Abstract

Radiative cooling power was computed as a function of the emittance ɛs of an exposed surface, air temperature, humidity, etc. from the lowtran 5 code. Meteorological data were then used to make semiquantitative estimates on how often frost will form on a surface with given ɛs. Practical tests, using SnO2-covered glass with ɛs ≈ 0.2, demonstrated that a low-emittance coating can prevent frost formation and maintain transparency of a window exposed to the clear sky.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Troinbe, “Perspectives sur l’Utilization des Rayonnements Solaires et Terrestres dans Certaines Régions du Monde,” Rev. Gen. Therm. 6, 1285 (1967).
  2. C. G. Granqvist, A. Hjortsberg, “Radiative Cooling to Low Temperatures: General Considerations and Application to Selectively Emitting SiO Films,” J. Appl. Phys. 52, 4205 (1981).
    [CrossRef]
  3. T. S. Eriksson, C. G. Granqvist, “Radiative Cooling Computed for Model Atmospheres,” Appl. Opt. 21, 4381 (1982).
    [CrossRef] [PubMed]
  4. P. Berdahl, R. Fromberg, “The Thermal Radiance of Clear Skies,” Sol. Energy 29, 299 (1982); P. Berdahl, M. Martin, “Emissivity of Clear Skies,” Sol. Energy 32, 663 (1984); M. Martin, P. Berdahl, “Summary of Results from the Spectral and Angular Sky Radiation Measurement Program,” Sol. Energy 33, 241 (1984); M. Martin, P. Berdahl, “Characteristics of Infrared Sky Radiation in the United States,” Sol. Energy 33, 321 (1984).
    [CrossRef]
  5. K. Ya. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).
  6. F. X. Kneizys et al., “Atmospheric Transmittance/Radiance Computer Code lowtran 5,” Air Force Geophysics Laboratory Technical Report AFGL-TR-80-0067 (Feb.1980).
  7. G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, New York, 1945).
  8. R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 1979), p. E-41.
  9. J. A. Duffie, W. A. Beckman, Solar Energy Thermal Processes (Wiley, New York, 1974), p. 83.
  10. SMHI (Swedish Meteorological and Hydrological Institute) Yearbook, “Meteorological Observations in Sweden,” Vol. 61, part 2.2 (1979); SMHI (Swedish Meteorological and Hydrological Institute) Yearbook Vol. 62, part 2.2 (1980); SMHI (Swedish Meteorological and Hydrological Institute) Yearbook Vol. 63, part 2.2 (1981).
  11. C. G. Granqvist, “Radiative Heating and Cooling with Spectrally Selective Surfaces,” Appl. Opt. 20, 2606 (1981); “Spectrally Selective Coatings for Energy Efficiency and Solar Applications,” Phys. Scr. 32, 401 (1985).
    [CrossRef] [PubMed]
  12. G. B. Smith, G. A. Niklasson, J. S. E. M. Svensson, C. G. Granqvist, “Noble-Metal-Based Transparent Infrared Reflectors: Experiments and Theoretical Analyses for Very Thin Gold Films,” J. Appl. Phys. 59, 571 (1986).
    [CrossRef]
  13. I. Hamberg, C. G. Granqvist, “Color Properties of Transparent and Heat-Reflecting MgF2-Coated Indium-Tin-Oxide Films,” Appl. Opt. 22, 609 (1983); “Evaporated Sn-Doped In2O3 Films: Basic Optical Properties and Applications to Energy-Efficient Windows,” J. Appl. Phys. 60, R123 (1986).
    [CrossRef] [PubMed]
  14. G. Laffay, G. Fadeuilhe, F. Schambourg, K. Keita, German Patent, Offenlegungsschrift 2833234 (1979).
  15. B. L. Adamson, Swedish Patent, Utläggningsskrift 7609860-7 (1979).

