Predicting Radiative Heat Transfer in Arbitrary Two and Three-Dimensional Participating Media

The radiative exchange method is introduced as a numerical method for the simulation of radiative heat transfer in an absorbing, emitting and isotropically scattering media. In this method, the integro-differential radiative balance equation is solved by using a new introduced concept for the exchange factor. Even though the radiative source term is calculated in a mesh structure that is coarser than the structure used in computational fluid dynamics, calculating the exchange factor between different coarse elements by using differential integration elements makes the result of the method close to that of integro-differential radiative equation. A set of equations for calculating exchange factors in two and threedimensional Cartesian coordinate system is presented, and the method is used in the simulation of radiative heat transfer in twodimensional rectangular case and a three-dimensional simple cube. The result of using this method in simulating different cases is verified by comparing them with those of using other numerical radiative models.

Authors:

• Mohammad Hadi Bordbar
• Timo Hyppänen

Keywords:

• Exchange factor
• Numerical simulation
• Thermal radiation.

References:

[1] R. Siegel, JR. Howell, Thermal radiation heat transfer, 3rd edition.
Hemisphere : Taylor and Francis, 1992.
[2] JR Howell "Application of Monte Carlo to heat transfer problems," in
Advances in heat transfer, vol. 5, JP Hartnett, TF Irvine, Ed. New York:
Academic Press, 1968.
[3] S.T. Flock, M.S. Patterson, B.C. Wilson, and D.R. Wyman, "Monte
Carlo modeling of light propagation in highly scattering tissuesÔÇöI:
model predictions and comparison with diffusion theory," IEEE Trans
Med Eng, vol. 36, pp.1162-1168, 1989.
[4] Y. Hasegawa, Y. Yamada, M. Tamura and Y. Nomura, "Monte Carlo
simulation of light transmission through living tissues," Appl. Opt., vol.
30 , pp. 4515-4520, 1991.
[5] N. G. Shah, New Method for the Computation of Radiation Heat
Transfer in Combustion Chambers Ph.D. Thesis, London: Imperial
College of Science and Technology, 1979.
[6] F. C. Lockwood, and N. G. Shah, ÔÇÿÔÇÿA New Radiation Solution Method
for Incorporation in General Combustion Prediction Procedures,-- Proc.
Eighteenth Symp. (Int.) Combustion, Pittsburgh, PA: The Combustion
Institute, pp.1405-1413,1981.
[7] J. B. Pessoa-Filho, and S. T. Thynell, ÔÇÿÔÇÿAn Approximate Solution to the
Radiative Transfer in Two-Dimensional Rectangular Enclosures,--
ASME J. Heat Transfer, vol. 119, pp. 738-745, 1997.
[8] S. Chandrasekhar. Radiative transfer. Clarendon Press, 1950.
[9] B.G. Carlson and K.D. Lathrop. "Transport theory - The method of
discrete ordinates." in Computing in reactor Physics, New York:
Gordon and Breach Ed., 1968.
[10] W.A. Fiveland. "Three-dimensional radiative heat transfer solutions by
the discrete-ordinates method." J. Thermophysics, vol. 2, pp.309-316,
1988.
[11] W.A. Fiveland and A.S. Jamaluddin. "Three-dimensional spectral
radiative heat transfer solutionsby the discrete ordinates method,"
J.Thermophysics, vol. 5(3), pp. 335-339, 1991.
[12] W.A. Fiveland and J.P. Jessee. "Comparison of discrete ordinates
method formulations for radiative heat transfer in multidimensional
geometries." Journal of Thermophysics and Heat Transfer, vol. 9, pp.
47-54, 1995.
[13] J.S. Truelove. "Three-dimensional radition in absorbing-emittingscattering
in using the discrete-ordinates approximation." Journal of
quantitative spectroscopy and radiative transfer, vol. 39, pp. 27-31,
1988.
[14] A.S. Jamaluddin and P.J. Smith. "Discrete-ordinates solution of
radiation transfer equation in nonaxisymmetric cylindrical enclosures,"
J. Thermophysics and Heat Transfer, vol. 6, pp. 242-245, 1992.
[15] G. D. Raithby, and E. H. Chui, "A finite volume method for predicting
radiant heat transfer in enclosures with participating media,"ASME
Journal of Heat Transfer, vol. 112, pp. 415-423, 1990.
[16] E. H. Chui, and G. D. Raithby, "Computation of radiant heat transfer on
a nonorthogonal mesh using the finite volume method," Numerical Heat
Transfer Part B, vol. 23, pp. 269-288, 1993.
[17] D. R. Rousse, and R. B. Baliga, "Formulation of a control-volume finite
element method for radiative transfer in participating media," Proc. 7th
Intl. Conf. on Num. Methods in Thermal Problems, Stanford, 1991, pp.
786-795.
[18] D. R. Rousse, "Numerical predictions of two-dimensional conduction,
convection and radiation heat transfer. I: formulation," International
Journal of Thermal Science, vol. 39, pp. 315-331, 2000.
[19] H. C. Hottel, and E. S. Cohen, "Radiant Heat Exchange in a Gas-Filled
Enclosure: Allowance for Nonuniformity of Gas Temperature", AIChE
J., vol. 4, pp.3-14, 1958.
[20] H.C. Hottel and A. F. Sarofim, Radiatiae Transfer. New York:
McCraw-Hill, 1967.
[21] J. M. Goyhénéche and J. F. Sacadura, "The Zone Method: A New
Explicit Matrix Relation to Calculate the Total Exchange Areas in
Anisotropically Scattering Medium Bounded by Anisotropically
Reflecting Walls" Journal of Heat Transfer, vol. 124, pp. 696-703,
2002.
[22] M.H. Bordbar, and T. Hyppänen, "Modeling of Radiation Heat Transfer
in a Boiler Furnace," Advanced Studies in Theoretical Physics, vol. 1,
pp.571-584, 2007.
[23] S. Maruyama,"Radiation Heat Transfer Between Arbitrary Three-
Dimensional Bodies with Specular and Diffuse Surfaces," Numer. Heat
Transfer, Part A, vol.24, pp.181-196, 1993.
[24] S. Maruyama, and T. Aihara, "Radiation Heat Transfer of Arbitrary
Three-Dimensional Absorbing, Emitting and Scattering Media and
Specular and Diffuse Surfaces" ASME J. Heat Transfer, vol. 119, pp.
129-136, 1997.
[25] T. H. Einstein, "Radiant heat transfer to absorbing gases. enclosed
between parallel flat plates with flow and conduction", NASA TR, R-
154, 1963.
[26] M.H. Bordbar and T. Hyppänen, "A New Numerical Method for
Radiation in Participating Media in Combination with CFD Calculation
for Other Modes of Heat Transfer", Proceeding of the 15th Conference
of Iranian Society of Mechanical Engineering (ISME2007), May 15-19,
Tehran, Iran, 2007.