Abstract

We report experimental measurement of radiation characteristics of fused quartz containing bubbles over the spectral region from 1.67 to 3.5 µm. The radiation characteristics were retrieved by an inverse method that minimizes the quadratic difference between the measured and the calculated spectral bidirectional transmittance and reflectance for different sample thicknesses. The theoretical spectral transmittances and reflectances were computed by solving the one-dimensional radiative transfer equation by the discrete-ordinates method for a nonemitting, homogeneous, and scattering medium. The results of the inversion were shown to be independent of the sample thickness for samples thicker than 3 mm and clearly demonstrate that bubbles have an effect on the radiation characteristics of fused quartz.

© 2004 Optical Society of America

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  1. M. F. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 1993).
  2. D. Baillis, J.-F. Sacadura, “Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization,” J. Quant. Spectrosc. Radiat. Transf. 67, 327–363 (2000).
    [CrossRef]
  3. J. Kuhn, H.-P. Ebert, M. C. Arduini-Schuster, D. Büttner, J. Fricke, “Thermal transport in polystyrene and polyurethane foam insulations,” Int. J. Heat Mass Transfer 35, 1795–1801 (1992).
    [CrossRef]
  4. G. Eeckhaut, A. Cunningham, “The elimination of radiative heat transfer in fine celled PU rigid foams,” J. Cell. Plastics 32, 528–552 (1996).
  5. M. Schuetz, L. Glicksman, “A basic study of heat transfer through foam insulation,” J. Cell. Plastics 20, 114–121 (1984).
    [CrossRef]
  6. L. R. Glicksman, M. Schuetz, M. Sinofsky, “Radiation heat transfer in foam insulation,” Int. J. Heat Mass Transfer 30, 187–197 (1987).
    [CrossRef]
  7. L. R. Glicksman, A. L. Marge, J. D. Moreno, “Radiation heat transfer in cellular foam insulation,” in Proceedings of the 28th National Heat Transfer Conference and Exhibition, HTD Vol. 203: Developments in Radiative Heat Transfer (American Society of Mechanical Engineers, New York, 1997), pp. 45–54.
  8. R. Viskanta, M. P. Mengüç, “Radiative transfer in combustion systems,” Prog. Energy Combust. Sci. 13, 97–160 (1987).
    [CrossRef]
  9. L. A. Dombrovsky, Radiation Heat Transfer in Disperse Systems (Begell House, New York, 1996).
  10. M. Rubin, “Optical properties of soda-lime silicate,” Sol. Energy Mater. 12, 275–288 (1985).
    [CrossRef]
  11. L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
    [CrossRef]
  12. A. G. Fedorov, R. Viskanta, “Radiative transfer in a semitransparent glass foam blanket,” Phys. Chem. Glasses 41, 127–135 (2000).
  13. A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
    [CrossRef]
  14. M. J. Hale, M. S. Bohn, “Measurement of the radiative transport properties of reticulated alumina foams,” in Proceedings of the ASME/ASES Joint Solar Engineering Conference, A. Kirkpatrick, W. Worek, eds. (Association of Mechanical Engineers, New York, 1993), pp. 507–515.
  15. T. J. Hendricks, J. R. Howell, “Absorption/scattering coefficients and scattering phase functions in reticulated porous ceramics,” J. Heat Transfer 118, 79–87 (1996).
    [CrossRef]
  16. D. Baillis, M. Raynaud, J.-F. Sacadura, “Determination of spectral radiative properties of open-cell foam: model validation,” J. Thermophys. Heat Transfer 14, 137–143 (2000).
    [CrossRef]
  17. D. Baillis, M. Arduini-Schuster, J.-F. Sacadura, “Identification of spectral radiative properties of polyurethane foam from hemispherical and bi-directional transmittance and reflectance measurements,” in Proceedings of the 3rd International Symposium on Radiation Transfer, M. P. Mengüc, N. Selcuk, eds. (Begell House, New York, 2001), pp. 474–482.
  18. D. Baillis, J.-F. Sacadura, “Identification of polyurethane foam radiative properties: influence of transmittance measurements number,” J. Thermophys. Heat Transfer 16, 200–206 (2002).
    [CrossRef]
  19. L. M. Moura, “Identification des propriétés radiatives des matériaux semi-transparent diffusants en situation de non-symmetrie azimutale du champ radiatif,” Ph.D. thesis (Institut National des Sciences Appliquées de Lyon, Lyon, France, 1998).
  20. W. L. Dunn, “Inverse Monte Carlo analysis,” J. Comput. Phys. 41, 154–166 (1981).
    [CrossRef]
  21. S. Subramaniam, M. P. Mengüç, “Solution of the inverse radiation problem for inhomogeneous and anisotropically scattering media using a Monte Carlo technique,” Int. J. Heat Mass Transfer 14, 253–266 (1991).
    [CrossRef]
  22. M. Take-Uchi, Y. Kurosaki, T. Kashiwagi, J. Yamada, “Determination of radiation properties of porous media by measuring emission,” J. Soc. Mech. Eng. Int. J. 31, 581–585 (1988).
  23. J. Yamada, Y. Kurosaki, “Estimation of a radiative property of scattering and absorbing media,” Int. J. Thermophys. 18, 547–556 (1997).
    [CrossRef]
  24. D. Doermann, “Modélisation des transferts thermiques dans des matériaux semitransparents de type mousse à pores ouverts et prédiction des propriétés radiatives,” Ph.D. thesis (Institut National des Sciences Appliquées de Lyon, Lyon, France, 1995).
  25. V. P. Nicolau, “Identification des propriétés radiatives des matèriaux semitransparent diffusants,” Ph.D. thesis (Institut National des Sciences Appliquées de Lyon, Lyon, France, 1994) (94 ISAL 0001).
  26. J. V. Beck, K. J. Arnold, Parameter Estimation in Engineering and Science (Wiley, New York, 1977).
  27. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, New York, 1992).
  28. W. S. Rodney, R. J. Spindler, “Index of refraction of fused quartz for ultraviolet, visible, and infrared wavelengths,” J. Opt. Soc. Am. 44, 677–679 (1954).
    [CrossRef]
  29. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965).
    [CrossRef]
  30. C. Z. Tan, J. Arndt, “Temperature dependence of refractive index of glass SiO2 in the infrared wavelength range,” J. Phys. Chem. Solids 61, 1315–1320 (2000).
    [CrossRef]
  31. C. Z. Tan, “Determination of refractive index of silica glass for infrared wavelengths by ir spectroscopy,” J. Non-Cryst. Solids 223, 158–163 (1998).
    [CrossRef]
  32. M. Raynaud, “Strategy for the experimental design and the estimation of parameters,” High Temp. High Press. 31, 1–15 (1999).
    [CrossRef]
  33. V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
    [CrossRef]
  34. R. G. C. Beerkens, “The role of gases in glass melting processes,” Glastech. Ber. 71, 369–380 (1995).
  35. R. Marlor, W. Anderson, Osram Sylvania Inc., Glass Technologies Headquarters, Exeter, New Hampshire 03833 (personal communication, July2002).

