# Radiative heat transfer in participating media — A review

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## Abstract

This paper presents an overview of various exact analytic and approximate numerical methods for the solution of radiative heat transfer problems in participating media. Review of each method is followed by its strengths and limitations. Importance of radiative heat transfer analysis and difficulties in the solution of radiative transfer problems have been emphasized.

## Keywords

Radiation participating media radiative transfer equation## References

- Abed A Al, Sacadura J F 1983 A Monte Carlo-finite difference method for coupled radiation-conduction heat transfer in semitransparent media.
*Trans. ASME J. Heat Transfer*105: 931–933Google Scholar - Abramzon M N, Lisin F N 1984 Methods for solving the radiant-transfer equations in cylindrical geometry.
*High Temperature*22: 95–100Google Scholar - Ahluwalia R K, Im K H 1981 Combined conduction, convection, gas radiation and particle radiation in MHD diffusers.
*Int. J. Heat Mass Transfer*24: 1421–1430MATHCrossRefGoogle Scholar - Avery L W, House L L, Skumanchi A 1969 Radiative transport in finite homogeneous cylinders by the Monte Carlo technique.
*J. Quant. Spectrosc. Radiat. Transfer*9: 519–531CrossRefGoogle Scholar - Azad F H, Modest M F 1981 Evaluation of the radiative heat flux in absorbing, emitting and linear-anisotropic scattering cylindrical media.
*Trans. ASME J. Heat Transfer*103: 350–356Google Scholar - Bayazitoglu Y, Higenyi J 1979 The higher-order differential equations of radiative transfer: P
_{3}approximation.*AIAA J.*17: 424–431Google Scholar - Blank D A 1992 Modified, discretized-intensity based, split radiation calculation procedure for use in full simulation studies of combustion in axi-symmetric piston engines.
*Numer. Heat Transfer*A22: 199–222CrossRefGoogle Scholar - Blank D A 1994 The cartesian collapsed-dimension method for use in numerical 2-D radiative calculations in absorbing-emitting media.
*Int. J. Numer. Methods Eng.*37: 3023–3036MATHMathSciNetCrossRefGoogle Scholar - Blank D A, Mishra S C 1995 Use of the 2-D collapsed dimension method in absorbing-emitting media with isotropic scattering. In
*Proceedings of the First International Symposium on Radiative Heat Transfer*(New York: Begell House) pp 138–151Google Scholar - Blank D A, Mishra S C 1996 Use of the 2-D collapsed dimension method in gray enclosures with absorbing-emitting-isotropic scattering media in radiative equilibrium.
*Numer. Heat Transfer*B30: 469–481Google Scholar - Carlson B G, Lathrop K D 1968 Transport theory — the method of discrete ordinates. In
*Computing methods in reactor physics*(eds) H Greenspan, C N Kebler, D Okrent (New York: Gordon & Breach) pp 269–308Google Scholar - Cess R D, Sparrow E M 1978
*Radiative heat transfer*Augmented edn. (Washington, DC: Hemisphere)Google Scholar - Chandrasekhar S 1960
*Radiative transfer*(New York: Dover)Google Scholar - Cheng P 1968 Thermal control and radiation. In
*Progress in astronautics and aeronautics*(ed.) C L Tien (New York: Gordon and Breach) p 171Google Scholar - Cheong K-B, Song T-H 1995 Examination of solution methods for the second-order discrete ordinate formulation.
*Numer. Heat Transfer*B27: 155–173Google Scholar - Chu C M, Churchill S W 1960 Numerical solution of problems in multiple scattering of electromagnetic radiation.
*J. Phys. Chem.*59: 855–863MathSciNetCrossRefGoogle Scholar - Chui E H-K 1990
*Modeling of radiative heat transfer in participating media by the finite volume method*. Ph D thesis, University of Waterloo, OntarioGoogle Scholar - Chung T J, Kim J Y 1984 Two-dimensional, combined-mode heat transfer by conduction, convection, and radiation in emitting, absorbing, and scattering media-solution by finite elements.
*Trans. ASME J. Heat Transfer*106: 448–452Google Scholar - Crosbie A L, Davidson G W 1985 Dirac-delta function approximations to the scattering phase function.
*J. Quant. Spectrosc. Radiat. Transfer*33: 391–409CrossRefGoogle Scholar - Crosbie A L, Dougherty R L 1980 Two-dimensional radiative transfer in a cylindrical geometry with anisotropic scattering.
*J. Quant. Spectrosc. Radiat. Transfer*25: 551–569CrossRefGoogle Scholar - Crosbie A L, Farrell J B 1984 Exact formulation of multiple scattering in a three-dimensional cylindrical geometry.
