American Journal of Physics and Applications
Volume 1, Issue 1, July 2013, Pages: 25-32
Received: Jun. 3, 2013;
Published: Jul. 10, 2013
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T. Sghaier, Dammam University,Kingdom of Saudi Arabia
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.
Study of Radiation in Spherical Media Using Moment Method, American Journal of Physics and Applications.
Vol. 1, No. 1,
2013, pp. 25-32.
G. C. Pomraning, C. E. Siewert, On the integral form of the equation of transfer for a homogeneous spheres. JQSRT1982; 28:503-6
C. E. Siewert, J. R Thomas, On coupled conductive radiative heat-transfer problems in a sphere. JQSRT 1991; 46:63-72
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.
G. Jia, Y. Yener, JW. Cipolla, Radiation between two concentric spheres separated by participating medium. JQSRT 1991;46:11-9.
E. M. Abulwafa, Radiative-transfer in a linearly-anisotropic spherical medium. JQSRT 1993;49:165-75.
R. viskanta, A. Grosbie, Radiative transfer between two concentric spheres separated by absorbing an emitting gray medium. JQSRT 1976;6:871-9.
S. T. Thynell, M. N. Ozisik Radiation transfer in an isotropically scattering homogeneous solid sphere. JQSRT; 1989; 33:187-96.
J. R. Tsai, M. N. Ozisik, F. J. Santarelli, Radiation in spherical symmetry with anisotropic scattering and variable properties. JQSRT 1989;42:187-96.
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.
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.
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.
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.
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.
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.
M. F. Modest, Radiative heat transfer, 2nd, Academic, SanDiego, CA3; 2003.
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.
IMSL Math Library. 1 ed. Houston, TX. (1997).