1986

G. B. Smith, G. A. Niklasson, J. S. E. M. Svensson, C. G. Granqvist, “Noble-Metal-Based Transparent Infrared Reflectors: Experiments and Theoretical Analyses for Very Thin Gold Films,” J. Appl. Phys. 59, 571 (1986).
[CrossRef]

1983

1982

T. S. Eriksson, C. G. Granqvist, “Radiative Cooling Computed for Model Atmospheres,” Appl. Opt. 21, 4381 (1982).
[CrossRef] [PubMed]

P. Berdahl, R. Fromberg, “The Thermal Radiance of Clear Skies,” Sol. Energy 29, 299 (1982); P. Berdahl, M. Martin, “Emissivity of Clear Skies,” Sol. Energy 32, 663 (1984); M. Martin, P. Berdahl, “Summary of Results from the Spectral and Angular Sky Radiation Measurement Program,” Sol. Energy 33, 241 (1984); M. Martin, P. Berdahl, “Characteristics of Infrared Sky Radiation in the United States,” Sol. Energy 33, 321 (1984).
[CrossRef]

1981

C. G. Granqvist, A. Hjortsberg, “Radiative Cooling to Low Temperatures: General Considerations and Application to Selectively Emitting SiO Films,” J. Appl. Phys. 52, 4205 (1981).
[CrossRef]

C. G. Granqvist, “Radiative Heating and Cooling with Spectrally Selective Surfaces,” Appl. Opt. 20, 2606 (1981); “Spectrally Selective Coatings for Energy Efficiency and Solar Applications,” Phys. Scr. 32, 401 (1985).
[CrossRef] [PubMed]

1979

SMHI (Swedish Meteorological and Hydrological Institute) Yearbook, “Meteorological Observations in Sweden,” Vol. 61, part 2.2 (1979); SMHI (Swedish Meteorological and Hydrological Institute) Yearbook Vol. 62, part 2.2 (1980); SMHI (Swedish Meteorological and Hydrological Institute) Yearbook Vol. 63, part 2.2 (1981).

1967

F. Troinbe, “Perspectives sur l’Utilization des Rayonnements Solaires et Terrestres dans Certaines Régions du Monde,” Rev. Gen. Therm. 6, 1285 (1967).

Adamson, B. L.

B. L. Adamson, Swedish Patent, Utläggningsskrift 7609860-7 (1979).

Beckman, W. A.

J. A. Duffie, W. A. Beckman, Solar Energy Thermal Processes (Wiley, New York, 1974), p. 83.

Berdahl, P.

P. Berdahl, R. Fromberg, “The Thermal Radiance of Clear Skies,” Sol. Energy 29, 299 (1982); P. Berdahl, M. Martin, “Emissivity of Clear Skies,” Sol. Energy 32, 663 (1984); M. Martin, P. Berdahl, “Summary of Results from the Spectral and Angular Sky Radiation Measurement Program,” Sol. Energy 33, 241 (1984); M. Martin, P. Berdahl, “Characteristics of Infrared Sky Radiation in the United States,” Sol. Energy 33, 321 (1984).
[CrossRef]

Duffie, J. A.

J. A. Duffie, W. A. Beckman, Solar Energy Thermal Processes (Wiley, New York, 1974), p. 83.

Eriksson, T. S.

Fadeuilhe, G.

G. Laffay, G. Fadeuilhe, F. Schambourg, K. Keita, German Patent, Offenlegungsschrift 2833234 (1979).

Fromberg, R.

P. Berdahl, R. Fromberg, “The Thermal Radiance of Clear Skies,” Sol. Energy 29, 299 (1982); P. Berdahl, M. Martin, “Emissivity of Clear Skies,” Sol. Energy 32, 663 (1984); M. Martin, P. Berdahl, “Summary of Results from the Spectral and Angular Sky Radiation Measurement Program,” Sol. Energy 33, 241 (1984); M. Martin, P. Berdahl, “Characteristics of Infrared Sky Radiation in the United States,” Sol. Energy 33, 321 (1984).
[CrossRef]

Granqvist, C. G.

Hamberg, I.

Herzberg, G.

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, New York, 1945).

Hjortsberg, A.