*J. Quant. Spectrosc. Radiat. Transfer*31: 397–416CrossRefGoogle Scholar - Crosbie A L, Koewing J W 1979 Two-dimensional radiative transfer in a finite scattering planar medium.
*J. Quant. Spectrosc. Radiat. Transfer*21: 573–595CrossRefGoogle Scholar - Crosbie A L, Schrenker R G 1982 Exact expressions for a radiative transfer in a three-dimensional rectangular geometry.
*J. Quant. Spectrosc. Radiat. Transfer*28: 507–526CrossRefGoogle Scholar - Crosbie A L, Schrenker R G 1983 Multiple scattering in a two-dimensional rectangular medium exposed to collimated radiation.
*J. Quant. Spectrosc. Radiat. Transfer*33: 101–125Google Scholar - Crosbie A L, Dougherty R L 1985 Two-dimensional linearly anisotropic scattering in a finite thick cylindrical medium exposed to a laser beam.
*J. Quant. Spectrosc. Radiat. Transfer*33: 487–520CrossRefGoogle Scholar - Crosbie A L, Schrenker R G 1985 Multiple scattering in a two-dimensional rectangular medium exposed to collimated radiation.
*J. Quant. Spectrosc. Radiat. Transfer*33: 101–125Google Scholar - Cumber P S 1995 Improvements to the discrete transfer method of calculating radiative heat transfer.
*Int. J. Heat Mass Transfer*38: 2251–2258MATHCrossRefGoogle Scholar - da Graca C, Fontes F T 1993 Multidimensional modeling of radiative heat transfer in scattering media.
*Trans. ASME J. Heat Transfer*115: 486–489Google Scholar - Davison B 1958
*Neutron transport theory*(Oxford: Clarendon)Google Scholar - Farmer J T, Howell J R 1994 Monte Carlo prediction of radiative heat transfer in inhomogeneous, anisotropic, nongray media.
*J. Thermophys. Heat Transfer*8: 133–139CrossRefGoogle Scholar - Fernandes R, Francis J, Reddy J N 1981 A finite element approach to combined conductive and radiation heat transfer in a planar medium. In
*Heat transfer and thermal control. Progress in aeronautics and astronautics*(New York: AIAA) pp 93–109Google Scholar - Fiveland W A 1984 Discrete-ordinate solutions of the radiative transport equation for rectangular enclosures.
*Trans. ASME J. Heat Transfer*106: 699–706Google Scholar - Fiveland W A 1987 Discrete ordinate methods for radiative heat transfer in isotropically and anisotropically scattering media.
*Trans. ASME J. Heat Transfer*109: 809–812Google Scholar - Fiveland W A 1988 Three-dimensional radiative heat transfer solutions by the discrete ordinate method.
*J. Thermophys. Heat Transfer*2: 309–316Google Scholar - Fleck J A 1961 The calculation of nonlinear radiation transport by Monte Carlo method: Statistical physics.
*Methods Comput. Phys.*1: 43–65Google Scholar - Gupta R P, Wall T F, Truelove J S 1983 Radiative scatter by fly ash in pulverized-coal-fired furnaces: Application of the Monte Carlo method to anisotropic scattering.
*Int. J. Heat Mass Transfer*26: 1649–1660CrossRefGoogle Scholar - Heaslet M A, Warming R F 1966 Theoretical predictions of radiative heat transfer in homogeneous cylindrical medium.
*J. Quant. Spectrosc. Radiat. Transfer*6: 751–774CrossRefGoogle Scholar - Higenyi J, Bayazitoglu Y 1980a Differential approximation of radiative heat transfer in a gray medium.
*Trans. ASME J. Heat Transfer*102: 719–723Google Scholar - Higenyi J, Bayazitoglu Y 1980b Radiative transfer of energy in a cylindrical enclosure with heat generation.
*AIAA J.*18: 723–726Google Scholar - Hottel H C, Cohen H S 1958 Radiant heat exchange in a gas filled enclosure: Allowance for nonuniformity of gas temperature.
*AIChE J.*4: 3–14CrossRefGoogle Scholar - Hottel H C, Sarofim A F 1967
*Radiative heat transfer*(New York: McGraw-Hill)Google Scholar - Hottel H C, Sarofim A F, Evans L B, Vasalos I A 1968 Radiative transfer in anisotropically scattering media: Allowance for fresnel reflection at the boundaries.
