Asymptotic analysis of conductive‐radiative heat transfer

Article type: Research Article

Authors: Laitinen, Mika T.

Affiliations: Numerola Oy (Ltd.), Väinönkatu 11 A, FIN‐40100 Jyväskylä, Finland E‐mail: Mika.Laitinen@numerola.fi

Abstract: In highly absorptive semitransparent material, conductive‐radiative heat transfer is often approximated by either diffusion approximation or Stefan–Boltzmann boundary condition. Using singular perturbations and boundary layer analysis, we derive rigorously these two approximations from the radiative transport equation. We prove error estimates for temperature and propose a variant of diffusion approximation which effectively describes the boundary layer behavior. To obtain these estimates, we prove stability and boundedness of solutions for conductive‐radiative heat equation independently of the radiation parameters.

Keywords: conductive‐radiative heat transfer, diffusion approximation, semitransparent media, Stefan–Boltzmann law

Journal: Asymptotic Analysis, vol. 29, no. 3-4, pp. 323-342, 2002