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Homogenized Models of Radiation Transfer in Multiphase Media

  • A. V. Gusarov
  • I. Smurov
Chapter

Abstract

The physical model of an absorbing scattering medium (ASM) and the corresponding mathematical model of the radiation transfer equation (RTE) were originally formulated to study dilute dispersed systems like fog [SiHo02]. Such media contain well-separated small particles (droplets), and so they are essentially heterogeneous. Therefore, even the derivation of the conventional RTE can be considered as a problem of homogenization. Nevertheless, homogenization of radiation transfer is often meant as a problem for the conventional RTE with oscillating coefficients [Pa05]. Oscillations with a period much smaller than the characteristic length scale of the problem can be averaged to obtain the effective coefficients of the homogenized RTE. Thus, from a physical point of view, a heterogeneous ASM with short-scale variations of the radiative properties is replaced by an equivalent homogeneous ASM with the effective radiative properties. Such a homogenization problem contains two small length scales of different size. The smallest scale is the size of the scattering inhomogeneity (particle) and the intermediate scale is the period of oscillations of the radiative properties.

The radiative properties of dilute dispersed media can be obtained from the scattering properties of a single particle [SiHo02], but considerable difficulties arise in dense dispersed systems where the volume fraction of the dispersed phases is comparable with the volume fraction of the matrix. The distances between the scatterers (particles) become comparable with their sizes in such systems, so that a mutual influence of the scatterers should be taken into account. This is referred to as dependent scattering. The current mathematical approach to dependent scattering is the RTE with modified radiative properties [BaSa00]. However, the applicability of the RTE to dense dispersed systems has never been rigorously proved.

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References

  1. [SiHo02]
    Siegel, R., Howell, J.R.: Thermal Radiation Heat Transfer, Taylor & Francis, Washington, D.C. (2002).Google Scholar
  2. [Pa05]
    Panasenko, G.: Multi-scale Modelling for Structures and Composites, Springer, Dordrecht (2005).Google Scholar
  3. [BaSa00]
    Baillis, D., Sacadura, J.F.: Thermal radiation properties of dispersed media: theoretical prediction and experimental characterisation. J. Quant. Spectrosc. Radiat. Transfer, 67, 327-363 (2000).CrossRefGoogle Scholar
  4. [Gu08]
    Gusarov, A.V.: Homogenization of radiation transfer in two-phase media with irregular phase boundaries. Phys. Rev. B, 77, article 144201 (2008).CrossRefGoogle Scholar
  5. [To02]
    Torquato, S.: Random Heterogeneous Materials, Springer, New York (2002).MATHGoogle Scholar
  6. [ZeIaTa06]
    Zeghondy, B., Iacona, E., Taine, J.: Determination of the anisotropic radiative properties of a porous material by radiative distribution function identification (RDFI). Internat. J. Heat Mass Transfer, 49, 2810-2819 (2006).CrossRefGoogle Scholar
  7. [GuKr05]
    Gusarov, A.V., Kruth, J.-P.: Modelling of radiation transfer in metallic powders at laser treatment. Internat. J. Heat Mass Transfer, 48, 3423-3434 (2005).CrossRefGoogle Scholar
  8. [SiKa92]
    Singh, B.P., Kaviany, M.: Modelling radiative heat transfer in packed beds. Internat. J. Heat Mass Transfer, 35, 1397-1405 (1992).CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.École Nationale d’Ingénieurs de Saint-Étienne (ENISE)Saint-ÉtienneFrance

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