Radiation Heat Transfer

  • M. Kaviany
Part of the Mechanical Engineering Series book series (MES)


In this chapter, heat transfer by radiation in porous media is examined. The medium may be treated either as a single continuum or as a collection of particles (i.e., scatterers). In the particle-based analysis, the interaction of radiation with a collection of elements of the solid matrix (e.g., particles in a packed bed) is considered. On the other hand, the continuum treatment attempts to obtain the effective radiative properties of the medium by using the element-based interaction along with a local volume-averaging procedure. This volume averaging is greatly simplified if it is assumed that the interaction of a particle with radiation is not affected by the presence of neighboring particles [i.e., the scattering (or absorption) is independent]. In case the assumption of independent scattering fails, the volume averaging must include dependent effects.


Heat Transfer Radiative Transfer Phase Function Representative Elementary Volume Radiation Heat Transfer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Azad, F. H., 1985, “Differential Approximation to Radiative Transfer in Semi- Transparent Media,” ASME J. Heat Transfer, 107, 478–481.CrossRefGoogle Scholar
  2. Bayazitoglu, Y. and Higenyi, J., 1979, “Higher Order Differential Equations of Radiative Transfer” AIAA J., 17, 424–431.ADSCrossRefGoogle Scholar
  3. Bohren, G. F. and Huffman, D. R., 1983, Absorption and Scattering Light by Small Particles, John Wiley.Google Scholar
  4. Born, M. and Wolf, E., 1988, Principles of Optics, Pergamon (Oxford).Google Scholar
  5. Brewster, M. Q., 1983, “Radiative Heat Transfer in Fluidized Bed Combustors,” ASME paper no. 83–WA/HT- 82.Google Scholar
  6. Brewster, M. Q., 1992, Thermal Radiative Transfer and Properties. Wiley and Sons, New York.Google Scholar
  7. Brewster, M. Q. and Tien, C.-L., 1982a, “Radiative Transfer in Packed and Fluidized Beds: Dependent versus Independent Scattering,” ASME J. Heat Transfer, 104, 573–579.CrossRefGoogle Scholar
  8. Brewster, M. Q. and Tien, C.-L., 1982b, “Examination of the Two Flux Model for Radiative Transfer in Particular Systems.” Int. J. Heat Mass Transfer, 25, 1905–1907.ADSMATHCrossRefGoogle Scholar
  9. Carlson, B. G. and Lathrop, K. D., 1968, “Transport Theory—The Method of Discrete Ordinates,” in Computing Methods in Reactor Physics, Gordon and Breach Science Pub., 171–266.Google Scholar
  10. Cartigny, J. D., Yamada, Y., and Tien, C.-L., 1986, “Radiative Heat Transfer with Dependent Scattering by Particles: Part 1—Theoretical Investigation,” ASME J. Heat Transfer, 108, 608–613.CrossRefGoogle Scholar
  11. Chai, J. C., Lee, L. S., and Patankar, S. V., 1994, “Finite Volume Method of Radiative Heat Transfer,” J. Thermophys. Heat Transfer, 8, 419–425.CrossRefGoogle Scholar
  12. Chan, C. K. and Tien, C.-L., 1974, “Radiative Transfer in Packed Spheres,” ASME J. Heat Transfer, 96, 52–58.CrossRefGoogle Scholar
  13. Chandrasekhar, S., 1960, Radiation Transfer, Dover.Google Scholar
  14. Chang, S. L. and Rhee, K. T., 1981, “Blackbody Radiation Functions,” Int. J. Comm. Heat Mass Transfer, 11, 451–455.CrossRefGoogle Scholar
  15. Chen, J. C. and Churchill, S. W., 1963, “Radiant Heat Transfer in Packed Beds,” AIChE J., 9, 35–41.CrossRefGoogle Scholar
  16. Cheng, P., 1969, “Two-Dimensional Radiating Gas Flow by a Moment Method,” AIAA J., 2, 1662–1664.Google Scholar