*Trans. ASME J. Heat Transfer*90: 56–62Google Scholar - Howell J R 1983 Radiative transfer in multi-dimensional enclosures with participating media. ASME, paper no. 83-HT-32Google Scholar
- Howell J R 1988 Thermal radiation in participating media: The past, the present, and some possible future.
*Trans. ASME J. Heat Transfer*110: 1220–1229Google Scholar - Howell J R, Perlmutter M 1964a Monte Carlo solution of radiant heat transfer in a nongray, nonisothermal gas with temperature-dependent properties.
*AIChE J.*10: 562–567CrossRefGoogle Scholar - Howell J R, Perlmutter M 1964b Monte Carlo solution of thermal transfer through radiant media between gray walls.
*Trans. ASME J. Heat Transfer*86: 116–122Google Scholar - Hsia H M, Love T J 1967 Radiative heat transfer between parallel plates separated by a nonisothermal medium with anisotropic scattering.
*Trans. ASME J. Heat Transfer*89: 197–204Google Scholar - Hyde D J, Truelove J S 1977 The discrete ordinate approximation for radiative heat transfer. Technical Report AERE-R 8502Google Scholar
- Khalil H, Shultis J K, Lester T W 1982 Comparison of three numerical methods for evaluation of radiant energy transfer in scattering and heat generating media.
*Numer. Heat Transfer*5: 235–252CrossRefGoogle Scholar - Kim T-K 1990
*Radiation and combined mode heat transfer analysis in absorbing, emitting, and Mie-anisotropic scattering media using S-N discrete ordinate method*. Ph D thesis, University of Minnesota, Minneapolis, MNGoogle Scholar - Kim T-K, Lee H 1988 Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular enclosures.
*Int. J. Heat Mass Transfer*31: 1711–1721CrossRefGoogle Scholar - Kobiyama M 1986 A study on the reduction of computing time of the Monte Carlo method applied to the radiative transfer.
*Bull. Jap. Soc. Mech. Eng.*29: 3000–3006Google Scholar - Kobiyama M, Taniguchi H, Saito T 1979 The numerical analysis of heat transfer combined with radiation and convection (1st report, the effect of two-dimensional radiative transfer between isothermal parallel plates).
*Bull. Jap. Soc. Mech. Eng.*22: 707–714Google Scholar - Kourgnaoff V 1952
*Basic methods in transfer problems*. (London: Oxford University Press)Google Scholar - Krook M 1955 On the solution of equation of transfer, I.
*Astrophys. J.*122: 488–497MathSciNetCrossRefGoogle Scholar - Kuo K 1986
*Principles of combustion*(New York: Wiley) chap. 7Google Scholar - Lathrop K D 1966 Use of discrete ordinate methods for solution of photon transport problems.
*Nuclear Sci. Eng.*24: 381–388Google Scholar - Lathrop K D 1968 Ray effects in discrete ordinate equations.
*Nuclear Sci. Eng.*32: 357–369Google Scholar - Lee C E 1962 The discrete S
_{n}approximation to transport theory. Technical Report Technical Information Series Report LA2595, Lawrence Livermore Laboratory.Google Scholar - Lewis E E, Miller W F Jr 1984
*Computational methods of neutron transport*(New York: John Wiley and Son)Google Scholar - Liu F, Garbett G S, Swithernbank J 1992 Effect of anisotropic scattering on radiative heat transfer using the p
_{1}-approximation.*Int. J. Heat Mass Transfer*35: 2491–2499CrossRefGoogle Scholar - Liu J, Tiwari S N 1994 Radiative interactions in chemically reacting compressible nozzle flows using Monte Carlo simulation. In:
*6th AIAA/ASME Joint Thermophysics and Heat Transfer Conference*, Colorado Springs, CO (AIAA) pp 1–13Google Scholar - Lockwood FC, Shah N G 1976 An improved flux model for the calculation of radiation heat transfer in combustion chambers. In:
*Proceedings of the 16th National Heat Transfer Conference*, St. Louis (ASME) pp 2–7Google Scholar - Lockwood F C, Shah N G 1981 A new radiation solution method for incorporation in general combustion prediction procedures. In
*Proceedings of the Eighteenth International Symposium on Combustion*(Pittsburg, PA: The Combustion Institute) pp 1405–1414Google Scholar - Love T J, Grosh R J 1965 Radiative heat transfer in absorbing, emitting, and scattering media.
*Trans. ASME J. Heat Transfer*87: 161–166Google Scholar - Loyalka S K 1969 Radiative heat transfer between parallel plates and concentric cylinders.
*Int. J. Heat Mass Transfer*12: 1513–1517CrossRefGoogle Scholar - Manickavasagam S, Menguc M P 1993 Effective optical properties of pulverized coal particles determined from FT-IR spectrometer experiments.
