Rosseland Radiation Model
The Rosseland Model (Diffusion approximation model) is applicable when the medium is optically thick i.e. the optical thickness is much greater than 1 where a is the absorption coefficient of the medium, σ is the scattering coefficient of the medium and L is the average path length. The radiative heat flux is approximated as [3], (2.13)
where qr is the radiative heat flux, Γ is the radiative diffusivity and G is the incident radiation. In contrast to the P-1 model (discussed in subsection 2.2.5) which uses a transport equation for G, the Rosseland model assumes that the incident radiation intensity is the black body intensity at that temperature of the medium. In other words [3], (2.14)
where n is refractive …show more content…
Depending on the number of path vectors, that many transport equations are solved.
One advantage of the DO model is that it takes into account the directional dependence of radiation and spans the complete range of optical thickness. So it can include the effects of anisotropy, semi-transparent walls, particulate effects, etc. A possible disadvantage of this model is that it becomes even more computationally intensive for finer angular discretization. The DO model is not used in the current case due to its inclusion of directional dependence of radiation intensity, which is not that in consideration here.
Discrete Transfer Radiation Model (DTRM)
This model assumes that, for a certain range of solid angles, the radiation from a surface element can be approximated to a single ray. Due to this simplification, the RTE reduces to the following equation, …show more content…
In the P-N method, mathematically speaking, the RTE reduces to a set of differential equations by approximating the intensity as a truncated series of transcendental functions whose terms are based on orthogonal spherical harmonics. The P-1 model uses only the zeroth and first order moments of the approximated intensity function. Physically, the basic assumption of the P-1 model is that the deviation of incident intensity in a participating medium can be expressed using local gradients of incident
The Rosseland Model (Diffusion approximation model) is applicable when the medium is optically thick i.e. the optical thickness is much greater than 1 where a is the absorption coefficient of the medium, σ is the scattering coefficient of the medium and L is the average path length. The radiative heat flux is approximated as [3], (2.13)
where qr is the radiative heat flux, Γ is the radiative diffusivity and G is the incident radiation. In contrast to the P-1 model (discussed in subsection 2.2.5) which uses a transport equation for G, the Rosseland model assumes that the incident radiation intensity is the black body intensity at that temperature of the medium. In other words [3], (2.14)
where n is refractive …show more content…
Depending on the number of path vectors, that many transport equations are solved.
One advantage of the DO model is that it takes into account the directional dependence of radiation and spans the complete range of optical thickness. So it can include the effects of anisotropy, semi-transparent walls, particulate effects, etc. A possible disadvantage of this model is that it becomes even more computationally intensive for finer angular discretization. The DO model is not used in the current case due to its inclusion of directional dependence of radiation intensity, which is not that in consideration here.
Discrete Transfer Radiation Model (DTRM)
This model assumes that, for a certain range of solid angles, the radiation from a surface element can be approximated to a single ray. Due to this simplification, the RTE reduces to the following equation, …show more content…
In the P-N method, mathematically speaking, the RTE reduces to a set of differential equations by approximating the intensity as a truncated series of transcendental functions whose terms are based on orthogonal spherical harmonics. The P-1 model uses only the zeroth and first order moments of the approximated intensity function. Physically, the basic assumption of the P-1 model is that the deviation of incident intensity in a participating medium can be expressed using local gradients of incident