffuse fraction

- =specular reflectivity=*(1-diffuse fraction)

- =spectral reflectivity==

- =specular direction

- Semi-transparent walls (Monte Carlo only)

Due to the dependence on 3 spatial coordinates, 2 local direction coordinates, s, and frequency, the formal solution of the radiative transfer equation is very time consuming and usually accomplished by the use of approximate models for the directional and spectral dependencies. For directional approximations, CFX includes `Rosseland`, `P-1`, `Discrete Transfer`, and `Monte Carlo`. For spectral approximations, CFX includes: `Gray`, `Multiband` and `Weighted Sum of Gray Gases`.

Release 18.2 - © ANSYS, Inc. All rights reserved.