Anisotropic radiation transfer in a plane medium with specularly-reflecting boundary conditions

Attia, M. T.; Madkour, M.A.; Abulwafa, Essam M.; Abdel-Naby, M.

doi:10.1016/0022-4073(92)90030-8

Cited by 14 publications

(6 citation statements)

References 8 publications

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“…Therefore, in the present work, the simultaneous conductive-radiative heat transfer in an inhomogeneous slab of diffuse and angular-dependent specular reflecting boundaries with anisotropic scattering is considered. A variational technique [13,14] is used to solve the radiative transfer equation in its integral form for linear anisotropic scattering [15]. Due to the nonlinear relation between the radiative transfer and the conductive energy, an iterative technique is used to solve the coupled problem.…”

Section: Introductionmentioning

confidence: 99%

Conductive-radiative heat transfer in an inhomogeneous slab with directional reflecting boundaries

Abulwafa¹

1999

J. Phys. D: Appl. Phys.

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Conductive-radiative heat transfer through an inhomogeneous, anisotropic scattering, turbid plane-parallel medium is considered. The medium is taken to be of diffuse and specular reflecting boundaries. The specular reflecting coefficients of the boundaries are considered to be angular dependent. The variational technique is used to solve the radiative problem while an iterative method is taken to include the nonlinearity effect of the temperature distribution of the medium from the conductive energy equation. The dimensionless temperature distribution and conductive, radiative and total net fluxes through the medium are calculated. The calculations for matched boundaries and a homogeneous, isotropic scattering slab are calculated and compared with other calculations to show good agreement. The calculations are carried out for mismatched boundaries, with homogeneous and inhomogeneous media. The results are given for isotropic and forward linear anisotropic scattering slabs.

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Section: Introductionmentioning

confidence: 99%

Conductive-radiative heat transfer in an inhomogeneous slab with directional reflecting boundaries

Abulwafa¹

1999

J. Phys. D: Appl. Phys.

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“…where l=1, 2, .., L with a 0 =1. It's well known that the problem equation (1) with general boundary conditions equations (2a) and (2b) can be linked to the corresponding source-free problem [26] x A T a , 3 8…”

Section: Examples Of Applicationsmentioning

confidence: 99%

Solution of the one-speed neutron transport equation in anisotropic scattering medium with a Pomraning-Eddington approximation approach

et al. 2019

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In this work, a combined modified K-integral approach and Pomraning-Eddington approximation to solve the neutron transport equation for general anisotropic scattering law is presented. This combined approach leads to the establishment of general expressions of the even e(x, μ) and odd o(x, μ) functions of the angular variable μ. Both functions are slowly varying in x. Furthermore, these expressions can be reduced to those reported in literature. In addition, the parameters such as OPEN ACCESS RECEIVED

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“…Attia et al [9] related the above problem to the corresponding source-free problem with specular boundary conditions. The source-free problem is represented by…”

Section: The Basic Equationsmentioning

confidence: 99%

“…Siewert et al [1] used the F N method, Benassi et al [2] used the P N method and El Wakil et al [3] used Pade's approximant technique. Özisik and Yener [4], Cengel et al [5], Cengel and Özisik [6,7], El Wakil et al [8] and Attia et al [9] used the Galerkin technique. In a recent work the Pomraning-Eddington approximation was used to solve the radiative transfer in turbid media using weight functions and variational techniques [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

The maximum-entropy technique for radiative transfer in turbid media with reflecting boundary conditions

Degheidy¹

1997

J. Phys. D: Appl. Phys.

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The problem of radiative transfer in an inhomogeneous finite medium with an internal energy source and bounding surfaces which reflect both specularly and diffusively is solved by using the maximum-entropy technique. The reflectivity R and transmissivity T for plane-parallel media are calculated and compared with results from published calculations that used other methods. The comparison shows that the maximum-entropy results are good and converge to the exact results.

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Anisotropic radiation transfer in a plane medium with specularly-reflecting boundary conditions

Cited by 14 publications

References 8 publications

Conductive-radiative heat transfer in an inhomogeneous slab with directional reflecting boundaries

Conductive-radiative heat transfer in an inhomogeneous slab with directional reflecting boundaries

Solution of the one-speed neutron transport equation in anisotropic scattering medium with a Pomraning-Eddington approximation approach

The maximum-entropy technique for radiative transfer in turbid media with reflecting boundary conditions

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