Radiation in Participating Media (Heat Transfer Interface)
This node should be used when radiation occurs in a medium not completely transparent, in which the radiation rays interact with the medium. It computes and adds in the heat transfer equation the radiative heat source term Qr (SI unit: W/m3), defined by:
where
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κ is the absorption coefficient (SI unit: m–1).
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G is the incident radiation (SI unit: W/m2), defined by
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 I(Ω) is the radiative intensity (SI unit: W/(m2·sr)) at a given position following the Ω direction, that satisfies the radiative transfer equation
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Ib(T) is the blackbody radiative intensity (SI unit: W/(m2·sr)), defined as
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 nr is the refractive index (dimensionless).
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σ is the Stefan-Boltzmann constant (SI unit: W/(m2·K4)).
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β = κ + σs is the extinction coefficient (SI unit: 1/m).
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σs is the scattering coefficient (SI unit: 1/m).
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φ(Ω′, Ω) is the scattering phase function (dimensionless).
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T is the temperature (SI unit: K).
It takes into account the absorbed and the emitted radiation, and depending on approximation method, also the scattered radiation.
Three approximation methods are available for the radiation discretization method. The characteristics of each of them are summarized in the following table.
Table 6-1: Discretization methods for Radiation in Participating Media (HT interface)
Option
Discrete ordinates method
P1 approximation
Rosseland approximation
Optical thickness validity
All
τ>>1
τ>>1
Scattering modeling
Linear
Polynomial
Linear
No
Computation of G
G not computed.
Thermal conductivity modified with
Computational cost
High: up to 80 additional degrees of freedom (Ii)
Medium: 1 additional degree of freedom (G)
Low: No additional degree of freedom
Models Inputs
There is one standard model input — the Temperature T. The default is to use the heat transfer interface’s dependent variable.
Radiation in Participating Media
This section sets the absorption and scattering properties of the participating medium.
It is available when Rosseland approximation is selected as the Radiation discretization method for the physics interface. Depending on the available quantities, the extinction coefficient βR can be specified directly or defined as the sum of the absorption and scattering coefficients. Also see Rosseland Approximation Theory.
The following options are available from the Specify media properties list:
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Absorption and scattering coefficients (default): in this case βR is defined as βR = κ + σs and the Absorption and Scattering sections display underneath.
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Extinction coefficient: the default Rosseland mean extinction coefficient βR should be specified directly.
Absorption
This section sets the absorption property of the participating medium, and is available in the following cases:
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Discrete ordinates method is selected as the Radiation discretization method, or
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P1 approximation is selected as the Radiation discretization method, or
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Rosseland approximation is selected as the Radiation discretization method, and Absorption and scattering coefficients is selected from the Specify media properties list.
The Absorption coefficient κ should be specified. It defines the amount of radiation, κI(Ω), that is absorbed by the medium.
Scattering
This section sets the scattering property of the participating medium, and is available in the following cases:
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Discrete ordinates method is selected as the Radiation discretization method, or
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P1 approximation is selected as the Radiation discretization method, or
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Rosseland approximation is selected as the Radiation discretization method, and Absorption and scattering coefficients is selected from the Specify media properties list.
The Scattering coefficient σs should be specified.
When Discrete ordinates method or P1 approximation is selected as the Radiation discretization method for the physics interface, choose in addition the Scattering type: Isotropic, Linear anisotropic, or Polynomial anisotropic (only with Discrete ordinates method). This provides options to approximate the scattering phase function using the cosine of the scattering angle, μ0:
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Isotropic (the default) corresponds to the scattering phase function φ(μ0) = 1.
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For Linear anisotropic it defines the scattering phase function as φ(μ0) = 1 + a1μ0. Enter the Legendre coefficient a1.
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For Polynomial anisotropic it defines the scattering phase function as
Enter each Legendre coefficient a1, …, a12 as required.
Initial Values
When Discrete ordinates method is selected as the Radiation discretization method for the physics interface, the Initial radiative intensity I should be specified. The default is ht.Ibinit, which is the blackbody radiative intensity at initial temperature.
When P1 approximation is selected as the Radiation discretization method for the physics interface, the Initial incident radiation G should be specified. The default is (4*pi)*ht.Ibinit, computed from the blackbody radiative intensity at initial temperature.
This section is not available when Rosseland approximation is selected as the Radiation discretization method for the physics interface.
Theory for Radiation in Participating Media
Discrete Ordinates Method (DOM)
Rosseland Approximation Theory
P1 Approximation Theory
Radiative Cooling of a Glass Plate: Application Library path Heat_Transfer_Module/Thermal_Radiation/glass_plate
Location in User Interface
Context menus
 Heat Transfer with Radiation in Participating Media>Radiation in Participating Media
More locations are available if the Radiation in participating media check box is selected under the Physical Model section. For example:
Heat Transfer in Solids>Radiation in Participating Media
Ribbon
Physics Tab with interface as Heat Transfer, Heat Transfer in Solids, Heat Transfer in Fluids, Heat Transfer in Porous Media, Heat Transfer in Building Materials, Bioheat Transfer, Heat Transfer with Surface-to-Surface Radiation or Heat Transfer with Radiation in Participating Media selected:
Domains>interface>Radiation in Participating Media