  17. Chern, B.-C., Howell, J. R., and Moon, T. J., 1994, “Dependent Scattering Effects on Wave Propagation through Filament-Wound Composites,” in Radiation Heat Transfer: Current Research, Bayazitoglu, Y., et al., Editors, ASME HTD Vol. 276, American Society of Mechanical Engineers.Google Scholar
  18. Chu, C. M. and Churchill, S. W., 1955, “Representation of Angular Distribution of Radiation Scattered by a Spherical Particle,” J. Opt. Soc. Amer., 45, 958–962.ADSCrossRefGoogle Scholar
  19. Condiff, D. WM 1987, “Anisotropic Scattering in Three Dimensional Differential Approximation for Radiation Heat Transfer,” Int. J. Heat Mass Transfer 30, 1371–1380.ADSCrossRefGoogle Scholar
  20. Crosbie, A. L. and Davidson, G. W., 1985, “Dirac-Delta Function Approximations to the Scattering Phase Function,” J. Quant. Spectrosc. Radiat. Transfer, 33, 391–409.ADSCrossRefGoogle Scholar
  21. Davison, B., 1957, Neutron Transport Theory, Oxford.Google Scholar
  22. Dcissler, R. G., 1961, “Diffusion Approximation for Thermal Radiation in Gases with Jump Boundary Condition,” ASME J. Heat Transfer, 86, 240–246.Google Scholar
  23. Driscoll, W. G. and Vaughan, W, eds., 1978, Handbook of Optics, McGraw-Hill.Google Scholar
  24. Drolen, B. L. and Tien, C.-L., 1987, “Independent and Dependent Scattering in Packed Spheres Systems,” J. Thermophys. Heat Transfer, 1, 63–68.ADSCrossRefGoogle Scholar
  25. Fiveland, W. A., 1987, “Discrete Ordinate Methods for Radiative Heat Transfer in Isotropically and Anisotropically Scattering Media,” ASME J. Heat Transfer, 109, 809–812.CrossRefGoogle Scholar
  26. Fiveland, W. A., 1988. “Three-Dimensional Radiative Heat Transfer Solutions by the Discrete-Ordinates Method,” J. Thermophys. Heat Transfer, 2, 309–316.CrossRefGoogle Scholar
  27. Glicksman, L., Schuetz, M., and Sinofsky, M., 1987, “Radiative Heat Transfer in Foam Insulation,” Int. J. Heat Mass Transfer, 30, 187–197.CrossRefGoogle Scholar
  28. Grosshandler, W. H. and Monterio, S. L. P., 1982, “Attenuation of Thermal Radiation by Pulverized Coal and Char,” ASME J. Heat Transfer, 104, 587–593.CrossRefGoogle Scholar
  29. Hendricks, T. J., 1993. Thermal Radiative Properties and Modelling of Reticulated Porous Ceramics, Ph. D. Thesis, The University of Texas at Austin.Google Scholar
  30. Hendricks, T. J. and Howell, J. R-, 1996, “Absorption/Scattering Coefficients and Scattering Phase Functions in Reticulated Porous Ceramics.” ASME J. Heat Transfer, 118, 79–87.CrossRefGoogle Scholar
  31. Hottel, H. C., Sarofiin, A. F., Dalzell, W. H., and Vasalos, I. A., 1971. A., 1971, “Optical Properties of Coatings, Effect of Pigment Concentration,” AIAA J., 9, 1895– 1898.Google Scholar
  32. Hottel, H. C., Sarofiin, A. F., Evans, L. B., and Vasalos, I. A, 1968, “Radiative Transfer in Anisotropically Scattering Media: Allowance for Fresnel Reflection at the Boundaries,” ASME J. Heat Transfer, 90, 56–62.Google Scholar
  33. Hottel, H. C., Sarofim, A. F., Vasalos, I. A., and Dalzell, W. H., 1970, “Multiple Scatter: Comparison of Theory with Experiment,” ASME J. Heat Transfer, 92, 285–291.CrossRefGoogle Scholar
  34. Hsieh, C. K. and Su, K. C., 1979, “Thermal Radiative Properties of Glass from 0.32 to 206 µm,” Solar Energy, 22, 37 43.Google Scholar
  35. Ishimaru, A. and Kuga, Y., 1982, “Attenuation Constant of a Coherent Field in a Dense Distribution of Particles,” J. Opt. Soc. Amer., 72, 1317–1320.ADSCrossRefGoogle Scholar
  36. Jamaluddin, A. S. and Smith, P. J., 1988, “Predicting Radiative Transfer in Axisymmetric Cylindrical Enclosure Using the Discrete Ordinatcs Method,” Combust. Sci. Technol., 62, 173–186.CrossRefGoogle Scholar
