This paper presents numerical schemes and comparison of predictions of radiative heat transfer for the first and the second order discrete ordinates methods (DOM1 and DOM2) using an interpolation scheme. The formulations are followed by derivation of numerical schemes for two-dimensional body fitted grids. With varying the optical depths and the numbers of grids and ordinates, radiative wall heat fluxes by DOM1 and DOM2 are calculated to compare with the exact solutions for three kinds of two-dimensional enclosures (square, quadrilateral, and J-shaped) containing absorbing/emitting and nonscattering media of known temperature with cold black walls. Emissive power and radiative wall heat fluxes by DOM1 and DOM2 are calculated to compare with zonal results for two-dimensional square enclosure containing absorbing/emitting and isotropically scattering medium of known uniform heat source with cold black walls. The results of DOM1 and DOM2 are in good agreement with the exact solutions or the zonal results. DOM1 gives more accurate results than DOM2 for most of the tested optical depths and the numbers of grids and ordinates. These methods appear as powerful candidates of very versatile radiation analysis tool. Their grid and ordinate dependencies are also discussed in depth.

Issue Section:
Radiative Transfer
Keywords:
Furnaces & Combustors, Numerical Methods, Radiation
Topics:
Interpolation, Radiation (Physics), Heat, Flux (Metallurgy), Combustion chambers, Electromagnetic scattering, Emissivity, Furnaces, Numerical analysis, Radiation scattering, Radiative heat transfer, Scattering (Physics), Temperature
1.
Chai
J. C.
,
Lee
H. S.
, and
Patankar
S. V.
,
1994
, “
Finite Volume Method for Radiation Heat Transfer
,”
Journal of Thermophysics and Heat Transfer
, Vol.
8
, No.
3
, pp.
419
–
425
.
2.
Chai
J. C.
,
Parthasarathy
G.
,
Lee
H. S.
, and
Patankar
S. V.
,
1995
, “
Finite Volume Radiative Heat Transfer Procedure for Irregular Geometries
,”
Journal of Thermophysics and Heat Transfer
, Vol.
9
, No.
3
, pp.
410
–
415
.
3.
Cheong
K. B.
, and
Song
T. H.
,
1995
, “
Examination of Solution Methods for the Second Order Discrete Ordinate Formulation
,”
Numerical Heat Transfer
, Part B, Vol.
27
, No.
2
, pp.
155
–
173
.
4.
Cheong, K. B., and Song, T. H., 1996, “Application of the Second Order Discrete Ordinate Method to a Radiation Problem in a Square Geometry,” in Radiative Transfer-1, Proceedings of the First International Symposium on Radiation Transfer, M. P. Menguc, ed., Begel House, New York, pp. 75–91.
5.
Chui
E. H.
, and
Raithby
G. D.
,
1993
, “
Computation of Radiant Heat Transfer on a Nonorthogonal Mesh Using the Finite-Volume Method
,”
Numerical Heat Transfer
, Part B, Vol.
23
, pp.
269
–
288
.
6.
Fiveland
W. A.
,
1984
, “
Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
106
, pp.
699
–
706
.
7.
Fiveland
W. A.
, and
Jessee
J. P.
,
1995
, “
Comparison of Discrete Ordinates Formulations for Radiative Heat Transfer in Multidimensional Geometries
,”
Journal of Thermophysics and Heat Transfer
, Vol.
9
, No.
1
, pp.
47
–
54
.
8.
Giridharan, M. G., Lowry, S., and Krishnan, A., 1995, “A Multi-block, BFC Radiation Model for Complex Geometries,” AIAA-95-2020, 30th AIAA Thermophysics Conference.
9.
Hyde, D. J., and Truelove, J. S., 1977, “HTFS RSI89: The Discrete Ordinate Approximation for Multidimensional Radiant Heat Transfer in Furnaces,” HTFS Report No. AERE-R8502.
10.
Jamaluddin
A. S.
, and
Smith
P. J.
,
1988
, “
Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method
,”
Combustion Science and Technology
, Vol.
59
, pp.
321
–
340
.
11.
Kim, T. K., 1990, “Radiation and Combined Mode Heat Transfer Analyses in Absorbing, Emitting, and Mie-Anisotropic Scattering Media Using the S-N Discrete Ordinates Method,” Ph.D. thesis, University of Minnesota, MN.
12.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1986, Numerical Recipes, Cambridge University Press, NY, pp. 121–130.
13.
Raithby
G. D.
, and
Chui
E. H.
,
1990
, “
A Finite-Volume Method for Predicting a Radiant Heat Transfer in Enclosures with Participating Media
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
112
, pp.
415
–
423
.
14.
Song, T. H., and Park, C. W., 1992, “Formulation and Application of the Second Order Discrete Ordinate Method,” Proceedings 5th ISTP in Thermal Engineering, pp. 833–841, Beijing.
15.
Truelove
J. S.
,
1987
, “
Discrete-Ordinate Solutions of the Radiation Transport Equation
,”
ASME JOURNAL OF HEAT TRANSFER
, Vol.
109
, pp.
1048
–
1051
.
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