Radiative Transfer Equation Solution for Many Scattering Types

Year 2024, Volume: 7 Issue: 1, 9 - 15, 15.01.2024

Dilek Aydın , Halide Koklu

https://doi.org/10.34248/bsengineering.1335553

Abstract

The radiative transfer equation is a mathematical equation that describes the changes in the number of photons within a specified volume of a medium over time, taking into account phenomena such as scattering, absorption, and re-emission resulting from photon interactions with the medium. In this study, the radiative transfer equation is considered for a finite slab which anisotropic scattering in a homogeneous medium. The equation solution is done by Legendre polynomials for linear anisotropic, pure quadratic and Rayleigh scattering types. The numerical results are displayed in the tables up to the 13th iteration of the Legendre polynomials. Tables are obtained using different scattering coefficients and single scattering albedo values. The results contain a wide range of data obtained from the method of solving the Legendre polynomial of the radiative transfer equation. Thus, with this study, the effect of different scattering types on the solution of the radiative transfer equation has been demonstrated.

Keywords

Radiative transfer equation, Legendre polynomial method, Anisotropic scattering

References

• Anlı F, Güngör S. 2005. General eigenvalue spektrum in a one-dimensional slab geometry transport equation. Nucl Sci Eng, 150: 1-6.
• Biçer M, Kaşkaş A. 2018. Solution of the radiative transfer equation for Rayleigh scattering using the infinite medium Green’s function. Astrophys Space Sci, 363: 46.
• Chandrasekhar S. 1950. Radiative transfer. Oxford University Press, London, UK.
• Chandrasekhar S. 1960. Radiative Transfer. Dover Publication, New York, US.
• Cherry SR, Sorenson JA, Phelps ME. 2012. Interaction of Radiation with Matter. J Nucl Med, 54(7): 63-85.
• Elghazaly A, El-Konsol S, Sabbah AS, Hosni M. 2017. Anisotropic radiation transfer in a two-layer inhomogeneous slab with reflecting boundaries. Int J Therm Sci, 120: 148-161.
• Güçlü İ. 2009. Legendre polynomial approach for solutions of higher order linear volterra integro-differential equations. MSc Thesis, Celal Bayar University, Insitute of Science, Manisa, Türkiye, pp: 84.
• Herman BM, Browning SR. 1965. A Numerical solution to the equation of radiative transfer. J Atmos Sci, 22(5): 559-566.
• Hussein A, Selim MM. 2012. Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Appl Math Comput, 218(13): 7193-7203.
• Sallah M, Selim MM. 2008. Continuous stochastic radiative transfer with Rayleigh scattering in semi-infinite atmospheric media. In Proceedings of the 3rd Environmental Physics Conference, 19-February 23, 2008, Aswan, Egypt.
• Stamnes K, Thomas GE, Stamnes JJ. 2017. Formulation of radiative transfer problems. Cambridge University Press, Cambridge, UK, pp: 186-226.
• Tapimo R, Tagne Kamdem HT, Yemele D. 2018. Homojen olmayan polarize düzlemsel atmosferde ışınım transfer analizi için ayrı bir küresel harmonik yöntemi. Astrofizik Uzay Bilim, 363(3): 52.
• Taşdelen M. 2017. Application 𝑺𝑵 method and AG phase functions to radiavite transfer equation of eigenvalue spektrum. MSc Thesis, Sütçü İmam University, Institute of Science, Kahramanmaraş, Türkiye, pp: 42.