2003 (1)

L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
[CrossRef]

2002 (1)

D. Baillis, J.-F. Sacadura, “Identification of polyurethane foam radiative properties: influence of transmittance measurements number,” J. Thermophys. Heat Transfer 16, 200–206 (2002).
[CrossRef]

2000 (6)

D. Baillis, M. Raynaud, J.-F. Sacadura, “Determination of spectral radiative properties of open-cell foam: model validation,” J. Thermophys. Heat Transfer 14, 137–143 (2000).
[CrossRef]

A. G. Fedorov, R. Viskanta, “Radiative transfer in a semitransparent glass foam blanket,” Phys. Chem. Glasses 41, 127–135 (2000).

A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
[CrossRef]

D. Baillis, J.-F. Sacadura, “Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization,” J. Quant. Spectrosc. Radiat. Transf. 67, 327–363 (2000).
[CrossRef]

C. Z. Tan, J. Arndt, “Temperature dependence of refractive index of glass SiO2 in the infrared wavelength range,” J. Phys. Chem. Solids 61, 1315–1320 (2000).
[CrossRef]

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

1999 (1)

M. Raynaud, “Strategy for the experimental design and the estimation of parameters,” High Temp. High Press. 31, 1–15 (1999).
[CrossRef]

1998 (1)

C. Z. Tan, “Determination of refractive index of silica glass for infrared wavelengths by ir spectroscopy,” J. Non-Cryst. Solids 223, 158–163 (1998).
[CrossRef]

1997 (1)

J. Yamada, Y. Kurosaki, “Estimation of a radiative property of scattering and absorbing media,” Int. J. Thermophys. 18, 547–556 (1997).
[CrossRef]

1996 (2)

G. Eeckhaut, A. Cunningham, “The elimination of radiative heat transfer in fine celled PU rigid foams,” J. Cell. Plastics 32, 528–552 (1996).

