Advertisement

Sadhana

, 23:213 | Cite as

Radiative heat transfer in participating media — A review

  • Subhash C Mishra
  • Manohar Prasad
Article

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

  1. 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
  2. Abramzon M N, Lisin F N 1984 Methods for solving the radiant-transfer equations in cylindrical geometry.High Temperature 22: 95–100Google Scholar
  3. 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
  4. 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
  5. 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
  6. Bayazitoglu Y, Higenyi J 1979 The higher-order differential equations of radiative transfer: P3 approximation.AIAA J. 17: 424–431Google Scholar
  7. 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
  8. 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
  9. Blank D A, Mishra S C 1995 Use of the 2-D collapsed dimension method in absorbing-emitting media with isotropic scattering. InProceedings of the First International Symposium on Radiative Heat Transfer (New York: Begell House) pp 138–151Google Scholar
  10. 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
  11. Carlson B G, Lathrop K D 1968 Transport theory — the method of discrete ordinates. InComputing methods in reactor physics (eds) H Greenspan, C N Kebler, D Okrent (New York: Gordon & Breach) pp 269–308Google Scholar
  12. Cess R D, Sparrow E M 1978Radiative heat transfer Augmented edn. (Washington, DC: Hemisphere)Google Scholar
  13. Chandrasekhar S 1960Radiative transfer (New York: Dover)Google Scholar
  14. Cheng P 1968 Thermal control and radiation. InProgress in astronautics and aeronautics (ed.) C L Tien (New York: Gordon and Breach) p 171Google Scholar
  15. 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
  16. Chu C M, Churchill S W 1960 Numerical solution of problems in multiple scattering of electromagnetic radiation.J. Phys. Chem. 59: 855–863MathSciNetCrossRefGoogle Scholar
  17. Chui E H-K 1990Modeling of radiative heat transfer in participating media by the finite volume method. Ph D thesis, University of Waterloo, OntarioGoogle Scholar
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. Cumber P S 1995 Improvements to the discrete transfer method of calculating radiative heat transfer.Int. J. Heat Mass Transfer 38: 2251–2258MATHCrossRefGoogle Scholar
  28. 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
  29. Davison B 1958Neutron transport theory (Oxford: Clarendon)Google Scholar
  30. 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
  31. Fernandes R, Francis J, Reddy J N 1981 A finite element approach to combined conductive and radiation heat transfer in a planar medium. InHeat transfer and thermal control. Progress in aeronautics and astronautics (New York: AIAA) pp 93–109Google Scholar
  32. Fiveland W A 1984 Discrete-ordinate solutions of the radiative transport equation for rectangular enclosures.Trans. ASME J. Heat Transfer 106: 699–706Google Scholar
  33. 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
  34. Fiveland W A 1988 Three-dimensional radiative heat transfer solutions by the discrete ordinate method.J. Thermophys. Heat Transfer 2: 309–316Google Scholar
  35. Fleck J A 1961 The calculation of nonlinear radiation transport by Monte Carlo method: Statistical physics.Methods Comput. Phys. 1: 43–65Google Scholar
  36. 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
  37. 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
  38. Higenyi J, Bayazitoglu Y 1980a Differential approximation of radiative heat transfer in a gray medium.Trans. ASME J. Heat Transfer 102: 719–723Google Scholar
  39. Higenyi J, Bayazitoglu Y 1980b Radiative transfer of energy in a cylindrical enclosure with heat generation.AIAA J. 18: 723–726Google Scholar
  40. 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
  41. Hottel H C, Sarofim A F 1967Radiative heat transfer (New York: McGraw-Hill)Google Scholar
  42. 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
  43. Howell J R 1983 Radiative transfer in multi-dimensional enclosures with participating media. ASME, paper no. 83-HT-32Google Scholar
  44. 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
  45. 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
  46. 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
  47. 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
  48. Hyde D J, Truelove J S 1977 The discrete ordinate approximation for radiative heat transfer. Technical Report AERE-R 8502Google Scholar
  49. 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
  50. Kim T-K 1990Radiation 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
  51. 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
  52. 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
  53. 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
  54. Kourgnaoff V 1952Basic methods in transfer problems. (London: Oxford University Press)Google Scholar
  55. Krook M 1955 On the solution of equation of transfer, I.Astrophys. J. 122: 488–497MathSciNetCrossRefGoogle Scholar
  56. Kuo K 1986Principles of combustion (New York: Wiley) chap. 7Google Scholar
  57. Lathrop K D 1966 Use of discrete ordinate methods for solution of photon transport problems.Nuclear Sci. Eng. 24: 381–388Google Scholar
  58. Lathrop K D 1968 Ray effects in discrete ordinate equations.Nuclear Sci. Eng. 32: 357–369Google Scholar
  59. Lee C E 1962 The discrete Sn approximation to transport theory. Technical Report Technical Information Series Report LA2595, Lawrence Livermore Laboratory.Google Scholar
  60. Lewis E E, Miller W F Jr 1984Computational methods of neutron transport (New York: John Wiley and Son)Google Scholar
  61. Liu F, Garbett G S, Swithernbank J 1992 Effect of anisotropic scattering on radiative heat transfer using the p1-approximation.Int. J. Heat Mass Transfer 35: 2491–2499CrossRefGoogle Scholar
  62. 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
