Participating media, radiative

TABLE 7.5 Monte Carlo Relations for Surface-Surface and Participating Media Radiative Exchange... 

Now the radiative transfer equation can be derived. Consider a ray of radiation passing through a participating medium. This ray will be attenuated along the path S. The amount of attenuation or change is related to the starting intensity and the distance it travels ... 

The overall change of radiative intensity as it passes through a participating medium is the net effect of attenuation by absorption and outscattering, augmentation by emission and in-scattering. Mathematically, this relationship is... 

Other areas of radiative transfer have been driven by increased capability of analysis due to the great strides in computer capability. Just a few years ago, two-dimensional problems of radiative transfer in enclosures with a participating medium were at the edge of computational capability. Now, these are routine, and many three-dimensional cases have been analyzed. Because of the need in applications such as utility steam generator design to analyze three-dimensional geometries with up to tens of thousands of surface and volume computational elements, much research is now focused on further increases in computational speed. Massively parallel computers may well provide the required computational capability for such problems. 

The medium that interacts with radiation may contain particles and gases which absorb and scatter the radiant energy. In combustion chambers, for example, soot, char, fly-ash, coal particles and spray droplets affect the propagation of radiant energy. Among various gases, carbon dioxide and water vapor are the major participants to radiative transfer, both in combustion chambers and in the atmosphere. 

R. L. Hoover, L. Weiming, A. Benmalek, and T. W. Tong, Sn Solutions for Radiative Heat Transfer in an L-Shaped Participating Medium, in R. D. Skocypec, S. T. Thynell, D. A. Kaminski, A. M. Smith, and T. Tong (eds.), Solution Methods for Radiative Transfer in Participating Media, ASME HTD vol. 325, ASME, New York, 1996. 

Since this formulation has no radiative properties from bounding walls, then it is not valid in boundaries and it is valid only inside the participating medium. Local effective thermal conductivity will be defined in the form of Eq. 13.6 Optically thick approximation is also known as diffusion approximation [8]. 

Simulation of multidimensional RHT in a participating medium remains so far difficult. Detailed comparison with experimental data [24] shows that the diffusion approximation of RHT via an additional radiative thermal conductivity (for example in Ref [25] to study Cap2 melt growth), does not describe the correct temperature distribution in the growth system. Thus, advanced models, such as the discreet exchange factor method [26] or the characteristics method [27, 28] are needed. 

Various theories have been proposed for horizontal transfer at the isoenergetic point. Gouterman considered a condensed system and tried to explain it in the same way as the radiative mechanism. In the radiative transfer, the two energy states are coupled by the photon or the radiation field. In the nonradiative transfer, the coupling is brought about by the phonon field of the crystalline matrix. But this theory is inconsistent with the observation that internal conversion occurs also in individual polyatomic molecules such as benzene. In such cases the medium does not actively participate except as a heat sink. This was taken into consideration in theories proposed by Robinson and Frosch, and Siebrand and has been further improved by Bixon and Jortner for isolated molecules, but the subject is still imperfectly understood. 

The emissivity of the gas media is a function of many parameters including gas pressure, temperature, partial pressures of radiatively participating species, and optical path length or characteristic dimension. Thus, if the concentration of the absorb-ing/emitting species is increased, the emissivity of the media increases as well. If the optical thickness of a medium tends to infinity, then the emissivity of such a medium tends to 1, which corresponds to the blackbody limit. At this limit, radiation becomes a totally diffusive process. 

---