RESEARCH PAPERS: Radiative Heat Transfer

Radiative Properties of Dense Fibrous Medium Containing Fibers in the Geometric Limit

[+] Author and Article Information
R. Coquard

 Centre Scientifique et Technique du Bâtiment (CSTB), 24 rue Joseph FOURIER, 38400 Saint Martin d’Hères, Francer.coquard@cstb.fr

D. Baillis

 Centre de Thermique de Lyon (CETHIL), UMR CNRS 5008, Domaine Scientifique de la Doua, INSA de Lyon, Bâtiment Sadi Carnot, 9 rue de la Physique, 69621 Villeurbanne Cedex, France

J. Heat Transfer 128(10), 1022-1030 (Mar 03, 2006) (9 pages) doi:10.1115/1.2345426 History: Received June 13, 2005; Revised March 03, 2006

The aim of this paper is to investigate the dependent regime in dense fibrous materials with size parameters ranging in the geometric optics limit. We use a method based on a Monte Carlo procedure which permits one to identify the radiative properties of dispersed media. This method is applied to materials made of opaque or semitransparent randomly oriented long circular cylinders representing the fibers. The results permit us to investigate the limit of validity of independent scattering hypothesis and to analyze the evolution of the extinction coefficient, scattering albedo and phase function of the fibrous material with the porosity and the reflecting properties of the particles when the shadowing effect due to geometric sized objects is not negligible. We also propose a correlation to estimate the radiative properties in dependent regime from the results of the independent scattering hypothesis. Thereafter, the radiative characteristics obtained are compared to those predicted by previous authors.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 2

Monte Carlo procedure in the sphere of radius Rsphere

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Figure 3

Monte Carlo procedure in the parallelepipedal box containing the arrangement ñ=3.0–0.0001.i

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Figure 4

Evolution of the calculated extinction coefficient with Rsphere for arrangements of infinite fibers with Rfib=0.1mm and different porosities

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Figure 5

Evolution of the average angular repartition S(θ) with Rsphere for an arrangement of finite fibers with Rfib=0.1mm a porosity ϵ=0.751 and different reflecting properties

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Figure 6

Comparison of the angular repartitions E(θ′)∕sin(θ′) and Eho(θ′)∕sin(θ′) by an arrangement of finite fibers with porosity ϵ=0.7965 with different reflecting properties and the associated homogeneous absorbing and scattering media

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Figure 7

Evolution of the dimensionless extinction coefficient βfib.Rfib calculated by the different method

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Figure 8

Evolution of the calculated albedo with the porosity of the material for opaque fibers with different reflectivities

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Figure 9

Evolution of the calculated albedo with the porosity of the material for semi-transparent fibers with different refractive index

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Figure 10

Evolution of the calculated scattering phase function Pfib(θ) with the porosity for medium made of opaque fibers with ρ=0.8

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Figure 11

Evolution of Pfib(θ)∙sinθ with the porosity for semi-transparent fibers with different complex refractive index

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Figure 1

Reflection and refraction at the interface between air and particles



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