  63. 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
  64. Lockwood F C, Shah N G 1981 A new radiation solution method for incorporation in general combustion prediction procedures. InProceedings of the Eighteenth International Symposium on Combustion (Pittsburg, PA: The Combustion Institute) pp 1405–1414Google Scholar
  65. 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
  66. Loyalka S K 1969 Radiative heat transfer between parallel plates and concentric cylinders.Int. J. Heat Mass Transfer 12: 1513–1517CrossRefGoogle Scholar
  67. 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
  68. 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
  69. Menguc M P, Viskanta R 1986 Radiative transfer in axisymmetric, finite cylindrical enclosures.Trans. ASME J. Heat Transfer 108: 271–276Google Scholar
  70. 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. InAdvances in mechanical engineering (ed.) T S Mruthyunjaya (New Delhi: Narosa) pp 1657–1668Google Scholar
  71. Modest M F 1993Radiative heat transfer (Singapore: McGraw-Hill)Google Scholar
  72. Murthy J Y, Choudhary D 1992 Computation of participating radiation in complex geometries. In28th National Heat Transfer Conference, San Diego, CA (ASME, Heat Transfer Div.) pp 153–160Google Scholar
  73. 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
  74. Noble J J 1975 The zone method: Explicit matrix relations for total exchange areas.Int. J. Heat Mass Transfer 18: 261–269CrossRefGoogle Scholar
  75. 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
  76. 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
  77. Ozisik M N 1973Radiative transfer and interactions with conduction and convection (New York: John Wiley & Sons)Google Scholar
  78. 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
  79. Pomraning G C 1973The equations of radiation hydrodynamics (Oxford: Pergamon)Google Scholar
  80. 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
  81. Raithby G D, Schneider G E 1988 InHandbook of numerical heat transfer (New York: John Wiley & Sons) pp 241–291Google Scholar
  82. Ratzel A C III, Howell J R 1983 Two-dimensional radiation in absorbing-emitting media using the PN approximation.Trans. ASME J. Heat Transfer 105: 333–340Google Scholar
  83. 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
  84. 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
  85. 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
  86. Shah N G 1979New method of computation of radiation heat transfer combustion chambers. Ph D thesis, Imperial College, University of London, LondonGoogle Scholar
  87. 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
  88. Shih T M, Ren A L 1985 Combined convective and radiative recirculating flows in enclosures.Numer. Heat Transfer 8: 149–167MATHCrossRefGoogle Scholar
  89. 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
  90. Siegel R, Howell J R 1981Radiative heat transfer 2nd edn (Washington, DC: Hemisphere)Google Scholar
  91. 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
  92. 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
  93. Smith T F, Byun K H, Ford M J 1986Heat transfer (Washington, DC: Hemisphere) vol. 2, pp 803–808Google Scholar
  94. Sokman C N, Razzaque M M 1987 Finite element analysis of conduction radiation heat transfer in an enclosure with heat flux boundary conditions. InRadiation, phase change heat transfer, and thermal systems (ASME Heat Transfer Div.) vol. 81, pp 17–23Google Scholar
  95. Steward F R, Tennankore K N 1979J. Inst. Energy 53: 107–112Google Scholar
  96. Stockham L W, Love T M 1968 Radiative heat transfer from a cylindrical cloud of particles.AIAA J. 6: 1935–1940Google Scholar
  97. 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
  98. Taniguchi H 1967 Temperature distribution of radiant gas calculated by Monte Carlo method.Bull. Jap. Soc. Mech. Eng. 10: 975–988Google Scholar
  99. 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
  100. Taniguchi H, Yang W J, Kudo K, Hayasaka H, Oguma M, Kusama M, Nakamachi I, Okigani N 1986Heat transfer (Washington, DC: Hemisphere) vol. 2, pp 757–762Google Scholar
  101. Tien C L 1988 Thermal radiation in packed and fluidized beds.Trans. ASME J. Heat Transfer 110: 1230–1242Google Scholar
  102. Tiwari S N, Liu J 1992 Investigation of radiative interaction in laminar flows of nongray gases using Monte Carlo simulation. InProceedings of the National Heat Transfer Conference, San Diego, CA (ASME) pp 187–195Google Scholar
  103. Truelove J S 1987 Discrete-ordinate solutions of the radiative transport equation.Trans. ASME J. Heat Transfer 109: 1048–1051Google Scholar
  104. 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
  105. Vaillon R, Lallemand M, Lemonnier D 1995 Radiative equilibrium in axisymmetric semitransparent gray shells using the discrete ordinate method. InProceedings of the First International Symposium on Radiative Heat Transfer, Kusadasi, TurkeyGoogle Scholar
  106. Vaillon R, Lallemand M, Lemonnier D 1996aEUROTHERM (eds) D Lemonnier, J B Savlnier, M Fiebig (Amsterdam: Elsevier) pp 1994–2000Google Scholar
  107. 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
  108. Varma S A 1979Pulverized coal combustion and gassification (New York: Plenum) pp 311–315Google Scholar
  109. Viskanta R, Menguc M P 1987 Radiation heat transfer in combustion systems.Prog. Energy Combust. Sci. 13: 97–160CrossRefGoogle Scholar
  110. Yang K T 1986 Numerical modeling of natural convection-radiation interactions in enclosures. InProceedings of the 8th International Heat Transfer Conference (Washington, DC: Hemisphere) vol. 1, pp 131–140Google Scholar
  111. 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
  112. 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

Copyright information

© Indian Academy of Sciences 1998

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of TechnologyGuwahatiIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of TechnologyKanpurIndia

Personalised recommendations