*Energy Fuels*7: 860–869CrossRefGoogle Scholar - Menguc M P, Viskanta R 1985 Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous, anisotropically scattering media.
*J. Quant. Spectrosc. Radiat. Transfer*33: 533–549CrossRefGoogle Scholar - Menguc M P, Viskanta R 1986 Radiative transfer in axisymmetric, finite cylindrical enclosures.
*Trans. ASME J. Heat Transfer*108: 271–276Google Scholar - Mishra S C, Blank D A, 1995 High to low optical thickness Monte Carlo solutions of the radiative heat transfer problems in 2-D rectangular enclosures with absorbing-emitting-isotropic scattering. In
*Advances in mechanical engineering*(ed.) T S Mruthyunjaya (New Delhi: Narosa) pp 1657–1668Google Scholar - Modest M F 1993
*Radiative heat transfer*(Singapore: McGraw-Hill)Google Scholar - Murthy J Y, Choudhary D 1992 Computation of participating radiation in complex geometries. In
*28th National Heat Transfer Conference*, San Diego, CA (ASME, Heat Transfer Div.) pp 153–160Google Scholar - Nelson H F, Look D C, Crosbie A L 1986 Two-dimensional radiative back-scattering from optically thick media.
*Trans. ASME J. Heat Transfer*108: 619–625Google Scholar - Noble J J 1975 The zone method: Explicit matrix relations for total exchange areas.
*Int. J. Heat Mass Transfer*18: 261–269CrossRefGoogle Scholar - O’Dell R D, Alcouffe R E 1987 Transport calculations for nuclear analysis: Theory and guidelines for effective use of transport codes. Technical Report La-10983-MS, Los Alamos National LaboratoryGoogle Scholar
- Ou S-C S, Kuo-Nan L 1982 Generalization of the spherical harmonics method to radiative transfer in multi-dimensional space.
*J. Quant. Spectrosc. Radiat. Transfer*28: 271–288CrossRefGoogle Scholar - Ozisik M N 1973
*Radiative transfer and interactions with conduction and convection*(New York: John Wiley & Sons)Google Scholar - Perlmutter M, Howell J R 1964 Radiant heat transfer through a gray gas between concentric cylinders using Monte Carlo.
*Trans. ASME J. Heat Transfer*86: 169–179Google Scholar - Pomraning G C 1973
*The equations of radiation hydrodynamics*(Oxford: Pergamon)Google Scholar - Raithby G D, Chui E H 1990 A finite volume method for predicting a radiant heat transfer in enclosures with participating media.
*Trans. ASME J. Heat Transfer*112: 415–423CrossRefGoogle Scholar - Raithby G D, Schneider G E 1988 In
*Handbook of numerical heat transfer*(New York: John Wiley & Sons) pp 241–291Google Scholar - Ratzel A C III, Howell J R 1983 Two-dimensional radiation in absorbing-emitting media using the P
_{N}approximation.*Trans. ASME J. Heat Transfer*105: 333–340Google Scholar - Razzaque M M, Klein D E, Howell J R 1983 Finite element solution of radiative heat transfer in a two-dimensional rectangular enclosures with gray participating media.
*Trans. ASME J. Heat Transfer*105: 933–936Google Scholar - Razzaque M M, Howell J R, Klein D E 1984 Coupled radiative and conductive heat transfer in a two-dimensional enclosure with gray participating media using finite elements.
*Trans. ASME J. Heat Transfer*106: 613–619Google Scholar - Roux J A, Smith A M 1974 Radiative transport analysis for plane geometry with isotropic scattering and arbitrary temperature.
*AIAA J*. 12: 1273–1277MATHMathSciNetGoogle Scholar - Shah N G 1979
*New method of computation of radiation heat transfer combustion chambers*. Ph D thesis, Imperial College, University of London, LondonGoogle Scholar - Shih T M, Chen Y N 1983 A discretized-intensity method proposed for two-dimensional systems enclosing radiative and conductive media.
*Numer. Heat Transfer*6: 117–134CrossRefGoogle Scholar - Shih T M, Ren A L 1985 Combined convective and radiative recirculating flows in enclosures.
*Numer. Heat Transfer*8: 149–167MATHCrossRefGoogle Scholar - Siddal R G, Seluck N 1979 Evaluation of a new six-flux model for radiative transfer in rectangular enclosures.