C. G. Granqvist, A. Hjortsberg, “Radiative Cooling to Low Temperatures: General Considerations and Application to Selectively Emitting SiO Films,” J. Appl. Phys. 52, 4205 (1981).
[CrossRef]

Keita, K.

G. Laffay, G. Fadeuilhe, F. Schambourg, K. Keita, German Patent, Offenlegungsschrift 2833234 (1979).

Kneizys, F. X.

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance Computer Code lowtran 5,” Air Force Geophysics Laboratory Technical Report AFGL-TR-80-0067 (Feb.1980).

Kondratyev, K. Ya.

K. Ya. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).

Laffay, G.

G. Laffay, G. Fadeuilhe, F. Schambourg, K. Keita, German Patent, Offenlegungsschrift 2833234 (1979).

Niklasson, G. A.

G. B. Smith, G. A. Niklasson, J. S. E. M. Svensson, C. G. Granqvist, “Noble-Metal-Based Transparent Infrared Reflectors: Experiments and Theoretical Analyses for Very Thin Gold Films,” J. Appl. Phys. 59, 571 (1986).
[CrossRef]

Schambourg, F.

G. Laffay, G. Fadeuilhe, F. Schambourg, K. Keita, German Patent, Offenlegungsschrift 2833234 (1979).

Smith, G. B.

G. B. Smith, G. A. Niklasson, J. S. E. M. Svensson, C. G. Granqvist, “Noble-Metal-Based Transparent Infrared Reflectors: Experiments and Theoretical Analyses for Very Thin Gold Films,” J. Appl. Phys. 59, 571 (1986).
[CrossRef]

Svensson, J. S. E. M.

G. B. Smith, G. A. Niklasson, J. S. E. M. Svensson, C. G. Granqvist, “Noble-Metal-Based Transparent Infrared Reflectors: Experiments and Theoretical Analyses for Very Thin Gold Films,” J. Appl. Phys. 59, 571 (1986).
[CrossRef]

Troinbe, F.

F. Troinbe, “Perspectives sur l’Utilization des Rayonnements Solaires et Terrestres dans Certaines Régions du Monde,” Rev. Gen. Therm. 6, 1285 (1967).

Appl. Opt.

J. Appl. Phys.

G. B. Smith, G. A. Niklasson, J. S. E. M. Svensson, C. G. Granqvist, “Noble-Metal-Based Transparent Infrared Reflectors: Experiments and Theoretical Analyses for Very Thin Gold Films,” J. Appl. Phys. 59, 571 (1986).
[CrossRef]

C. G. Granqvist, A. Hjortsberg, “Radiative Cooling to Low Temperatures: General Considerations and Application to Selectively Emitting SiO Films,” J. Appl. Phys. 52, 4205 (1981).
[CrossRef]

Rev. Gen. Therm.

F. Troinbe, “Perspectives sur l’Utilization des Rayonnements Solaires et Terrestres dans Certaines Régions du Monde,” Rev. Gen. Therm. 6, 1285 (1967).

SMHI (Swedish Meteorological and Hydrological Institute) Yearbook

SMHI (Swedish Meteorological and Hydrological Institute) Yearbook, “Meteorological Observations in Sweden,” Vol. 61, part 2.2 (1979); SMHI (Swedish Meteorological and Hydrological Institute) Yearbook Vol. 62, part 2.2 (1980); SMHI (Swedish Meteorological and Hydrological Institute) Yearbook Vol. 63, part 2.2 (1981).

Sol. Energy

P. Berdahl, R. Fromberg, “The Thermal Radiance of Clear Skies,” Sol. Energy 29, 299 (1982); P. Berdahl, M. Martin, “Emissivity of Clear Skies,” Sol. Energy 32, 663 (1984); M. Martin, P. Berdahl, “Summary of Results from the Spectral and Angular Sky Radiation Measurement Program,” Sol. Energy 33, 241 (1984); M. Martin, P. Berdahl, “Characteristics of Infrared Sky Radiation in the United States,” Sol. Energy 33, 321 (1984).
[CrossRef]

Other

K. Ya. Kondratyev, Radiation in the Atmosphere (Academic, New York, 1969).

F. X. Kneizys et al., “Atmospheric Transmittance/Radiance Computer Code lowtran 5,” Air Force Geophysics Laboratory Technical Report AFGL-TR-80-0067 (Feb.1980).

