On the radiative transfer in a spherical medium

Atalay, M.A.

doi:10.1016/j.ijthermalsci.2005.04.011

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…The Mie phase function for media containing spherical particles is given by (Modest, 2013;Dombrovsky and Baillis, 2010;Crosbie and Davidson, 1985) (Θ) = 4 2 ( , , Θ) 2 (5) ⁄ here, ( , , Θ)is the unpolarized radiation intensity, and the scattering angle, Θ, is defined as Θ = μμ ′ + √1 − 2 √1 − ′2 cos( − ′ ) (6) The diffuse incidence boundary conditions for Eq. (1) can be written as (Atalay, 2006;Sutton, H. W., Ozisik, 1979) Romuald Tapimo and Hervé Thierry Tagne Kamdem / American Journal of Heat and Mass Transfer (2016) Vol. 3 No.…”

Section: Radiative Heat Transfer Problemmentioning

confidence: 99%

“…4 pp. 280-295 285 Fourier transform of the radiative intensity moments approach (Atalay, 2006). In the linear algebra approach, the coupled differential equations of radiance moments can be solved using either a direct shooting method (Li and Tong, 1990) or by using finite differencing for space differential couple to a matrix algorithm methods (Evans, 1993).…”

Section: Numerical Solutionmentioning

confidence: 99%

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A Spherical Harmonic Formulation for Radiative Heat Transfer Analysis

Tapimo¹,

Kamdem²

2016

AJHMT

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This paper presents a formulation of the spherical harmonics method for analyzing radiative heat transfer through participating planar media. The proposed approach expand only the radiative intensity into a finite series of Legendre polynomials, while the scattering phase function is directly averaged over incident and scattered radiations without its expansion in series of Legendre polynomials as classical spherical harmonics method assumes. A matrix algorithm formulation is then implemented, which enable computer of spherical harmonics solution for higher order without difficulty. Radiative heat transfer through anisotropic scattering media under diffuse incidence is examined. The Mie theory for spherical particles is used to account scattering phase function of participating isotropic media. Different scattering phase functions, scattering albedo and optical thicknesses are used in the numerical analysis. Excellent agreements on radiative heat fluxes, hemispherical transmittance and reflectance are obtained between spherical harmonics methods with and without expansion of scattering phase function in series of Legendre polynomials. For high angular discretization, computational time requirements of each of the two spherical harmonics methods are comparable, while the present spherical harmonics formulation is time consuming for low order angular discretization. However, for low and high angular discretizations, spherical harmonics with and without scattering phase function expansion in series of Legendre polynomials computational times are extremely small. The results also indicate that for the same angular discretization order, spherical harmonics methods are more accurate than the discrete ordinates method.

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Section: Radiative Heat Transfer Problemmentioning

confidence: 99%

Section: Numerical Solutionmentioning

confidence: 99%

A Spherical Harmonic Formulation for Radiative Heat Transfer Analysis

Tapimo¹,

Kamdem²

2016

AJHMT

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Some Benchmark Results in Spherical Media Radiative Transfer Problems

Yilmazer

Kocar

2009

Transport Theory and Statistical Physics

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A comparative study on classical polynomial approximations to the transport equation in spherical media albedo problems

Yilmazer

Kocar

2008

Kerntechnik

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The ultraspherical polynomial approximation which unifies all classical polynomial sequences in a unique form is used to calculate the albedo for isotropic scattering in a homogeneous spherical medium. This is the most general polynomial approach in the sense that it includes all classical polynomial methods to solve the transport equation such as and methods. For the first time an antisymmetric polynomial (ultraspherical polynomial) solution to the corresponding pseudo-slab problem is proposed. Very accurate and consistent albedo values are obtained for a variety of methods when compared to the literature. It is also shown that various approximations differ only in convergency characteristics; some converge monotonically, some in the mean.

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On the radiative transfer in a spherical medium

Cited by 3 publications

References 22 publications

A Spherical Harmonic Formulation for Radiative Heat Transfer Analysis

A Spherical Harmonic Formulation for Radiative Heat Transfer Analysis

Some Benchmark Results in Spherical Media Radiative Transfer Problems

A comparative study on classical polynomial approximations to the transport equation in spherical media albedo problems

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