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Discrete Eigenvalues of the Radiative Transfer Equation with Legendre and Chebyshev Polynomials Solutions

Year 2023, , 2594 - 2603, 01.12.2023

Hatice Asel Zilayaz , Halide Koklu

https://doi.org/10.21597/jist.1280514

Abstract

The radiation transfer equation has been considered for finite slab with isotropic scattering in homogeneous medium. The Legendre and Chebyshev polynomials are used to solve the radiative transfer equation to determine the discrete eigenvalues of the system for various single scattering albedo. The numerical results are performed for high level iterations of the PN and TN methods. The numerical values are tabulated and compared with the previous works. It is shown that our results are in very good agreement with previous studies.

Keywords

Eigenvalue Problem Radiative Transfer Chebyshev Polynomials

References

  • Arnold, D. K. and Miguel, M. (2002). Chebyshev Spectral Methods for Radiative Transfer, SIAM Journal on Scientific Computing, 23(6), 2074-2094.
  • Anli, F. Yaşa, F. Güngör, S. et al. (2006). TN approximation to neutron transport equation and application to critical slab problem, Journal of Quantitative Spectroscopy and Radiative Transfer, 101(1), 129-134.
  • Case, K. M. and Zweifel P. F. (1967). Linear Transport Theory, Addison-Wesley Publishing Company, 342.
  • Chandrasekhar, S. (1934). The radiative equilibrium of extended stellar atmospheres, Monthly notices of the royal astronomical society, 94(5), 444-458.
  • Davison, B. and Sykes, J.B. (1958). Neutron Transport Theory, Physics Today, 11(2), 30-32.
  • Duderstadt. J. J., Martin R., 1978. Transport Theory. A WILEY-Interscience Pubucation
  • Köklü, H. and Özer, O. (2021). Critical Size of a Slab Reactor with Neutron Transport Theory of the Triplet Anisotropic Scattering, The International Journal of Materials and Engineering Technology, 3(2), 98-108.
  • Kosirev, N.A. (1934). Radiative equilibrium of the extended photosphere, Monthly notices of the royal astronomical society, 94(5), 430-443.
  • Liemert, A. and Kienle, A. (2011). Analytical solution of the radiative transfer equation for infinite-space fluence. Physical Review A, 83(1); 015804(1-4).
  • Machali, H.M., Haggag, M.H. and Al-Gorashi, A.K. (2013). On The Use of a Spatial Chebyshev Polynomials Together with The Collocation Method in Solving Radiative Transfer Problem in a Slab, Arab Journal of Nuclear Sciences and Applications, 46(3), 167-185.
  • Menguc M. P. and Viskanta R. (1982), Comparison of radiative transfer approximations for a highly forward scattering planar medium, Journal of Quantitative Spectroscopy and Radiative Transfer, 29(5), 381-394.
  • Milne, E.A. (1921). Radiative equilibrium in the outer layers of a star, Monthly notices of the royal astronomical society, 81(5), 361-375.
  • Ozisik, M. N. and Shouman S. M. (1980), Source Function Expansion Method for Radiative Transfer in a Two-Layer Slab, Journal of Quantitative Spectroscopy and Radiative Transfer, 24(6),441-449.
  • Pomraning, G. C. and Erdmann, R.C. (1970). Photon Transmission Through a Hot Electron Atmosphere, Journal of Quantitative Spectroscopy and Radiative Transfer, 10(2), 133-141.
  • Pomraning, G. C. (1973). A Simple Calculation of the Time Dependence of the Second Spatial Moment, Nuclear Science and Engineering, 52(1),144-145.
  • Stacey, W. M. (1957). Nuclear Reactor Physics. John Wiley and Sons Inc, 10(9).
  • Taşdelen, M., (2017). Radiyatif Transfer Denkleminde SN Metodu ve Ag Faz Fonksiyonu ile Özdeğer Spektrumu (Yüksek Lisans Tezi), Kahramanmaraş Sütçü İmam Üniversitesi, Kahramanmaraş.
  • Taşdelen, N. (2017). Radiyatif Transfer Denkleminde Metodu ve Faz Fonksiyonu ile Özdeğer Spektrumu (Yüksek Lisans Tezi), Kahramanmaraş Sütçü İmam Üniversitesi, Kahramanmaraş.
  • Yılmazer, A. and Kocar, C. (2009). Some Benchmark Results in Spherical Media Radiative Transfer Problems, Transport Theory and Statistical Physics, 38(5), 273–292.