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, New York, 1945).

R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 1979), p. E-41.

J. A. Duffie, W. A. Beckman, Solar Energy Thermal Processes (Wiley, New York, 1974), p. 83.

G. Laffay, G. Fadeuilhe, F. Schambourg, K. Keita, German Patent, Offenlegungsschrift 2833234 (1979).

B. L. Adamson, Swedish Patent, Utläggningsskrift 7609860-7 (1979).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Spectral zenith radiance for two model atmospheres as computed from the lowtran 5 code. The lower graphs in parts (a) and (b) refer to the model atmospheres, and the upper graphs show corresponding blackbody spectra for the shown values of boundary level temperature Ta. Shaded areas indicate the maximum available cooling power. The relative humidity (RHa) at the boundary level is shown.

Fig. 2
Fig. 2

Amount of water vapor in air at different temperatures for three magnitudes of the relative humidity (RHa). The solid circle pertains to the mid-latitude winter (MW) model atmosphere.

Fig. 3
Fig. 3

Calculated radiated power at ambient temperature for the mid-latitude winter (MW) and subarctic winter (SW) atmospheres. The water vapor profiles for these model atmospheres were used to obtain the data points. Arrows signify the integrated amounts of water vapor.

Fig. 4
Fig. 4

Estimated relationships between power and temperature difference for (a) a blackbody and (b) a low-emittance surface with ɛs = 0.3. Dotted lines refer to the mid-latitude winter (MW) atmosphere. Solid lines denote the performance on exposure to the same atmosphere, albeit having the shown magnitudes of relative humidity (RHa) in the boundary layer. Dashed lines indicate the nonradiative heat influx due to conduction and convection in still air.

Fig. 5
Fig. 5

Three-dimensional diagrams showing relationships between air temperature Ta, surface emittance ɛs, and relative humidity for air in contact with the surface RHs. The diagrams pertain to four different values of the relative humidity of the air RHa. Black areas signify conditions leading to frost formation.

Fig. 6
Fig. 6

Map of Sweden showing the number of days predicted to give frost on a blackbodylike surface (condition A) and on a low-emittance surface (condition B) at four different locations.

Fig. 7
Fig. 7

Spectral infrared reflectance at 25° angle of incidence for bare and SnO2-coated glass as measured on a Perkin-Elmer 580 B double-beam spectrophotometer equipped with an air dryer.

Fig. 8
Fig. 8

Photo of glass plates placed on thin stand-offs ~2 cm above a table and freely exposed to the clear sky for a full night. The left-hand plate has an upward-facing blackbodylike surface and is covered with heavy frost. The right-hand plate has an upward-facing low-emittance surface and is frost-free and hence specularly reflecting.

Fig. 9
Fig. 9

Photo of two cars parked outdoors during a clear night. The right-hand car has a standard windscreen covered with heavy frost. The left-hand car is equipped with a low-emittance-coated windscreen which is almost frost-free.

Tables (2)

Tables Icon

Table I Values of Air Temperature (Ta) and Relative Humidity of the Air (RHa) Leading to Frost Formation on Surfaces (Emittance Üs) Exposed to Atmospheres Resembling the Mid-Latitude Winter Model

Tables Icon

Table II Number of Days During Three Consecutive Years with the Shown Values of Relative Humidity In the Air and Fulfilling the Following Conditions: A, Ta < +5°C, v < 2 ms−1, Cloud Cover < 25%; B, Ta < 0°C, v < 2 ms−1, Cloud Cover < 25%; Data were Taken Outside Gothenburg, Sweden

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

P c = P rad - k Δ T ,
P rad = π 0 π / 2 d ( sin 2 θ ) 0 d λ ɛ s [ L b b ( λ , T s ) - L a ( θ , λ ) ] ,
Δ T = T a - T s .
k = 5.7 + 3.8 v

Metrics