  37. Jeans, J. H., 1917, “The Equation of Radiative Transfer of Energy,” Monthly Notices of Royal Astronomical Society, 78, 445 461.Google Scholar
  38. Jodrey, W. S. and Tory, E. M., 1979, “Simulation of Random Packing of Spheres,” Simulation, Jan., 1–12.Google Scholar
  39. Joseph, J. H., Wiscombe, W. J., and Weinman, J. A., 1976, “The Delta-Eddington Approximations for Radiative Heat Transfer,” J. Atm. Sci., 34, 1408–1422.Google Scholar
  40. Kamiuto, K., 1990, “Correlated Radiative Transfer in Packed Bed-Sphere Systems,” J. Quant. Spectrosc. Rxidiat. Transfer, 43, 39–43.ADSCrossRefGoogle Scholar
  41. Kaviany, M., 1985, “One-Dimensional Conduction-Radiation Heat IVansfer Between Parallel Surfaces Subject to Convective Boundary Conditions,” Int. J. Heat Mass Transfer, 28, 497–499.CrossRefGoogle Scholar
  42. Kerker, M., 1969, The Scattering of Light and Other Electromagnetic Radiation, Academic.Google Scholar
  43. Kerker, M., Schciner, P., and Cooke, D. D., 1978, “The Range of Validity of Rayleigh and Mie Limits for Lorentz-Mie Scattering,” J. Opt. Soc. Amert 68, 135–137.ADSCrossRefGoogle Scholar
  44. Ku, J. C. and Felske, J. D., 1984, “The Range of Validity of the Rayleigh Limit for Computing Mie Scattering and Extinction Efficiencies,” J. Quant. Spectrosc. Radiat. Transfer, 31, 569–574.ADSCrossRefGoogle Scholar
  45. Kudo, K., Yang W., Tanaguchi, H., and Hayasaka, H., 1987, “Radiative Heat Transfer in Packed Spheres by Monte Carlo Method,” Heat Transfer in High Technology and Power Engineering Proceedings, Hemisphere, 529–540.Google Scholar
  46. Kumar, S., Majumdar, A., and Tien, C.-L., 1990, “The Differential-Discrete Ordinate Method for Solution of the Equation of Radiative Transfer,” ASME J. Heat Transfer, 112, 424–429.CrossRefGoogle Scholar
  47. Kumar, S. and Tien, C.-L., 1990, “Dependent Scattering and Absorption of Radiation by Small Particles,” ASME J. Heat Transfer, 112, 178–185.CrossRefGoogle Scholar
  48. Lee, H. and Buckius, R. O., 1982, “Scaling Anisotropic Scattering in Radiation Heat Transfer for a Planar Medium,” ASME J. Heat Transfer, 104, 68–75.ADSCrossRefGoogle Scholar
  49. Lee, H. and Buckius, R. O., 1983, “Reducing Scattering to Non-Scattering Problems in Radiation Heat Transfer,” Int. J. Heat Mass Transfer, 26, 1055–1062.ADSCrossRefGoogle Scholar
  50. Lee, H. and Buckius, R. O., 1986, “Combined Mode Heat Transfer Analysis Utilizing Radiation Scaling,” ASME J. Heat Transfer, 108, 626–632.ADSCrossRefGoogle Scholar
  51. Lee, S. C., 1990, “Scattering Phase Function for Fibrous Media,” Int. J. Heat Mass Transfer, 33, 2183–2190.ADSCrossRefGoogle Scholar
  52. Lee, S. C-, White, S-, and Grzesik, J. A., 1994, “Effective Radiative Properties of Fibrous Composites Containing Spherical Particles,” J. Thermoph. Heat Transfer, 8, 400–405.CrossRefGoogle Scholar
  53. Liou, K.-N. and Hansen, J. E., 1971, “Intensity and Polarization for Single Scattering Polydisperse Spheres: A Comparison of Ray-Optics and Mie Scattering,” J. Atmospheric Sci., 28, 995–1004.ADSCrossRefGoogle Scholar
  54. Lorrain, P. and Corson, D. R., 1970, Electromagnetic Fields and Wave, Second Edition, Freeman and Co., 422–551.Google Scholar
  55. Mazza, G. D., Berto, C. A., and Barreto, G. F., 1991, “Evaluation of Radiative Heat Transfer Properties in Dense Particulate Media,” Powder Tech., 67, 137– 144.CrossRefGoogle Scholar
  56. McKellar, B. H. J. and Box, M. A., 1981, “The Scaling Group of the Radiative Transfer Equation,” J. Atmospheric Sci., 38, 1063–1068.MathSciNetADSCrossRefGoogle Scholar
  57. Mengüc, M. P. and Viskanta, R., 1982, “Comparison of Radiative Heat Transfer Approximations for Highly Forward Scattering Planar Medium,” ASME paper no. 82–HT–20.Google Scholar
