Numerical solution of radiative heat transfer problems in irregular domains with specular (Fresnel) boundaries. Axisymmetric case
Matematičeskoe modelirovanie, Tome 16 (2004) no. 10, pp. 15-28.

Voir la notice de l'article provenant de la source Math-Net.Ru

Numerical method is proposed for the solution of axisymmetric radiative transfer problems in irregular domains both with diffuse and specular (Fresnel) boundaries, it is a combination of the discrete ordinates and ray tracing methods. The method is directly generalized to two-dimensional and threedimensional Cartesian cases.
@article{MM_2004_16_10_a1,
     author = {V. M. Mamedov and S. A. Rukolaine},
     title = {Numerical solution of radiative heat transfer problems in irregular domains with specular {(Fresnel)} boundaries. {Axisymmetric} case},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {15--28},
     publisher = {mathdoc},
     volume = {16},
     number = {10},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_10_a1/}
}
TY  - JOUR
AU  - V. M. Mamedov
AU  - S. A. Rukolaine
TI  - Numerical solution of radiative heat transfer problems in irregular domains with specular (Fresnel) boundaries. Axisymmetric case
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 15
EP  - 28
VL  - 16
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_10_a1/
LA  - ru
ID  - MM_2004_16_10_a1
ER  - 
%0 Journal Article
%A V. M. Mamedov
%A S. A. Rukolaine
%T Numerical solution of radiative heat transfer problems in irregular domains with specular (Fresnel) boundaries. Axisymmetric case
%J Matematičeskoe modelirovanie
%D 2004
%P 15-28
%V 16
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2004_16_10_a1/
%G ru
%F MM_2004_16_10_a1
V. M. Mamedov; S. A. Rukolaine. Numerical solution of radiative heat transfer problems in irregular domains with specular (Fresnel) boundaries. Axisymmetric case. Matematičeskoe modelirovanie, Tome 16 (2004) no. 10, pp. 15-28. http://geodesic.mathdoc.fr/item/MM_2004_16_10_a1/

[1] R. Viskanta, M. P. Menguc, “Radiative heat transfer in combustion systems”, Progr. Energy Combust. Sci., 13 (1987), 97–160 | DOI

[2] C. W. Lan, “Three-dimensional simulation of floating-zone growth of oxide crystals”, J. Crystal Growth, 247 (2003), 597–612 | DOI

[3] V. S. Yuferev, O. N. Budenkova, M. G. Vasilyev, S. A. Rukolaine, et al., “Variations of solid-liquid interface in the $BGO$ low thermal gradient $Cz$ growth for diffuse and specular crystal side surface”, J. Crystal Growth, 253 (2003), 383–397 | DOI

[4] B. J. van der Linden, Radiative heat transfer in glass: the Algebraic Ray Trace method, Thesis, Techn. Univ. Eindhoven, 2002, 157 pp.

[5] L. P. Bass, A. M. Voloschenko, T. A. Germogenova, Metody diskretnykh ordinat v zadachakh o perenose izlucheniya, IPM im. M. V. Keldysha, M., 1986, 231 pp.

[6] W. A. Fiveland, J. P. Jessee, “Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries”, J. Thermophysics and Heat Transfer, 9 (1995), 47–54 | DOI

[7] M. Sakami, V. Le Dez, A. Charette, “Radiative heat transfer in three-dimensional enclosures of complex geometry by using the discrete ordinates method”, J. Quant. Spectrosc. Radiat. Transfer, 59 (1998), 117–136 | DOI

[8] M. A. Ramankutty, A. L. Crosbie, “Modified discrete ordinates solution of radiative transfer in threedimensional rectangular enclosures”, J. Quant. Spectrosc. Radiat. Transfer, 60 (1998), 103–134 | DOI

[9] D. Balsam, “Fast and accurate discrete ordinates methods for multidimensional radiative transfer. Part I, basic methods”, J. Quant. Spectrosc. Radiat. Transfer, 69 (2001), 671–707 | DOI

[10] S. A. Rukolaine, V. S. Yuferev, “Discrete ordinates quadrature schemes based on the angular interpolation of radiation intensity”, J. Quant. Spectrosc. Radiat. Transfer, 69 (2001), 257–275 | DOI

[11] M. N. Otsisik, Slozhnyi teploobmen, Mir, M., 1976, 616 pp.

[12] G. I. Marchuk, V. I. Lebedev, Chislennye metody v teorii perenosa neitronov, Atomizdat, M., 1981, 456 pp. | MR

[13] S. A. Rukolaine, M. G. Vasilyev, V. S. Yuferev, V. M. Mamedov, “A numerical scheme for the solution of axisymmetric radiative transfer problems in irregular domains filled by media with opaque and transparent diffuse and specular boundaries”, J. Quant. Spectr. Radiative Transfer, 2003 (to appear)

[14] E. H. Chui, G. D. Raithby, P. M. J. Hughes, “Prediction of Radiative Transfer in Cylindrical Enclosures with the Finite Volume Method”, J. Thermophysics and Heat Transfer, 6 (1992), 605–611 | DOI

[15] L. P. Bass, O. V. Nikolaeva, “Uluchshennaya skhema rascheta perenosa izlucheniya v silno geterogennykh sredakh i pustotakh”, Matem. modelirovanie, 9:10 (1997), 63–72 | Zbl