In internal combustion engines, radiation heat transfer mainly comes from two sources: (1) the high temperature burned gas, and (2) soot particles. Radiation heat transfer is not negligible compared to the convective heat transfer when there is substantial amount of soot or high temperature flame in the combustion chamber. The radiative gas species that consist of polar gas molecules as well as soot particles emit radiation at high temperature, which is transmitted through the combustion chamber gas and absorbed by the walls.

A simplified model is implemented in Ansys Forte by introducing the “Optically Thin” assumption [10] . Under this assumption, local gas does not absorb radiation from other parts of the gas, and each radiating point has an unimpeded, isotropic view of the cold surroundings. If we consider the radiating zone to have a high temperature (), and the surroundings as the combustion chamber walls at a lower temperature (), the radiative heat loss per unit volume in the radiative region is calculated as:

(10–1)

in which σ is the Stefan-Boltzmann constant, is the partial pressure of species in the gas mixture, is the Planck mean absorption coefficient of species , is the mean absorption coefficient of the soot particles.

The radiative loss term () is applied per fluid cell and is one of the source terms in the fluid flow’s energy conservation equation (see Equation 2–5 ). The total amount of radiative loss in a region is calculated by adding up the loss term () in each fluid cell in the region. Due to energy conservation, the radiation heat is transferred from the fluid to the walls in the region, whose averaged temperature is defined as the surrounding temperature () in Equation 10–1 .

The Planck mean absorption coefficient of individual gas species is calculated as polynomial fit with respect to temperature. Refer to Gas Species Radiation Absorption Coefficients in the Chemkin Input Manual for more details about how the polynomial fit is set up.

The mean absorption coefficient of the soot particles is approximately calculated as:

(10–2)

in which is the soot volume fraction, and is a user input and has dimensions of [length * temperature]-1. It has a default value of 700 m^-1K^-1. For more details about the derivation of Equation 10–2 , refer to Particulate Absorption Coefficient in the Chemkin Theory Manual .