Abstract

An apparatus for the transient calorimetric technique used for measuring the total hemispherical emissivities of metals has been developed. Measurements have been made on specimens of copper and aluminum in the temperature range of 330–630 K. An exact analysis is given of the conduction heat loss through thermocouple leads suspending the specimen. From the numerical results of the lead-wire heat loss, the significant effect of a guard heater employed in the apparatus is illustrated. By taking account of the heat loss, the emissivities of the specimens are accurately evaluated and are compared with the data of previous investigators.

© 1985 Optical Society of America

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References

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  1. K. G. Ramanathan, S. H. Yen, “High-temperature emissivities of copper, aluminum, and silver,” J. Opt. Soc. Am. 67, 32–38 (1977).
    [CrossRef]
  2. E. A. Estalote, K. G. Ramanathan, “Low-temperature emissivities of copper and aluminum,” J. Opt. Soc. Am. 67, 39–44 (1977).
    [CrossRef]
  3. R. Smalley, A. J. Sievers, “The total hemispherical emissivity of copper,” J. Opt. Soc. Am. 68, 1516–1518 (1978).
    [CrossRef]
  4. G. Best, “Emissivities of copper and aluminum,” J. Opt. Soc. Am. 39, 1009–1011 (1949).
    [CrossRef]
  5. R. E. Gaumer, L. A. McKellar, E. R. Streed, K. L. Frame, J. R. Grammer, “Calorimetric determinations of thermal radiation characteristics,” in Progress in International Research on Thermodynamic and Transport Properties, J. F. Masi, D. H. Tsai, eds. (Academic, New York, 1962), pp. 575–587.
  6. W. J. McG. Tegart, The Electrolytic and Chemical Polishing of Metals (Pergamon, New York, 1959), p. 61.
  7. V. E. Lyusternik, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 55.
  8. T. E. Pochapsky, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 3.
  9. M. J. Laubitz, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 165.
  10. G. F. Sager, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 566.
  11. D. C. Wallace, P. H. Sidles, G. C. Danielson, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 105.
  12. E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972), p. 774.
  13. C. Davisson, J. R. Weeks, “The relation between the total thermal emissive power of a metal and its electrical resistivity,” J. Opt. Soc. Am. 8, 581–605 (1924).
    [CrossRef]
  14. G. L. Zuppardo, K. G. Ramanathan, “Anomalous emissivities of nickel and iron near their Curie temperatures,” J. Opt. Soc. Am. 61, 1607–1612 (1971).
    [CrossRef]
  15. B. T. Barnes, W. E. Forsythe, E. Q. Adams, “The total emissivity of various materials at 100–500°C,” J. Opt. Soc. Am. 37, 804–807 (1947).
    [CrossRef] [PubMed]
  16. H. Masuda, M. Higano, “Measurement of total hemispherical emissivities of metals by using a calorimetric technique,” Trans. Jpn. Soc. Mech. Eng. 50, 3051–3058 (1984).
    [CrossRef]
  17. B. Window, G. Harding, “Thermal emissivity of copper,” J. Opt. Soc. Am. 71, 354–357 (1981).
    [CrossRef]
  18. H. E. Bennett, “Influence of surface roughness, surface damage, and oxide films on emittance,” in Symposium on Thermal Radiation of Solids, S. Katzoff, ed., NASA SP-55 (U.S. Government Printing Office, Washington, D.C., 1965), pp. 145–152.

1984 (1)

H. Masuda, M. Higano, “Measurement of total hemispherical emissivities of metals by using a calorimetric technique,” Trans. Jpn. Soc. Mech. Eng. 50, 3051–3058 (1984).
[CrossRef]

1981 (1)

1978 (1)

1977 (2)

1971 (1)

1949 (1)

1947 (1)

1924 (1)

Adams, E. Q.

Barnes, B. T.

Bennett, H. E.

H. E. Bennett, “Influence of surface roughness, surface damage, and oxide films on emittance,” in Symposium on Thermal Radiation of Solids, S. Katzoff, ed., NASA SP-55 (U.S. Government Printing Office, Washington, D.C., 1965), pp. 145–152.

Best, G.

Buyco, E. H.

V. E. Lyusternik, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 55.

T. E. Pochapsky, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 3.

D. C. Wallace, P. H. Sidles, G. C. Danielson, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 105.

Danielson, G. C.

D. C. Wallace, P. H. Sidles, G. C. Danielson, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 105.

Davisson, C.

Drake, R. M.

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972), p. 774.