T. J. Hendricks, J. R. Howell, “Absorption/scattering coefficients and scattering phase functions in reticulated porous ceramics,” J. Heat Transfer 118, 79–87 (1996).
[CrossRef]

1995 (1)

R. G. C. Beerkens, “The role of gases in glass melting processes,” Glastech. Ber. 71, 369–380 (1995).

1992 (1)

J. Kuhn, H.-P. Ebert, M. C. Arduini-Schuster, D. Büttner, J. Fricke, “Thermal transport in polystyrene and polyurethane foam insulations,” Int. J. Heat Mass Transfer 35, 1795–1801 (1992).
[CrossRef]

1991 (1)

S. Subramaniam, M. P. Mengüç, “Solution of the inverse radiation problem for inhomogeneous and anisotropically scattering media using a Monte Carlo technique,” Int. J. Heat Mass Transfer 14, 253–266 (1991).
[CrossRef]

1988 (1)

M. Take-Uchi, Y. Kurosaki, T. Kashiwagi, J. Yamada, “Determination of radiation properties of porous media by measuring emission,” J. Soc. Mech. Eng. Int. J. 31, 581–585 (1988).

1987 (2)

L. R. Glicksman, M. Schuetz, M. Sinofsky, “Radiation heat transfer in foam insulation,” Int. J. Heat Mass Transfer 30, 187–197 (1987).
[CrossRef]

R. Viskanta, M. P. Mengüç, “Radiative transfer in combustion systems,” Prog. Energy Combust. Sci. 13, 97–160 (1987).
[CrossRef]

1985 (1)

M. Rubin, “Optical properties of soda-lime silicate,” Sol. Energy Mater. 12, 275–288 (1985).
[CrossRef]

1984 (1)

M. Schuetz, L. Glicksman, “A basic study of heat transfer through foam insulation,” J. Cell. Plastics 20, 114–121 (1984).
[CrossRef]

1981 (1)

W. L. Dunn, “Inverse Monte Carlo analysis,” J. Comput. Phys. 41, 154–166 (1981).
[CrossRef]

1965 (1)

1954 (1)

Anderson, W.

R. Marlor, W. Anderson, Osram Sylvania Inc., Glass Technologies Headquarters, Exeter, New Hampshire 03833 (personal communication, July2002).

Arduini-Schuster, M.

D. Baillis, M. Arduini-Schuster, J.-F. Sacadura, “Identification of spectral radiative properties of polyurethane foam from hemispherical and bi-directional transmittance and reflectance measurements,” in Proceedings of the 3rd International Symposium on Radiation Transfer, M. P. Mengüc, N. Selcuk, eds. (Begell House, New York, 2001), pp. 474–482.

Arduini-Schuster, M. C.

J. Kuhn, H.-P. Ebert, M. C. Arduini-Schuster, D. Büttner, J. Fricke, “Thermal transport in polystyrene and polyurethane foam insulations,” Int. J. Heat Mass Transfer 35, 1795–1801 (1992).
[CrossRef]

Arndt, J.

C. Z. Tan, J. Arndt, “Temperature dependence of refractive index of glass SiO2 in the infrared wavelength range,” J. Phys. Chem. Solids 61, 1315–1320 (2000).
[CrossRef]

Arnold, K. J.

J. V. Beck, K. J. Arnold, Parameter Estimation in Engineering and Science (Wiley, New York, 1977).

Baillis, D.

D. Baillis, J.-F. Sacadura, “Identification of polyurethane foam radiative properties: influence of transmittance measurements number,” J. Thermophys. Heat Transfer 16, 200–206 (2002).
[CrossRef]

D. Baillis, J.-F. Sacadura, “Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization,” J. Quant. Spectrosc. Radiat. Transf. 67, 327–363 (2000).
[CrossRef]

D. Baillis, M. Raynaud, J.-F. Sacadura, “Determination of spectral radiative properties of open-cell foam: model validation,” J. Thermophys. Heat Transfer 14, 137–143 (2000).
[CrossRef]

D. Baillis, M. Arduini-Schuster, J.-F. Sacadura, “Identification of spectral radiative properties of polyurethane foam from hemispherical and bi-directional transmittance and reflectance measurements,” in Proceedings of the 3rd International Symposium on Radiation Transfer, M. P. Mengüc, N. Selcuk, eds. (Begell House, New York, 2001), pp. 474–482.

