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RESEARCH PAPERS: Radiative Heat Transfer

Radiative Heat Transfer Using Isotropic Scaling Approximation: Application to Fibrous Medium

[+] Author and Article Information
Hervé Thierry Tagne

Centre de Thermique de Lyon (CETHIL)— UMR 5008 CNRS INSA de Lyon/Université Claude Bernard—Lyon 1 Bât. Sadi Carnot, 69621 Villeurbanne, France

Dominique Doermann Baillis1

Centre de Thermique de Lyon (CETHIL)— UMR 5008 CNRS INSA de Lyon/Université Claude Bernard—Lyon 1 Bât. Sadi Carnot, 69621 Villeurbanne, Francedominique.baillis@insa-lyon.fr

1

Corresponding author.

J. Heat Transfer 127(10), 1115-1123 (May 12, 2005) (9 pages) doi:10.1115/1.2035108 History: Received December 21, 2004; Revised May 12, 2005

The applicability of the isotropic scaling approximation to heat transfer analysis in fibrous medium is discussed. The isotropic scaling model allows the transformation of an anisotropic scattering problem to an isotropic one. The scaled parameters are derived for general anisotropic scattering and for radiative properties dependent of the incidence radiation. Three different isotropic scaling approaches are considered: Directional isotropic scaling, mean isotropic scaling, and P1 isotropic scaling; corresponding to isotropic scaling parameters function of incident radiation, arithmetic mean over all incident direction of radiative properties, and mean on weighted radiative properties, respectively. The discrete ordinate method is used to solve the radiative transfer equation through fibrous medium. The fibers in the medium are randomly oriented either in space or parallel to the boundaries. Numerical results presented for a pure radiation problem show good accuracy on radiative heat flux between the exact solution and solution obtained with both P1 and directional isotropic scaling while using mean isotropic scaling is unsuitable. Using isotropic scaling approximation to model radiative heat transfer is faster than the exact solution and required few quadratures to converge.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of scattering by a fiber at oblique incidence

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Figure 2

Scattering phase function versus scattering angle: (a) medium 2, (b) medium 3

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Figure 3

Extinction/scattering coefficients versus incident direction

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Figure 4

Bias scattering factor versus incident direction

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Figure 5

Relative error versus Gauss quadrature: Fiber randomly oriented in space

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Figure 6

Relative error versus Gauss quadrature for fiber parallel to the boundaries: (a) thickness is 0.1cm, (b) thickness is 1.0cm, and (c) thickness is 3.0cm

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