Eckert, E. R. G.

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972), p. 774.

Estalote, E. A.

Forsythe, W. E.

Frame, K. L.

R. E. Gaumer, L. A. McKellar, E. R. Streed, K. L. Frame, J. R. Grammer, “Calorimetric determinations of thermal radiation characteristics,” in Progress in International Research on Thermodynamic and Transport Properties, J. F. Masi, D. H. Tsai, eds. (Academic, New York, 1962), pp. 575–587.

Gaumer, R. E.

R. E. Gaumer, L. A. McKellar, E. R. Streed, K. L. Frame, J. R. Grammer, “Calorimetric determinations of thermal radiation characteristics,” in Progress in International Research on Thermodynamic and Transport Properties, J. F. Masi, D. H. Tsai, eds. (Academic, New York, 1962), pp. 575–587.

Grammer, J. R.

R. E. Gaumer, L. A. McKellar, E. R. Streed, K. L. Frame, J. R. Grammer, “Calorimetric determinations of thermal radiation characteristics,” in Progress in International Research on Thermodynamic and Transport Properties, J. F. Masi, D. H. Tsai, eds. (Academic, New York, 1962), pp. 575–587.

Harding, G.

Higano, M.

H. Masuda, M. Higano, “Measurement of total hemispherical emissivities of metals by using a calorimetric technique,” Trans. Jpn. Soc. Mech. Eng. 50, 3051–3058 (1984).
[CrossRef]

Ho, C. Y.

M. J. Laubitz, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 165.

G. F. Sager, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 566.

Klemens, P. G.

G. F. Sager, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 566.

M. J. Laubitz, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 165.

Laubitz, M. J.

M. J. Laubitz, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 165.

Lyusternik, V. E.

V. E. Lyusternik, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 55.

Masuda, H.

H. Masuda, M. Higano, “Measurement of total hemispherical emissivities of metals by using a calorimetric technique,” Trans. Jpn. Soc. Mech. Eng. 50, 3051–3058 (1984).
[CrossRef]

McKellar, L. A.

R. E. Gaumer, L. A. McKellar, E. R. Streed, K. L. Frame, J. R. Grammer, “Calorimetric determinations of thermal radiation characteristics,” in Progress in International Research on Thermodynamic and Transport Properties, J. F. Masi, D. H. Tsai, eds. (Academic, New York, 1962), pp. 575–587.

Pochapsky, T. E.

T. E. Pochapsky, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 3.

Powell, R. W.

M. J. Laubitz, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 165.

G. F. Sager, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 566.

Ramanathan, K. G.

Sager, G. F.

G. F. Sager, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 566.

Sidles, P. H.

D. C. Wallace, P. H. Sidles, G. C. Danielson, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 105.

Sievers, A. J.

Smalley, R.

Streed, E. R.

R. E. Gaumer, L. A. McKellar, E. R. Streed, K. L. Frame, J. R. Grammer, “Calorimetric determinations of thermal radiation characteristics,” in Progress in International Research on Thermodynamic and Transport Properties, J. F. Masi, D. H. Tsai, eds. (Academic, New York, 1962), pp. 575–587.

Tegart, W. J. McG.

W. J. McG. Tegart, The Electrolytic and Chemical Polishing of Metals (Pergamon, New York, 1959), p. 61.

Touloukian, Y. S.

V. E. Lyusternik, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 55.

T. E. Pochapsky, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 3.

M. J. Laubitz, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 165.

G. F. Sager, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 566.

D. C. Wallace, P. H. Sidles, G. C. Danielson, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 105.

Wallace, D. C.

D. C. Wallace, P. H. Sidles, G. C. Danielson, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 105.

Weeks, J. R.

Window, B.

Yen, S. H.

Zuppardo, G. L.

J. Opt. Soc. Am. (8)

Trans. Jpn. Soc. Mech. Eng. (1)

H. Masuda, M. Higano, “Measurement of total hemispherical emissivities of metals by using a calorimetric technique,” Trans. Jpn. Soc. Mech. Eng. 50, 3051–3058 (1984).
[CrossRef]

Other (9)

H. E. Bennett, “Influence of surface roughness, surface damage, and oxide films on emittance,” in Symposium on Thermal Radiation of Solids, S. Katzoff, ed., NASA SP-55 (U.S. Government Printing Office, Washington, D.C., 1965), pp. 145–152.