Beck, J. V.

J. V. Beck, K. J. Arnold, Parameter Estimation in Engineering and Science (Wiley, New York, 1977).

Beerkens, R. G. C.

R. G. C. Beerkens, “The role of gases in glass melting processes,” Glastech. Ber. 71, 369–380 (1995).

Bohn, M. S.

M. J. Hale, M. S. Bohn, “Measurement of the radiative transport properties of reticulated alumina foams,” in Proceedings of the ASME/ASES Joint Solar Engineering Conference, A. Kirkpatrick, W. Worek, eds. (Association of Mechanical Engineers, New York, 1993), pp. 507–515.

Büttner, D.

J. Kuhn, H.-P. Ebert, M. C. Arduini-Schuster, D. Büttner, J. Fricke, “Thermal transport in polystyrene and polyurethane foam insulations,” Int. J. Heat Mass Transfer 35, 1795–1801 (1992).
[CrossRef]

Cunningham, A.

G. Eeckhaut, A. Cunningham, “The elimination of radiative heat transfer in fine celled PU rigid foams,” J. Cell. Plastics 32, 528–552 (1996).

Dianov, E. M.

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

Doermann, D.

D. Doermann, “Modélisation des transferts thermiques dans des matériaux semitransparents de type mousse à pores ouverts et prédiction des propriétés radiatives,” Ph.D. thesis (Institut National des Sciences Appliquées de Lyon, Lyon, France, 1995).

Dombrovsky, L. A.

L. A. Dombrovsky, Radiation Heat Transfer in Disperse Systems (Begell House, New York, 1996).

Dunn, W. L.

W. L. Dunn, “Inverse Monte Carlo analysis,” J. Comput. Phys. 41, 154–166 (1981).
[CrossRef]

Ebert, H.-P.

J. Kuhn, H.-P. Ebert, M. C. Arduini-Schuster, D. Büttner, J. Fricke, “Thermal transport in polystyrene and polyurethane foam insulations,” Int. J. Heat Mass Transfer 35, 1795–1801 (1992).
[CrossRef]

Eeckhaut, G.

G. Eeckhaut, A. Cunningham, “The elimination of radiative heat transfer in fine celled PU rigid foams,” J. Cell. Plastics 32, 528–552 (1996).

Fedorov, A. G.

A. G. Fedorov, R. Viskanta, “Radiative transfer in a semitransparent glass foam blanket,” Phys. Chem. Glasses 41, 127–135 (2000).

A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
[CrossRef]

Fricke, J.

J. Kuhn, H.-P. Ebert, M. C. Arduini-Schuster, D. Büttner, J. Fricke, “Thermal transport in polystyrene and polyurethane foam insulations,” Int. J. Heat Mass Transfer 35, 1795–1801 (1992).
[CrossRef]

Glicksman, L.

M. Schuetz, L. Glicksman, “A basic study of heat transfer through foam insulation,” J. Cell. Plastics 20, 114–121 (1984).
[CrossRef]

Glicksman, L. R.

L. R. Glicksman, M. Schuetz, M. Sinofsky, “Radiation heat transfer in foam insulation,” Int. J. Heat Mass Transfer 30, 187–197 (1987).
[CrossRef]

L. R. Glicksman, A. L. Marge, J. D. Moreno, “Radiation heat transfer in cellular foam insulation,” in Proceedings of the 28th National Heat Transfer Conference and Exhibition, HTD Vol. 203: Developments in Radiative Heat Transfer (American Society of Mechanical Engineers, New York, 1997), pp. 45–54.

Hale, M. J.

M. J. Hale, M. S. Bohn, “Measurement of the radiative transport properties of reticulated alumina foams,” in Proceedings of the ASME/ASES Joint Solar Engineering Conference, A. Kirkpatrick, W. Worek, eds. (Association of Mechanical Engineers, New York, 1993), pp. 507–515.

Hendricks, T. J.

