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Research Papers: Radiative Heat Transfer

Hyperbolic Conduction–Radiation in Participating and Inhomogeneous Slab With Double Spherical Harmonics and Lattice Boltzmann Methods

[+] Author and Article Information
Guillaume Lambou Ymeli

Laboratoire de Mécanique et de Modélisation
des Systèmes Physiques (L2MSP),
Department of Physics/Faculty of Science,
University of Dschang,
P.O. Box 67,
Dschang, Cameroon
e-mail: ymeliguillaume@yahoo.fr

Hervé Thierry Tagne Kamdem

Laboratoire de Mécanique et de Modélisation
des Systèmes Physiques (L2MSP),
Department of Physics/Faculty of Science,
University of Dschang,
P.O. Box 67,
Dschang, Cameroon
e-mails: herve.kamdem@univ-dschang.org;
ttagne@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 14, 2016; final manuscript received November 15, 2016; published online January 24, 2017. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 139(4), 042703 (Jan 24, 2017) (14 pages) Paper No: HT-16-1203; doi: 10.1115/1.4035315 History: Received April 14, 2016; Revised November 15, 2016

This work deals with the combined mode of non-Fourier conduction and radiation transfer in isotropically/anisotropically scattering, homogeneous, and inhomogeneous planar media with reflective boundaries subjected to the constant internal temperature of the medium and the externally isotropic diffuse incidence at one boundary. An analytical double spherical harmonics method (DPN) is proposed to solve the radiative problem. The non-Fourier conduction is described with the Cattaneo–Vernotte model, and the governing hyperbolic energy equation is solved using the lattice Boltzmann method (LBM). For radiative problems through the layer/layered media, the radiative heat fluxes, hemispherical radiative intensities, transmissivity, and reflectivity are found, while for coupled conduction and radiation, the temperature distributions are found for various optical thicknesses, space-dependent scattering albedo, conduction–radiation parameters, and boundary reflectivities. Results of the present work are in excellent agreement with those available in the literature. Moreover, these results demonstrate that the proposed analytical double spherical method is an efficient, robust, and accurate method for radiative transfer through inhomogeneous layer/layered planar media analysis. Furthermore, it is observed that space-dependent scattering albedo and boundary reflectivities have a very significant effect in the hyperbolic sharp wave front of non-Fourier conduction.

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Figures

Grahic Jump Location
Fig. 1

Exit radiative intensities at the transparent boundaries for ω=0.5+z/L: (a) downstream value  I− and (b) upstream value  I+

Grahic Jump Location
Fig. 2

Temperature distribution at two time levels with Nc=0.25 and σe=1.0 and for different (a) numbers of layers and (b) approximation orders

Grahic Jump Location
Fig. 3

Temperature distribution with  ω=0.0 and  σe=1.0 and for different values of conduction–radiation parameter: (a) Nc=0.1, (b) Nc=0.25, (c) Nc=1.0, and (d) Nc=2.5

Grahic Jump Location
Fig. 4

Temperature distribution at two time levels for  ω=0.5 and  σe=1.0 for different values of conduction–radiation parameter: (a)  Nc=0.025 and (b) Nc=1.0

Grahic Jump Location
Fig. 5

Effect of diffuse and specular reflectivity on the temperature distribution for ω=0.5,  Nc=0.25, and σe=1.0 at two time levels: (a)  ξ=0.3 and (b)  ξ=0.6

Grahic Jump Location
Fig. 6

Effect of diffuse and specular reflectivity on the temperature distribution for   ω=0.5,  Nc=0.025, and   σe=1.0 at two time levels: (a)  ξ=0.3 and (b)  ξ=0.6

Grahic Jump Location
Fig. 7

Effect of linear variation of scattering albedo on the temperature distribution computed with 100 layers for  Nc=0.25 and   σe=1.0 with dimensionless time: (a)  ξ=0.3 and (b)  ξ=0.6

Grahic Jump Location
Fig. 8

Effect of quadratic variation of scattering albedo on the temperature distribution computed with 100 layers for  Nc=0.25 and σe=1.0 with dimensionless time: (a)  ξ=0.3 and (b)  ξ=0.6

Grahic Jump Location
Fig. 9

Effect of linear variation of scattering albedo on the temperature distribution computed with 100 layers for  Nc=0.025 and   σe=1.0 with dimensionless time: (a)  ξ=0.3 and (b)  ξ=0.6

Grahic Jump Location
Fig. 10

Effect of quadratic variation of scattering albedo on the temperature distribution computed with 100 layers for  Nc=0.025 and σe=1.0 with dimensionless time: (a)  ξ=0.3 and (b)  ξ=0.6

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