Radiation transfer theory and the computational methods

DOI: 10.1615/thermopedia.000072

The physical basis of the majority of solutions for many problems of radiation transfer in both nature studies and engineering applications is the notion of radiation transfer in an absorbing and scattering medium as some macroscopic process, which can be described by a phenomenological transfer theory and radiative transfer equation for spectral radiation intensity. It is of great importance that the problems, for which the radiation transfer theory can be applied, are quite numerous and contain the thermal radiation of various participating media. In the present topic of the Radiation Area, we use the following main assumptions concerning a medium properties and radiative transfer:

  • The radiation propagation is more rapid than any change of physical parameters, therefore the radiation intensity field is quasi-steady;
  • The radiative properties on the medium do not depend directly on the radiation intensity, but they vary only with temperature;
  • The wave polarization can be ignored in radiative transfer calculations;
  • The radiation scattering is not accompanied by any frequency variation.

It may be of interest to remember the history of developing the radiation transfer theory including the analytical and computational methods. The astrophysics, particularly the study of star photospheres, was the first branch of science which initiates the theoretical foundations and analytical methods of the radiation transfer theory in the beginning of the 20th century. One can read about it in classic books by Chandrasekhar (1960) and Sobolev (1969).

A new very important period was related to the nuclear physics because transport of neutrons is described by a similar equation. Some well-known analytical and numerical methods of the general neutron/photon transport theory have been developed at that time. The books by Davison (1957), Case and Zweifel (1967), Williams (1971), and Marchuk and Lebedev (1986) can be recommended to a reader for detailed study of the specific of these problems. Computational modeling of neutron transport in nuclear reactors was one of the first engineering applications of the theory.

In parallel with the nuclear studies, the radiation transfer theory was used and further developed by researchers working in the field of atmospheric optics and thermal radiation transfer in the atmosphere. One can refer to early books by Sobolev (1975) and Goody and Yung (1989) and also to recent monographs by Liou (2002) and Kokhanovsky (2006) on this subject.

Starting from sixteenth of the twenties century, the high-temperature processes in thermal engineering provide a great field for modifications and practical applications of the radiation transfer theory. One can remember such problems as radiation heat transfer in furnaces and combustion chambers of rocket engines, the radiative heating of space vehicles in the atmosphere, the radiative-conductive heat transfer in material processing and in highly porous thermal insulations. There is a large body of publications in this field which is very close to the Thermopedia objective. In this introductory article, we give the references to few books only: by Özişik (1973), Adzerikho et al. (1992), Dombrovsky (1996), and Viskanta (2005). Note, that the specific of many engineering problems considered in these books is a combined heat transfer by radiation, conduction, and convection. The interaction of different heat transfer modes makes the mathematical formulation too complicated for analytical study or direct numerical simulation. It was a motivation of the interest to the use and modification of simplified approaches developed by physicists and mathematicians in astrophysics and nuclear engineering.

It is interesting that the present-day period in the history of radiation transfer theory and its applications is characterized by increasing efforts in solving the specific problems of medical imaging and diagnosis. This problem appears to be very complicated. The new developments concerning the optical tomography and the propagation of infrared radiation in a biological tissue can be found in review papers by Arridge (1999), Gibson et al. (2005), Tarvainen et al. (2005) and also in some more recent particular publications.

For systematic study of the radiation transfer theory including the theoretical basis and the computational methods one can recommend the excellent textbooks by Sparrow and Cess (1978), Siegel and Howell (2002) and Modest (2003).

In a set of articles following from this introduction, a reader can find a basic knowledge with the references to the above mentioned textbooks and also to some interesting archive papers. The most important results of the present-day studies reported recently in journal papers are also included. The latter is expected to be important for potential readers who should know the state-of-the-art in the computational radiative transfer in participating media.

Some articles of this topic are not ready at the moment and you might find the words “to be prepared” instead of the article. Nevertheless, the “radiation” team will do the best to complete this work as soon as possible. Moreover, we are going to update the contents of this topic regularly to follow the new methods and findings in the computational radiative transfer field.


Adzerikho, K.S., Nogotov, E.F., and Trofimov, V.P. (1992) Radiative Heat Transfer in Two-Phase Media, New York: CRC Press.

Arridge, S.R. (1999) Optical tomography in medical imaging, Inverse Problems, 15(2): R41-R93.

Case, K.M. and Zweifel, P.F. (1967) Linear Transport Theory, Reading (MA): Addison-Wesley.

Chandrasekhar, S. (1950) Radiative Transfer, Oxford: Oxford Univ. Press (also Dover Publ., 1960).

Davison, B. (1957) Neutron Transport Theory, London: Oxford Univ. Press.

Dombrovsky, L.A. (1996) Radiation Heat Transfer in Disperse Systems, New York: Begell House.

Gibson, A.P., Hebden, J.C., and Arridge, S.R. (2005) Recent advances in diffuse optical imaging, Phys. Med. Biol., 50(4): R1-R43.

Goody, R.M. and Yung, Y.L. (1989) Atmospheric Radiation: Theoretical Basis, Second ed., New York: Oxford Univ. Press.

Kokhanovsky, A.A. (2006) Cloud Optics, Ser. “Atmospheric and Oceanographic Science Library”, v. 34, Berlin: Springer.

Liou, K.N. (2002) An Introduction to Atmospheric Radiation, Second ed., Int. Geophys. Ser., v. 84, San Diego: Acad. Press.

Marchuk, G.I. and Lebedev, V.I. (1986) Numerical Methods in the Theory of Neutron Transport, New York: Harwood.

Modest, M.F. (2003) Radiative Heat Transfer, Second Edition, New York: Acad. Press.

Özişik, M.N. (1973) Radiative Transfer and Interaction with Conduction and Convection, New York: Wiley.

Siegel, R. and Howell, J.R. (2002) Thermal Radiation Heat Transfer, Fourth Edition, New York: Taylor & Francis.

Sobolev, V.V. (1969) Course of Theoretical Astrophysics, Springfield: NASA Tech. Transl. F-531 (original Russian edition – Moscow: Nauka, 1967).

Sobolev, V.V. (1975) Light Scattering in Planetary Atmospheres, Oxford: Pergamon Press (original Russian edition – Moscow: Nauka, 1972).

Sparrow, E.M. and Cess, R.D. (1978) Radiation Heat Transfer, New York: McGraw-Hill.

Tarvainen, T., Vauhkonen, M., Kolehmainen, V., Arridge, S.R., and Kaipio, J.P. (2005) Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions, Phys. Med. Biol., 50(20): 4913-4930.

Viskanta, R. (2005) Radiative Transfer in Combustion Systems: Fundamentals and Applications, New York: Begell House.

Williams, M.M.R. (1971) Mathematical Methods in Particle Transport Theory, New York: Wiley.

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