Study of Radiation in Spherical Media Using Moment Method

T. Sghaier

doi:doi:10.11648/j.ajpa.20130101.15

| Peer-Reviewed

Study of Radiation in Spherical Media Using Moment Method

T. Sghaier

Published in American Journal of Physics and Applications (Volume 1, Issue 1)

Received: 3 June 2013 Published: 10 July 2013

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

A moment technique is presented to improve the performance of the discrete ordinates method when solving the radiation problems in spherical media. In this approach the angular derivative term of the discretized 1-D radiative transfer equation is derived from an expansion of the radiative intensity on the basis of angular moments. The set of resulting differential equations, obtained by the application of the SN method associated to moment method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the moment approximation compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order SN calculations.

Published in	American Journal of Physics and Applications (Volume 1, Issue 1)
DOI	10.11648/j.ajpa.20130101.15
Page(s)	25-32
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

RTE, Spherical Medium, Angular Derivative Term, DOM, Moment Method

References

[1]	G. C. Pomraning, C. E. Siewert, On the integral form of the equation of transfer for a homogeneous spheres. JQSRT1982; 28:503-6
[2]	C. E. Siewert, J. R Thomas, On coupled conductive radiative heat-transfer problems in a sphere. JQSRT 1991; 46:63-72
[3]	Hsin-sen Chu, Weng Ling-Chia, Tsen. Combined conduction and radiation in absorbing, emitting and isotropically-scattering concentric spherical media. JQSRT 1991;46:251-7.
[4]	G. Jia, Y. Yener, JW. Cipolla, Radiation between two concentric spheres separated by participating medium. JQSRT 1991;46:11-9.
[5]	E. M. Abulwafa, Radiative-transfer in a linearly-anisotropic spherical medium. JQSRT 1993;49:165-75.
[6]	R. viskanta, A. Grosbie, Radiative transfer between two concentric spheres separated by absorbing an emitting gray medium. JQSRT 1976;6:871-9.
[7]	S. T. Thynell, M. N. Ozisik Radiation transfer in an isotropically scattering homogeneous solid sphere. JQSRT; 1989; 33:187-96.
[8]	J. R. Tsai, M. N. Ozisik, F. J. Santarelli, Radiation in spherical symmetry with anisotropic scattering and variable properties. JQSRT 1989;42:187-96.
[9]	T. Sghaier, M. S. Sifaoui, A. Soufiani, Study of radiation in spherical media using discrete ordinates method associated with the finite Legendre transform JQRST 2000; 64:339-51.
[10]	H. Trabelsi, T. Sghaier, M. S. Sifaoui, A theoretical study of radiation between spheres using a modified discrete ordinates method associated with Legendre transform. JQSRT 2005; 415-28.
[11]	N. Aouled-Dlala, T. Sghaier, E. Seddiki, Numerical solution of conductive and radiative heat transfer in concentric spherical and cylindrical medium. JQSRT 2007; 443-57.
[12]	M. Y. Kim, J. H. Cho, S. W. Baek, Radiative heat transfer between two concentric spheres separated by a two phase mixture of non gray particules using the modified discrete ordinates method. JQSRT; 2008;1607-1621.
[13]	B. W. Li, Y. S. Sun, S. W. Zhang DW SW. Chebyshev collocation spectral methods for coupled radiation and conduction in concentric spherical partipating medium. Journal of Heat Transfer 2009; vol 131.
[14]	S C. Mishra, C. H. Krishna, M. Y. Kim, Lattice Boltzmann method and modifiede discrete ordinates method applied to radiative transport in a spherical medium with and without conduction. Numerical Heat Transfer Part A,58,852-81,2010.
[15]	M. F. Modest, Radiative heat transfer, 2nd, Academic, SanDiego, CA3; 2003.
[16]	K. Sen, S. J. Wilson, Generalised eddington approximation for radiative transfer problems in spherically symmetric moving media. Astrophysics and space science 2003; 203- 227-40.
[17]	IMSL Math Library. 1 ed. Houston, TX. (1997).