  58. Mengüc, M. P. and Viskanta, R., 1985a, “On the Radiative Properties of Poly-dispersions: A Simplified Approach,” Combust. Sci. Technol., 44, 143–149.CrossRefGoogle Scholar
  59. Mengüc, M. P and Viskanta, R., 1985b, “Radiative Transfer in Three- Dimensional Rectangulated Enclosures Containing Inhomogeneous, Anisotropically Scattering Media,” J. Quant. Spectrosc. Radiat. Transfer, 33, 533–549.ADSCrossRefGoogle Scholar
  60. Mengüc, M. P. and Viskanta, R., 1986, “An Assessment of Spectral Radiative Heat Transfer Predictions for a Pulverized Coal- Fired Furnace,” in Proceedings of 8th International Heat and Mass Conference (San Francisco), 2, 815–820.Google Scholar
  61. Modest, M. F., 1993, Radiative Heat Transfer, McGraw-Hill, New York.Google Scholar
  62. Modest, M. F. and Azad, F. H., 1980, “The Differential Approximation for Radiative Transfer in an Emitting, Absorbing and Anisotropically Scattering Medium,” J. Quant. Spectrosc. Radiat. Transfer, 23, 117–120.ADSCrossRefGoogle Scholar
  63. Nelson, H. F., Look, D. C., and Crosbie, A. L., 1986, “Two-Dimensional Radiative Back-Scattering from Optically Thick Media,” ASME J. Heat Transfer, 108, 619–625.CrossRefGoogle Scholar
  64. Ozisik, M. N., 1985, Radiative Transfer and Interaction with Conduction and Convection, Werbel and Peck.Google Scholar
  65. Palik, E. D., ed., 1985. Handbook of Optical Constants of Solids, Academic Press.Google Scholar
  66. Papini, M., 1989, “Study of the Relationship Between Materials and Their Radiative Properties: Application to Natural Fibers for Spectral Wavelength Range 0.25–2.5 µm,” Infrared Phys., 29, 35–41.CrossRefGoogle Scholar
  67. Penndorf, R. B., 1962, “Scattering and Extinction for Small Absorbing and Non-absorbing Aerosols,” J. Opt. Soc. Amer., 8, 896–904.ADSGoogle Scholar
  68. Raithby, G. D. and Chui, E. H., 1990, “A FiniteVolume Method for Predicting a Radiant Heat Transfer in Enclosures with Participating Media,” ASME J. Heat Transfer, 112, 415–423.ADSCrossRefGoogle Scholar
  69. Ratzel, A. C., 1981, “P-N Differential Approximation for Solution of One- and Two-Dimensional Radiation and Conduction Energy Transfer in Gray Participating Media,” Ph.D. thesis, University of Texas at Austin.Google Scholar
  70. Ratzel, A. C. and Howell, J. R., 1983, “Two Dimensional Radiation in Absorbing- Emitting Media Using the P-N Approximation,” ASME J. Heat Transfer, 105, 333–340.CrossRefGoogle Scholar
  71. Rish, J. W. and Roux, J. A., 1987, “Heat Transfer Analysis of Fiberglass Insulations with and without Foil Radiant Barriers,” J. Thermophys. Heat Transfer, 1, 43–49.CrossRefGoogle Scholar
  72. Selamet, A., 1989, Radiation Affected Laminar Flame Propagation, Ph.D. thesis, University of Michigan.Google Scholar
  73. Selamet, A. and Arpaci, V. S., 1989, “Rayleigh Limit Penndorf Extension,” Int. J. Heat Mass Transfer, 32, 1809–1820.ADSMATHCrossRefGoogle Scholar
  74. Siegel, R. and Howell, J. R., 1981, Thermal Radiation Heat Transfer, Second Edition, McGraw-Hill.Google Scholar
  75. Siegel, R., and Howell, J. R., 1992, Thermal Radiation Heat Transfer, Third Edition, Hemisphere, Washington.Google Scholar
  76. Singh, B. P. and Kaviany, M., 1991, “Independent Theory Versus Direct Simulation of Radiative Heat TVansfer in Packed Beds,” Int. J. Heat Mass Transfer, 34, 2869–2881.MATHCrossRefGoogle Scholar
  77. Singh, B. P. and Kaviany, M., 1992, “Modeling Radiative Heat Transfer in Packed Beds,” Int. J. Heat Mass Transfer, 35, 1397–1405.CrossRefGoogle Scholar