Legendre ve Chebyshev Polinomları Çözümü ile Radyasyon Transfer Denkleminin Kesikli Özdeğerleri

Year 2023, , 2594 - 2603, 01.12.2023

Hatice Asel Zilayaz , Halide Koklu

https://doi.org/10.21597/jist.1280514

Abstract

Işınım transfer denklemi, homojen ortamda izotropik saçılmalı, sonlu plaka sistemi için ele alınmıştır. Legendre ve Chebyshev polinomları, çeşitli tekil saçılma albedolarıyla sistemin kesikli özdeğerlerini belirlemek üzere ışınım transfer denklemini çözmekte kullanılmıştır. Sayısal sonuçlar, PN ve TN yöntemlerinin yüksek seviye tekrarlama basamakları için gerçekleştirilmiştir. Sayısal değerler tablolaştırılmış ve önceki çalışmalarla karşılaştırılmıştır. Sonuçlarımızın önceki çalışmalarla çok iyi uyum içinde olduğu gösterilmiştir.

Keywords

Özdeğer Problemi Işınım Transfer Denklemi Chebyshev Polinomları

References

  • Arnold, D. K. and Miguel, M. (2002). Chebyshev Spectral Methods for Radiative Transfer, SIAM Journal on Scientific Computing, 23(6), 2074-2094.
  • Anli, F. Yaşa, F. Güngör, S. et al. (2006). TN approximation to neutron transport equation and application to critical slab problem, Journal of Quantitative Spectroscopy and Radiative Transfer, 101(1), 129-134.
  • Case, K. M. and Zweifel P. F. (1967). Linear Transport Theory, Addison-Wesley Publishing Company, 342.
  • Chandrasekhar, S. (1934). The radiative equilibrium of extended stellar atmospheres, Monthly notices of the royal astronomical society, 94(5), 444-458.
  • Davison, B. and Sykes, J.B. (1958). Neutron Transport Theory, Physics Today, 11(2), 30-32.
  • Duderstadt. J. J., Martin R., 1978. Transport Theory. A WILEY-Interscience Pubucation
  • Köklü, H. and Özer, O. (2021). Critical Size of a Slab Reactor with Neutron Transport Theory of the Triplet Anisotropic Scattering, The International Journal of Materials and Engineering Technology, 3(2), 98-108.
  • Kosirev, N.A. (1934). Radiative equilibrium of the extended photosphere, Monthly notices of the royal astronomical society, 94(5), 430-443.
  • Liemert, A. and Kienle, A. (2011). Analytical solution of the radiative transfer equation for infinite-space fluence. Physical Review A, 83(1); 015804(1-4).
  • Machali, H.M., Haggag, M.H. and Al-Gorashi, A.K. (2013). On The Use of a Spatial Chebyshev Polynomials Together with The Collocation Method in Solving Radiative Transfer Problem in a Slab, Arab Journal of Nuclear Sciences and Applications, 46(3), 167-185.
  • Menguc M. P. and Viskanta R. (1982), Comparison of radiative transfer approximations for a highly forward scattering planar medium, Journal of Quantitative Spectroscopy and Radiative Transfer, 29(5), 381-394.
  • Milne, E.A. (1921). Radiative equilibrium in the outer layers of a star, Monthly notices of the royal astronomical society, 81(5), 361-375.
  • Ozisik, M. N. and Shouman S. M. (1980), Source Function Expansion Method for Radiative Transfer in a Two-Layer Slab, Journal of Quantitative Spectroscopy and Radiative Transfer, 24(6),441-449.
  • Pomraning, G. C. and Erdmann, R.C. (1970). Photon Transmission Through a Hot Electron Atmosphere, Journal of Quantitative Spectroscopy and Radiative Transfer, 10(2), 133-141.
  • Pomraning, G. C. (1973). A Simple Calculation of the Time Dependence of the Second Spatial Moment, Nuclear Science and Engineering, 52(1),144-145.
  • Stacey, W. M. (1957). Nuclear Reactor Physics. John Wiley and Sons Inc, 10(9).
  • Taşdelen, M., (2017). Radiyatif Transfer Denkleminde SN Metodu ve Ag Faz Fonksiyonu ile Özdeğer Spektrumu (Yüksek Lisans Tezi), Kahramanmaraş Sütçü İmam Üniversitesi, Kahramanmaraş.
  • Taşdelen, N. (2017). Radiyatif Transfer Denkleminde Metodu ve Faz Fonksiyonu ile Özdeğer Spektrumu (Yüksek Lisans Tezi), Kahramanmaraş Sütçü İmam Üniversitesi, Kahramanmaraş.
  • Yılmazer, A. and Kocar, C. (2009). Some Benchmark Results in Spherical Media Radiative Transfer Problems, Transport Theory and Statistical Physics, 38(5), 273–292.
There are 19 citations in total.