T. J. Hendricks, J. R. Howell, “Absorption/scattering coefficients and scattering phase functions in reticulated porous ceramics,” J. Heat Transfer 118, 79–87 (1996).
[CrossRef]

Howell, J. R.

T. J. Hendricks, J. R. Howell, “Absorption/scattering coefficients and scattering phase functions in reticulated porous ceramics,” J. Heat Transfer 118, 79–87 (1996).
[CrossRef]

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, New York, 1992).

Kashiwagi, T.

M. Take-Uchi, Y. Kurosaki, T. Kashiwagi, J. Yamada, “Determination of radiation properties of porous media by measuring emission,” J. Soc. Mech. Eng. Int. J. 31, 581–585 (1988).

Kuhn, J.

J. Kuhn, H.-P. Ebert, M. C. Arduini-Schuster, D. Büttner, J. Fricke, “Thermal transport in polystyrene and polyurethane foam insulations,” Int. J. Heat Mass Transfer 35, 1795–1801 (1992).
[CrossRef]

Kurosaki, Y.

J. Yamada, Y. Kurosaki, “Estimation of a radiative property of scattering and absorbing media,” Int. J. Thermophys. 18, 547–556 (1997).
[CrossRef]

M. Take-Uchi, Y. Kurosaki, T. Kashiwagi, J. Yamada, “Determination of radiation properties of porous media by measuring emission,” J. Soc. Mech. Eng. Int. J. 31, 581–585 (1988).

Malitson, I. H.

Marge, A. L.

L. R. Glicksman, A. L. Marge, J. D. Moreno, “Radiation heat transfer in cellular foam insulation,” in Proceedings of the 28th National Heat Transfer Conference and Exhibition, HTD Vol. 203: Developments in Radiative Heat Transfer (American Society of Mechanical Engineers, New York, 1997), pp. 45–54.

Marlor, R.

R. Marlor, W. Anderson, Osram Sylvania Inc., Glass Technologies Headquarters, Exeter, New Hampshire 03833 (personal communication, July2002).

Mengüç, M. P.

S. Subramaniam, M. P. Mengüç, “Solution of the inverse radiation problem for inhomogeneous and anisotropically scattering media using a Monte Carlo technique,” Int. J. Heat Mass Transfer 14, 253–266 (1991).
[CrossRef]

R. Viskanta, M. P. Mengüç, “Radiative transfer in combustion systems,” Prog. Energy Combust. Sci. 13, 97–160 (1987).
[CrossRef]

Modest, M. F.

M. F. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 1993).

Moreno, J. D.

L. R. Glicksman, A. L. Marge, J. D. Moreno, “Radiation heat transfer in cellular foam insulation,” in Proceedings of the 28th National Heat Transfer Conference and Exhibition, HTD Vol. 203: Developments in Radiative Heat Transfer (American Society of Mechanical Engineers, New York, 1997), pp. 45–54.

Moura, L. M.

L. M. Moura, “Identification des propriétés radiatives des matériaux semi-transparent diffusants en situation de non-symmetrie azimutale du champ radiatif,” Ph.D. thesis (Institut National des Sciences Appliquées de Lyon, Lyon, France, 1998).

Nicolau, V. P.

V. P. Nicolau, “Identification des propriétés radiatives des matèriaux semitransparent diffusants,” Ph.D. thesis (Institut National des Sciences Appliquées de Lyon, Lyon, France, 1994) (94 ISAL 0001).

Pilon, L.

L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
[CrossRef]

Plotnichenko, V. G.

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

Raynaud, M.

D. Baillis, M. Raynaud, J.-F. Sacadura, “Determination of spectral radiative properties of open-cell foam: model validation,” J. Thermophys. Heat Transfer 14, 137–143 (2000).
[CrossRef]

M. Raynaud, “Strategy for the experimental design and the estimation of parameters,” High Temp. High Press. 31, 1–15 (1999).
[CrossRef]

Rodney, W. S.

Rubin, M.

M. Rubin, “Optical properties of soda-lime silicate,” Sol. Energy Mater. 12, 275–288 (1985).
[CrossRef]

Sacadura, J.-F.