*Trans. IChE.*7: 163–169Google Scholar - Siegel R, Howell J R 1981
*Radiative heat transfer*2nd edn (Washington, DC: Hemisphere)Google Scholar - Sistino A J 1982 Mean beam length and zone method (without and with scattering) for a cylindrical enclosure. ASME paper no. 82-HT-3Google Scholar
- Smith T F, Shen Z F, Al-Turki A M 1985 Radiative and conductive transfer in a cylindrical enclosure for a real gas.
*Trans. ASME J. Heat Transfer*104: 482–485Google Scholar - Smith T F, Byun K H, Ford M J 1986
*Heat transfer*(Washington, DC: Hemisphere) vol. 2, pp 803–808Google Scholar - Sokman C N, Razzaque M M 1987 Finite element analysis of conduction radiation heat transfer in an enclosure with heat flux boundary conditions. In
*Radiation, phase change heat transfer, and thermal systems*(ASME Heat Transfer Div.) vol. 81, pp 17–23Google Scholar - Steward F R, Tennankore K N 1979
*J. Inst. Energy*53: 107–112Google Scholar - Stockham L W, Love T M 1968 Radiative heat transfer from a cylindrical cloud of particles.
*AIAA J.*6: 1935–1940Google Scholar - Tan Z 1989 Radiative heat transfer in multidimensional emitting, absorbing, and anisotropic scattering media — mathematical formulation and numerical method.
*Trans. ASME J. Heat Transfer*111: 141–147Google Scholar - Taniguchi H 1967 Temperature distribution of radiant gas calculated by Monte Carlo method.
*Bull. Jap. Soc. Mech. Eng.*10: 975–988Google Scholar - Taniguchi H 1969 The radiative heat transfer of gas in a three dimensional system calculated by Monte Carlo method.
*Bull. Jap. Soc. Mech. Eng.*12: 67–78MathSciNetGoogle Scholar - Taniguchi H, Yang W J, Kudo K, Hayasaka H, Oguma M, Kusama M, Nakamachi I, Okigani N 1986
*Heat transfer*(Washington, DC: Hemisphere) vol. 2, pp 757–762Google Scholar - Tien C L 1988 Thermal radiation in packed and fluidized beds.
*Trans. ASME J. Heat Transfer*110: 1230–1242Google Scholar - Tiwari S N, Liu J 1992 Investigation of radiative interaction in laminar flows of nongray gases using Monte Carlo simulation. In
*Proceedings of the National Heat Transfer Conference*, San Diego, CA (ASME) pp 187–195Google Scholar - Truelove J S 1987 Discrete-ordinate solutions of the radiative transport equation.
*Trans. ASME J. Heat Transfer*109: 1048–1051Google Scholar - Truelove J S 1988 Three-dimensional radiation in absorbing—emitting-scattering media using the discrete-ordinate approximation.
*J. Quant. Spectrosc. Radiat. Transfer*39: 27–31CrossRefGoogle Scholar - Vaillon R, Lallemand M, Lemonnier D 1995 Radiative equilibrium in axisymmetric semitransparent gray shells using the discrete ordinate method. In
*Proceedings of the First International Symposium on Radiative Heat Transfer*, Kusadasi, TurkeyGoogle Scholar - Vaillon R, Lallemand M, Lemonnier D 1996a
*EUROTHERM*(eds) D Lemonnier, J B Savlnier, M Fiebig (Amsterdam: Elsevier) pp 1994–2000Google Scholar - Vaillon R, Lallemand M, Lemonnier D 1996b Radiative heat transfer in orthogonal curvilinear coordinates using the discrete ordinate method.
*J. Quant. Spectrosc. Radiat. Transfer*55: 7–17CrossRefGoogle Scholar - Varma S A 1979
*Pulverized coal combustion and gassification*(New York: Plenum) pp 311–315Google Scholar - Viskanta R, Menguc M P 1987 Radiation heat transfer in combustion systems.
*Prog. Energy Combust. Sci.*13: 97–160CrossRefGoogle Scholar - Yang K T 1986 Numerical modeling of natural convection-radiation interactions in enclosures. In
*Proceedings of the 8th International Heat Transfer Conference*(Washington, DC: Hemisphere) vol. 1, pp 131–140Google Scholar - Yang Y S, Howell J R, Klein D E 1983 Radiative heat transfer through a randomly packed bed of spheres by the Monte carlo method.
*Trans. ASME J. Heat Transfer*105: 325–332CrossRefGoogle Scholar - Yuen W W, Takara E E 1994 Development of a generalized zonal method for analysis of radiative transfer in absorbing and anisotropically scattering media.
*Numer. Heat Transfer*B25: 75–96Google Scholar

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© Indian Academy of Sciences 1998