Cite This Article

Plain Text BibTeX RIS

APA Style

T. Sghaier. (2013). Study of Radiation in Spherical Media Using Moment Method. American Journal of Physics and Applications, 1(1), 25-32. https://doi.org/10.11648/j.ajpa.20130101.15

Copy | Download

ACS Style

T. Sghaier. Study of Radiation in Spherical Media Using Moment Method. Am. J. Phys. Appl. 2013, 1(1), 25-32. doi: 10.11648/j.ajpa.20130101.15

Copy | Download

AMA Style

T. Sghaier. Study of Radiation in Spherical Media Using Moment Method. Am J Phys Appl. 2013;1(1):25-32. doi: 10.11648/j.ajpa.20130101.15

Copy | Download

@article{10.11648/j.ajpa.20130101.15,
  author = {T. Sghaier},
  title = {Study of Radiation in Spherical Media Using Moment Method},
  journal = {American Journal of Physics and Applications},
  volume = {1},
  number = {1},
  pages = {25-32},
  doi = {10.11648/j.ajpa.20130101.15},
  url = {https://doi.org/10.11648/j.ajpa.20130101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20130101.15},
  abstract = {A moment technique is presented to improve the performance of the discrete ordinates method when solving the radiation problems in spherical media. In this approach the angular derivative term of the discretized 1-D radiative transfer equation is derived from an expansion of the radiative intensity on the basis of angular moments. The set of resulting differential equations, obtained by the application of the SN method associated to moment method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the moment approximation compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order SN calculations.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Study of Radiation in Spherical Media Using Moment Method
AU  - T. Sghaier
Y1  - 2013/07/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajpa.20130101.15
DO  - 10.11648/j.ajpa.20130101.15
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 25
EP  - 32
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20130101.15
AB  - A moment technique is presented to improve the performance of the discrete ordinates method when solving the radiation problems in spherical media. In this approach the angular derivative term of the discretized 1-D radiative transfer equation is derived from an expansion of the radiative intensity on the basis of angular moments. The set of resulting differential equations, obtained by the application of the SN method associated to moment method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the moment approximation compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order SN calculations.
VL  - 1
IS  - 1
ER  -

Copy | Download

Author Information

T. Sghaier

Dammam University,Kingdom of Saudi Arabia

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

T. Sghaier. (2013). Study of Radiation in Spherical Media Using Moment Method. American Journal of Physics and Applications, 1(1), 25-32. https://doi.org/10.11648/j.ajpa.20130101.15

Copy | Download

ACS Style

T. Sghaier. Study of Radiation in Spherical Media Using Moment Method. Am. J. Phys. Appl. 2013, 1(1), 25-32. doi: 10.11648/j.ajpa.20130101.15

Copy | Download

AMA Style

T. Sghaier. Study of Radiation in Spherical Media Using Moment Method. Am J Phys Appl. 2013;1(1):25-32. doi: 10.11648/j.ajpa.20130101.15

Copy | Download

@article{10.11648/j.ajpa.20130101.15,
  author = {T. Sghaier},
  title = {Study of Radiation in Spherical Media Using Moment Method},
  journal = {American Journal of Physics and Applications},
  volume = {1},
  number = {1},
  pages = {25-32},
  doi = {10.11648/j.ajpa.20130101.15},
  url = {https://doi.org/10.11648/j.ajpa.20130101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20130101.15},
  abstract = {A moment technique is presented to improve the performance of the discrete ordinates method when solving the radiation problems in spherical media. In this approach the angular derivative term of the discretized 1-D radiative transfer equation is derived from an expansion of the radiative intensity on the basis of angular moments. The set of resulting differential equations, obtained by the application of the SN method associated to moment method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the moment approximation compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order SN calculations.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Study of Radiation in Spherical Media Using Moment Method
AU  - T. Sghaier
Y1  - 2013/07/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajpa.20130101.15
DO  - 10.11648/j.ajpa.20130101.15
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 25
EP  - 32
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20130101.15
AB  - A moment technique is presented to improve the performance of the discrete ordinates method when solving the radiation problems in spherical media. In this approach the angular derivative term of the discretized 1-D radiative transfer equation is derived from an expansion of the radiative intensity on the basis of angular moments. The set of resulting differential equations, obtained by the application of the SN method associated to moment method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the moment approximation compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order SN calculations.
VL  - 1
IS  - 1
ER  -

Copy | Download