The Monte Carlo radiation model simulates the underlying processes that govern the system of interest (that is, the physical interactions between photons and their environment). A photon is selected from a photon source and tracked through the system until its weight falls below some minimum, at which point it “dies”. Each time the photon experiences an “event”, (for example, a surface intersection, scattering, or absorption), the physical quantities of interest are updated. This process generates a complete “history” of that photon in the system. Many photon histories need to be generated to get good estimates of the physical quantities of interest in a system. Photon sources are selected (that is, “sampled”) on the basis of emitted radiation, each band being treated independently for non-gray models.
This section provides details about the equations used in the MC model. For information about setting up the model, see Setting Up the MC Model in the User's Guide.
For the radiative transfer equation (RTE), the Monte Carlo model assumes that the
intensity is proportional to the differential angular flux of photons and treats 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, the spectral radiative heat flux 
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 cell, the distance traveled, you can obtain the mean total intensity.
By following a typical selection of photons and tallying, in each volume cell, 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 cell, 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 can 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) selection is done properly, the Monte Carlo tallying automatically integrates over the spectrum. Boundary conditions for the non-gray DO model are applied on a band basis. The treatment within a band is the same as that for the gray DO model.
The Monte Carlo radiation model generates photons in a stochastic (random) manner and will therefore produce speckled results if the target number of histories is relatively small. Increasing the target number of histories produces a smoother and more accurate solution, but at the expense of higher computation effort.
The treatment at boundaries is similar to that of the DO model for gray radiation. For further details, see the sections on boundary condition treatment for the DO model.
Note: External walls with boundary source and shell conduction is not supported (shell conduction is disabled if you enable both).