## 8.5. Monte Carlo Model

The Monte Carlo model assumes that the intensity is proportional to the differential angular flux of photons and you can think of the radiation field as a photon gas. For this gas, is the probability per unit length that a photon is absorbed at a given frequency. Therefore, the mean radiation intensity, is proportional to the distance traveled by a photon in unit volume at , in unit time.

Similarly is proportional to the rate of incidence of photons on the surface at , because volumetric absorption is proportional to the rate of absorption of photons.

By following a typical selection of photons and tallying, in each volume element, the distance traveled, you can obtain the mean total intensity.

By following a typical selection of photons and tallying, in each volume element, the distance times the absorption coefficient, you can obtain the mean total absorbed intensity.

By following a typical selection of photons and tallying, in each volume element, the distance times the scattering coefficient, you can obtain the mean total scattered intensity.

By also tallying the number of photons incident on a surface and this number times the emissivity, you obtain the mean total radiative flux and the mean absorbed flux.

Note that no discretization of the spectrum is required because differential quantities are not usually important for heat transfer calculations. Providing that the spectral (Multiband or Weighted Sum of Gray Gases) selection is done properly, the Monte Carlo tallying automatically integrates over the spectrum.

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