Handbook of Thermal Science and Engineering pp 933-978 | Cite as

# Radiative Transfer Equation and Solutions

## Abstract

Radiative transfer equation (RTE) is the governing equation of radiation propagation in participating media, which plays a central role in the analysis of radiative transfer in gases, semitransparent liquids and solids, porous materials, and particulate media, and is important in many scientific and engineering disciplines. There are different forms of RTEs that are suitable for different applications, including the RTE under different coordinate systems, the transformed RTE having good numerical properties, the RTE for refractive media, etc. This chapter gives a comprehensive overview and introduction of the different forms of RTEs. Furthermore, several fundamental numerical methods for solving RTEs are introduced with the focus on the deterministic methods, such as the spherical harmonics method, discrete-ordinate method, finite volume method, and finite element method. The understanding of the numerical errors for solving the RTEs, including their origin and effects on numerical results, and the related accuracy improvement strategies are reviewed and discussed.

## Notes

### Acknowledgements

The authors thank the supports by National Nature Science Foundation of China (Nos. 51336002, 51421063). The support by the Fundamental Research Funds for the Central Universities (Grant No. HIT. NSRIF. 2013094, HIT.BRETIII.201415) are also greatly acknowledged.

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