D. Baillis, J.-F. Sacadura, “Identification of polyurethane foam radiative properties: influence of transmittance measurements number,” J. Thermophys. Heat Transfer 16, 200–206 (2002).
[CrossRef]

D. Baillis, M. Raynaud, J.-F. Sacadura, “Determination of spectral radiative properties of open-cell foam: model validation,” J. Thermophys. Heat Transfer 14, 137–143 (2000).
[CrossRef]

D. Baillis, J.-F. Sacadura, “Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization,” J. Quant. Spectrosc. Radiat. Transf. 67, 327–363 (2000).
[CrossRef]

D. Baillis, M. Arduini-Schuster, J.-F. Sacadura, “Identification of spectral radiative properties of polyurethane foam from hemispherical and bi-directional transmittance and reflectance measurements,” in Proceedings of the 3rd International Symposium on Radiation Transfer, M. P. Mengüc, N. Selcuk, eds. (Begell House, New York, 2001), pp. 474–482.

Schuetz, M.

L. R. Glicksman, M. Schuetz, M. Sinofsky, “Radiation heat transfer in foam insulation,” Int. J. Heat Mass Transfer 30, 187–197 (1987).
[CrossRef]

M. Schuetz, L. Glicksman, “A basic study of heat transfer through foam insulation,” J. Cell. Plastics 20, 114–121 (1984).
[CrossRef]

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, New York, 1992).

Sinofsky, M.

L. R. Glicksman, M. Schuetz, M. Sinofsky, “Radiation heat transfer in foam insulation,” Int. J. Heat Mass Transfer 30, 187–197 (1987).
[CrossRef]

Sokolov, V. O.

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

Spindler, R. J.

Subramaniam, S.

S. Subramaniam, M. P. Mengüç, “Solution of the inverse radiation problem for inhomogeneous and anisotropically scattering media using a Monte Carlo technique,” Int. J. Heat Mass Transfer 14, 253–266 (1991).
[CrossRef]

Take-Uchi, M.

M. Take-Uchi, Y. Kurosaki, T. Kashiwagi, J. Yamada, “Determination of radiation properties of porous media by measuring emission,” J. Soc. Mech. Eng. Int. J. 31, 581–585 (1988).

Tan, C. Z.

C. Z. Tan, J. Arndt, “Temperature dependence of refractive index of glass SiO2 in the infrared wavelength range,” J. Phys. Chem. Solids 61, 1315–1320 (2000).
[CrossRef]

C. Z. Tan, “Determination of refractive index of silica glass for infrared wavelengths by ir spectroscopy,” J. Non-Cryst. Solids 223, 158–163 (1998).
[CrossRef]

Viskanta, R.

L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
[CrossRef]

A. G. Fedorov, R. Viskanta, “Radiative transfer in a semitransparent glass foam blanket,” Phys. Chem. Glasses 41, 127–135 (2000).

A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
[CrossRef]

R. Viskanta, M. P. Mengüç, “Radiative transfer in combustion systems,” Prog. Energy Combust. Sci. 13, 97–160 (1987).
[CrossRef]

Yamada, J.

J. Yamada, Y. Kurosaki, “Estimation of a radiative property of scattering and absorbing media,” Int. J. Thermophys. 18, 547–556 (1997).
[CrossRef]

M. Take-Uchi, Y. Kurosaki, T. Kashiwagi, J. Yamada, “Determination of radiation properties of porous media by measuring emission,” J. Soc. Mech. Eng. Int. J. 31, 581–585 (1988).

Glastech. Ber. (1)

R. G. C. Beerkens, “The role of gases in glass melting processes,” Glastech. Ber. 71, 369–380 (1995).

High Temp. High Press. (1)

M. Raynaud, “Strategy for the experimental design and the estimation of parameters,” High Temp. High Press. 31, 1–15 (1999).
[CrossRef]

Int. J. Heat Mass Transfer (3)

S. Subramaniam, M. P. Mengüç, “Solution of the inverse radiation problem for inhomogeneous and anisotropically scattering media using a Monte Carlo technique,” Int. J. Heat Mass Transfer 14, 253–266 (1991).
[CrossRef]

J. Kuhn, H.-P. Ebert, M. C. Arduini-Schuster, D. Büttner, J. Fricke, “Thermal transport in polystyrene and polyurethane foam insulations,” Int. J. Heat Mass Transfer 35, 1795–1801 (1992).
[CrossRef]

L. R. Glicksman, M. Schuetz, M. Sinofsky, “Radiation heat transfer in foam insulation,” Int. J. Heat Mass Transfer 30, 187–197 (1987).
[CrossRef]

Int. J. Thermophys. (1)

J. Yamada, Y. Kurosaki, “Estimation of a radiative property of scattering and absorbing media,” Int. J. Thermophys. 18, 547–556 (1997).
[CrossRef]

J. Am. Ceram. Soc. (2)

L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
[CrossRef]

A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
[CrossRef]

J. Cell. Plastics (2)

G. Eeckhaut, A. Cunningham, “The elimination of radiative heat transfer in fine celled PU rigid foams,” J. Cell. Plastics 32, 528–552 (1996).

