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Radiative Transfer Equation and Solutions

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Handbook of Thermal Science and Engineering

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.

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Acknowledgements

The authors thank the supports by National Nature Science Foundation of China (Nos. 51336002, 51421063). The supports 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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Authors and Affiliations

  1. School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, China

    J. M. Zhao & L. H. Liu

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  1. J. M. Zhao
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  2. L. H. Liu
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Correspondence to J. M. Zhao .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota, USA

    Francis A. Kulacki

Section Editor information

  1. Politecnica/COPPE, Universidade Federal do Rio de Janeiro,, Rio de Janeiro, Brasília, Brazil

    Renato Cotta

  2. Department of Mechanical Engineering, University of California, Riverside, California, USA

    Kambiz Vafai

  3. Herff College of Engineering, The University of Memphis, Memphis, Tennessee, USA

    Sumanta Acharya

  4. Gas Technology Institute, Illinois, Illinois, USA

    Yaroslav Chudnovsky

  5. Rm 8260, University of Toronto, Toronto, Ontario, Canada

    Javad Mostaghimi

  6. Cekmeköy Campus, Özyegin University, Çekmeköy - Istanbul, Turkey

    Pinar Mengüc

  7. Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, California, USA

    Vijay K. Dhir

  8. Çekmeköy Campus, Özyeğin University, Nişantepe District, Orman Street, 34794, Çekmeköy - Istanbul, Turkey

    Pinar Mengüç

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Zhao, J.M., Liu, L.H. (2017). Radiative Transfer Equation and Solutions. In: Kulacki, F. (eds) Handbook of Thermal Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-32003-8_56-1

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  • DOI: https://doi.org/10.1007/978-3-319-32003-8_56-1

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