Radiative transfer and flux theory

Reuven Segev, Joe Goddard

Research output: Contribution to journalArticlepeer-review

Abstract

The fundamental phenomenological equations of radiative transfer, e.g., Lambert's cosine rule and the radiant transport equation, are derived from an analysis based on the Cauchy flux theory of continuum mechanics. For the classical case, where the radiance is distributed regularly over the unit sphere, it is shown that Lambert's rule follows from a balance law for the transfer of radiative power in each direction u on the sphere, together with the appropriate Cauchy postulates and the additional assumption that the corresponding flux vector field ju be parallel to u. The standard radiant transport equation follows from the additional assumption that radiant flux is given as the advection of radiant energy density. A theory is also presented for the singular limit of isolated rays, where the distribution of radiance on the sphere reduces to a Borel measure.

Original languageEnglish
Pages (from-to)327-344
Number of pages18
JournalMathematics and Mechanics of Solids
Volume20
Issue number3
DOIs
StatePublished - 16 Mar 2015

Keywords

  • Cauchy
  • Radiative transfer
  • flux
  • radiation
  • radiometry
  • singular distribution
  • stress

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