R. E. Gaumer, L. A. McKellar, E. R. Streed, K. L. Frame, J. R. Grammer, “Calorimetric determinations of thermal radiation characteristics,” in Progress in International Research on Thermodynamic and Transport Properties, J. F. Masi, D. H. Tsai, eds. (Academic, New York, 1962), pp. 575–587.

W. J. McG. Tegart, The Electrolytic and Chemical Polishing of Metals (Pergamon, New York, 1959), p. 61.

V. E. Lyusternik, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 55.

T. E. Pochapsky, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 3.

M. J. Laubitz, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 165.

G. F. Sager, quoted by Y. S. Touloukian, R. W. Powell, C. Y. Ho, P. G. Klemens, Thermophysical Properties of Matter, Vol. 1 (IFI/Plenum, New York, 1970), p. 566.

D. C. Wallace, P. H. Sidles, G. C. Danielson, quoted by Y. S. Touloukian, E. H. Buyco, Thermophysical Properties of Matter, Vol. 4 (IFI/Plenum, New York, 1970), p. 105.

E. R. G. Eckert, R. M. Drake, Analysis of Heat and Mass Transfer (McGraw-Hill, New York, 1972), p. 774.

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Figures (10)

Fig. 1
Fig. 1

Schematic drawing of emissivity apparatus: 1, vacuum chamber; 2, upper liquid-nitrogen bath; 3, lower liquid-nitrogen bath; 4, specimen; 5, support; 6, terminals; 7, thermocouple leads for specimen; 8, guard heater; 9, furnace; 10, thermocouple leads for guard heater.

Fig. 2
Fig. 2

Physical model and symbols for the thermocouple lead.

Fig. 3
Fig. 3

Cooling curves of temperature (Ts) versus time for Cu I and aluminum.

Fig. 4
Fig. 4

Expression of the cooling curve as an exponential function; Cu I.

Fig. 5
Fig. 5

Cooling rate (−dTs/dt) versus temperature (Ts) curves for Cu I and aluminum.

Fig. 6
Fig. 6

Temperature distributions of the thermocouple leads connecting with Cu I: solid lines, iron lead; dotted-dashed lines, con-stantan lead; dashed lines, simple analysis (both iron and constan-tan leads).

Fig. 7
Fig. 7

Lead-wire heat loss for Cu I: solid line, exact analysis for Tg = 333 K; dashed line, simple analysis for Tg = 333 K; dotted–dashed line, exact analysis for leads without guard heater, assuming that L = 100 mm and Tg = 173 K.

Fig. 8
Fig. 8

Lead-wire heat loss for aluminum: solid line, exact analysis for Tg = 333 K; dashed line, simple analysis for Tg = 333 K; dotted-dashed line, exact analysis for leads without guard heater, assuming that L = 100 mm and Tg = 173 K.

Fig. 9
Fig. 9

Total hemispherical emissivity of copper: ○, present work, mechanically polished specimen Cu I; ●, present work, electropolished specimen Cu II; lines A and A′, results by least squares for Cu I and Cu II data, respectively; line B, result by least squares for Cu I data obtained by simple analysis of Qt; +, Ramanathan and Yen,1 mechanically polished sphere; ▵, Smalley and Sievers,3 mechanically polished plate.

Fig. 10
Fig. 10

Total hemispherical emissivity of aluminum: ○, present work, mechanically polished specimen aluminum; line A, result by least squares for aluminum data, line B, result by least squares for aluminum data obtained by simple analysis of Qt; +, Ramanathan and Yen,1 electropolished plate.

Tables (2)

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Table 1 Physical Description of the Disk Specimens

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Table 2 h, Values Obtained by the Present Research on Copper and Aluminum

Equations (10)

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h , s ( T s ) = m s C p , s ( T s ) d T s d t | T s Q t Q gas σ A s ( T s 4 T 4 ) ,
T n t = k n C p , n ρ n 2 T n x 2 4 h , n σ D n C p , n ρ n ( T n 4 T 4 ) , n = 1 , 2
d 2 T n ( 0 ) d x 2 = 4 h , n σ k n D n ( T n ( 0 ) 4 T 4 ) , n = 1 , 2 ,
T n ( 0 ) = T s ( 0 ) at x = 0 ,
T n ( 0 ) = T g at x = L ,
m s C p , s d T s d t = h , s σ A s ( T s 4 T 4 ) ( Q t , 1 + Q t , 2 ) ,
Q t , n = π D n 2 k n 4 T n x | x = 0 .
T s = T s ( 0 ) for t = 0 .
T n ( t , L ) = T g .
T s = a exp ( b t ) .

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