  78. Singh, B. P. and Kaviany, M., 1994, “Effect of Particle Conductivity on Radiative Heat Transfer in Packed Beds,” Int. J. Heat Mass Transfer, 37, 2579–2583.CrossRefGoogle Scholar
  79. Sparrow, E. M. and Cess, R. D., 1978, Radiative Heat Transfer, McGraw-Hill.Google Scholar
  80. Tien, C.-L., 1988, “Thermal Radiation in Packed and Fluidized Beds,” ASME J. Heat Transfer, 110, 1230–1242.CrossRefGoogle Scholar
  81. Tien, C.-L. and Drolen, B. L., 1987, “Thermal Radiation in Particulate Media with Dependent and Independent Scattering,” Annual Review of Numerical Fluid Mechanics and Heat Transfer, 1, 1–32.Google Scholar
  82. Tong, T. W. and Swathi, P. S., 1987, “Radiative Heat Transfer in Emitting- Absorbing-Scattering Spherical Media,” J. Thermophys. Heat Transfer, 1,162–170.ADSCrossRefGoogle Scholar
  83. Tong, T. W. and Tien, C.-L., 1983, “Radiative Heat Transfer in Fibrous Insulations—Part 1: Analytical Study,” ASME J. Heat Transfer, 105, 70–75.CrossRefGoogle Scholar
  84. Tong, T. W., Yang, Q. S., and Tien, C.-L., 1983, “Radiative Heat Transfer in Fibrous Insulations—Part 2: Experimental Study,” ASME J. Heat Transfer, 105, 76–81.CrossRefGoogle Scholar
  85. Truelove, J. S., 1987, “Discrete Ordinates Solutions of the Radiative Transport Equation,” ASME J. Heat Transfer, 109, 1048–1051.CrossRefGoogle Scholar
  86. Tseng, J. W. C., Xia, Y., and Strieder, W., 1992, “Monte Carlo Calculations of Wall-to-Random-Bed View Factors: Impermeable Spheres and Fibers,” AIChE J., 38, 955–958.CrossRefGoogle Scholar
  87. van de Hulst, H. C., 1981, Light Scattering by Small Particles, Dover.Google Scholar
  88. Vortmeyer, D., 1978, “Radiation in Packed Solids,” in Proceedings of 6th International Heat Transfer Conference (Toronto), 6, 525–539.Google Scholar
  89. Wang, K. Y. and Tien, C.-L., 1983, “Thermal Insulation in Flow Systems: Combined Radiation and Convection Through a Porous Segment,” ASME, paper no. 83-WA/HT-81.Google Scholar
  90. Weast, R. C-, ed., 1987, Handbook of Chemistry and Physics, 68th ed., C.R.C. Press.Google Scholar
  91. Weaver, J. H., ed., 1981, Optical Properties of Metals, Fachuvnfarmationszentrum Energie, Physik, Mathematik Gmbh.Google Scholar
  92. Wiscombe, W. J., 1977, “The Delta-M Method: Rapid Yet Accurate Flux Calculations for Strongly Asymmetric Phase Functions,” J. Atm. Sci., 34, 1408–1422.ADSCrossRefGoogle Scholar
  93. Wolf, J. R., Tseng, J. W. C., and Strieder, W., 1990, “Radiative Conductivity for a Random Void Solid Medium with Diffusely Reflecting Surfaces,” Int. J. Heat Mass Transfer, 33, 725–734.CrossRefGoogle Scholar
  94. Xia, Y. and Strieder, W., 1994a, “Complementary Upper and Lower Truncated Sum, Multiple Scattering Bounds on the Effective Emissivity,” Int. J. Heat Mass Transfer, 37, 443–450.ADSMATHCrossRefGoogle Scholar
  95. Xia, Y. and Strieder, W., 1994b, “Variational Calculation of the Effective Emissivity for a Random Bed,” Int. J. Heat Mass Transfer, 37, 451–460.ADSMATHCrossRefGoogle Scholar
  96. Yamada, Y., Cartigny, J. D., and Tien, C.-L., 1986, “Radiative Transfer with Dependent Scattering by Particles: Part 2—Experimental Investigation,” ASME J. Heat Transfer, 108, 614–618.CrossRefGoogle Scholar
  97. Yang, Y. S., Howell, J. R., and Klein, D. E., 1983, “Radiative Heat Transfer Through a Randomly Packed Bed of Spheres by the Monte Carlo Method,” ASME J. Heat Transfer, 105, 325–332.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • M. Kaviany
    • 1
  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of MichiganAnn ArborUSA

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