M. Schuetz, L. Glicksman, “A basic study of heat transfer through foam insulation,” J. Cell. Plastics 20, 114–121 (1984).
[CrossRef]

J. Comput. Phys. (1)

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Figures (10)

Fig. 1
Fig. 1

Schematic of the experimental apparatus used to measure the spectral transmittance and reflectance.

Fig. 2
Fig. 2

Reflectance measurements in the directions between 170° and 180° with θa=5°.

Fig. 3
Fig. 3

Digital photograph of a 3-mm-thick fused quartz sample containing bubbles (porosity≈10%).

Fig. 4
Fig. 4

Bubble size distribution obtained from more than 120 images of individual bubbles.

Fig. 5
Fig. 5

Schematic of the idealized liquid layer containing bubbles and the coordinate system.

Fig. 6
Fig. 6

Illustration of the effect of the number of directions accounted for in the results of the inversion algorithm for spectral single-scattering albedo of the 5.6-mm-thick sample.

Fig. 7
Fig. 7

Retrieved extinction coefficient, single-scattering albedo and Henyey–Greenstein asymmetry factor determined by an inverse method for each sample.

Fig. 8
Fig. 8

Average retrieved extinction, single-scattering albedo, and Henyey–Greenstein asymmetry factor by an inverse method for each sample and their standard deviations.

Fig. 9
Fig. 9

Average retrieved absorption (top) and scattering (bottom) coefficients.

Fig. 10
Fig. 10

Comparison between the average measured spectral transmittance with error bars corresponding to Te,λ(θi)±Δi and the numerical results obtained with the averaged retrieved radiation characteristics for (top) θi=0° and Δi=9% and (bottom) θi=3.32° and Δi=25%.

Tables (1)

Tables Icon

Table 1 Twenty-Four Directions and Corresponding Weighting Factors for the Quadrature with Divergence Half-Angle Equal to 1.27°

Equations (18)

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kR=16n2σT33βR,
n2βR=π4σT3 0 (nλc)2βλ dIb,λdT dλ,
θ0=arctan(RA/f2),
Te,λ(θ)=Iλ(θ)I0,λdω0,
F[ωλ, βλ, Φ(θi)]=i=1n[Tt,λ(θi)-Te,λ(θi)]2.
μi Iλ(τλ, μi)τλ=-Iλ(τλ, μi)+ωλ2 j=1nwj[Φ(μj, μi)Iλ(τλ, μj)+Φ(-μj, μi)Iλ(τλ,-μj)]
Iλ(0, μj)=r21Iλ(0,-μj)+(nλc)2(1-r12)δμ0,μjIλ(0, μ0),μj>0,
Iλ(τλ,L, μj)=r21Iλ(τλ,L,-μj),μj<0,
r12=12 sin2(θ-χ)sin2(θ+χ)+tan2(θ-χ)tan2(θ+χ),
r12=(nλc-1)2(nλc+1)2.
nλc sin χj=sin θj.
Iλ(0, μi)=r12δμ0,-μiIλ(0, μ0)+1nλc2(1-r21)Iλ(0, μj), μi<0,
Iλ(τλ,L, μi)=(1/nλc)2(1-r21)Iλ(τλ,L, μj), μi>0,
Φλ(θ)=1-g2(1+g2-2g cos θ)3/2.
(nλc)2=1-0.6961663λ2λ2-(0.0684043)2+0.4079426λ2λ2-(0.1162414)2+0.8974794λ2λ2-(9.896161)2.
T¯λ(θi)=14 k=14Tk,λ(θi),
Δi=1T¯λ(θi) 13 k=14[Tk,λ(θi)-T¯λ(θi)]21/2.
κλ=βλ(1-ωλ),σλ=βλωλ.

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