Details

Primary Language English
Subjects Metrology, Applied and Industrial Physics
Journal Section Fizik / Physics
Authors

Hatice Asel Zilayaz 0009-0002-1899-0068

Halide Koklu 0000-0003-1787-6693

Early Pub Date November 30, 2023
Publication Date December 1, 2023
Submission Date April 10, 2023
Acceptance Date July 3, 2023
Published in Issue Year 2023

Cite

APA Zilayaz, H. A., & Koklu, H. (2023). Discrete Eigenvalues of the Radiative Transfer Equation with Legendre and Chebyshev Polynomials Solutions. Journal of the Institute of Science and Technology, 13(4), 2594-2603. https://doi.org/10.21597/jist.1280514
AMA Zilayaz HA, Koklu H. Discrete Eigenvalues of the Radiative Transfer Equation with Legendre and Chebyshev Polynomials Solutions. Iğdır Üniv. Fen Bil Enst. Der. December 2023;13(4):2594-2603. doi:10.21597/jist.1280514
Chicago Zilayaz, Hatice Asel, and Halide Koklu. “Discrete Eigenvalues of the Radiative Transfer Equation With Legendre and Chebyshev Polynomials Solutions”. Journal of the Institute of Science and Technology 13, no. 4 (December 2023): 2594-2603. https://doi.org/10.21597/jist.1280514.
EndNote Zilayaz HA, Koklu H (December 1, 2023) Discrete Eigenvalues of the Radiative Transfer Equation with Legendre and Chebyshev Polynomials Solutions. Journal of the Institute of Science and Technology 13 4 2594–2603.
IEEE H. A. Zilayaz and H. Koklu, “Discrete Eigenvalues of the Radiative Transfer Equation with Legendre and Chebyshev Polynomials Solutions”, Iğdır Üniv. Fen Bil Enst. Der., vol. 13, no. 4, pp. 2594–2603, 2023, doi: 10.21597/jist.1280514.
ISNAD Zilayaz, Hatice Asel - Koklu, Halide. “Discrete Eigenvalues of the Radiative Transfer Equation With Legendre and Chebyshev Polynomials Solutions”. Journal of the Institute of Science and Technology 13/4 (December 2023), 2594-2603. https://doi.org/10.21597/jist.1280514.
JAMA Zilayaz HA, Koklu H. Discrete Eigenvalues of the Radiative Transfer Equation with Legendre and Chebyshev Polynomials Solutions. Iğdır Üniv. Fen Bil Enst. Der. 2023;13:2594–2603.
MLA Zilayaz, Hatice Asel and Halide Koklu. “Discrete Eigenvalues of the Radiative Transfer Equation With Legendre and Chebyshev Polynomials Solutions”. Journal of the Institute of Science and Technology, vol. 13, no. 4, 2023, pp. 2594-03, doi:10.21597/jist.1280514.
Vancouver Zilayaz HA, Koklu H. Discrete Eigenvalues of the Radiative Transfer Equation with Legendre and Chebyshev Polynomials Solutions. Iğdır Üniv. Fen Bil Enst. Der. 2023;13(4):2594-603.