Abstract

At the Istituto Termometrico Italiano a spherical cavity has been constructed as a radiation source in absolute temperature measurements. In theoretical prediction of its effective emissivity, a discrepancy appears between Gouffé’s and DeVos’s formulas. In this paper the authors discuss the approximations involved in DeVos’s process and report corrections suitable to improve the precision of the results. With such corrections, computations based on both formulas agree within a wide variation range.

© 1966 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Buckley, Phil. Mag. 4, 753 (1927).
  2. H. Buckley, Phil. Mag. 6, 447 (1928).
  3. H. Buckley, Phil. Mag. 17, 576 (1934).
  4. A. Gouffé, Rev. Opt. 24, 1 (1945).
  5. J. C. DeVos, Physica 20, 669 (1954).
    [CrossRef]
  6. P. Campanaro, A. Cibrario, A. Rosso, G. Ruffino, “Simulatore di corpo nero con regolazione au omatica della temperatura”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).
  7. P. Moon, J. Opt. Soc. Am. 30, 195 (1940).
    [CrossRef]
  8. P. Campanaro, T. Ricolfi, “Calcolo e realizzazione di simulatori del radiatore integrate”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).
  9. C. S. Williams, J. Opt. Soc. Am. 51, 566 (1961).
  10. C. L. Sanders, B. A. Stevens, Rev. Opt. 33, 179 (1954).
  11. D. E. Edwards, Univ. Mich. Res. Inst., Rept. No. 2144–105-T.
  12. S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
    [CrossRef]
  13. E. M. Sparrow, V. K. Jonsson, J. Opt. Soc. Am. 53, 816 (1963).
    [CrossRef]

1965 (1)

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
[CrossRef]

1963 (1)

1961 (1)

C. S. Williams, J. Opt. Soc. Am. 51, 566 (1961).

1954 (2)

C. L. Sanders, B. A. Stevens, Rev. Opt. 33, 179 (1954).

J. C. DeVos, Physica 20, 669 (1954).
[CrossRef]

1945 (1)

A. Gouffé, Rev. Opt. 24, 1 (1945).

1940 (1)

1934 (1)

H. Buckley, Phil. Mag. 17, 576 (1934).

1928 (1)

H. Buckley, Phil. Mag. 6, 447 (1928).

1927 (1)

H. Buckley, Phil. Mag. 4, 753 (1927).

Buckley, H.

H. Buckley, Phil. Mag. 17, 576 (1934).

H. Buckley, Phil. Mag. 6, 447 (1928).

H. Buckley, Phil. Mag. 4, 753 (1927).

Campanaro, P.

P. Campanaro, A. Cibrario, A. Rosso, G. Ruffino, “Simulatore di corpo nero con regolazione au omatica della temperatura”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).

P. Campanaro, T. Ricolfi, “Calcolo e realizzazione di simulatori del radiatore integrate”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).

Cibrario, A.

P. Campanaro, A. Cibrario, A. Rosso, G. Ruffino, “Simulatore di corpo nero con regolazione au omatica della temperatura”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).

DeVos, J. C.

J. C. DeVos, Physica 20, 669 (1954).
[CrossRef]

Edwards, D. E.

D. E. Edwards, Univ. Mich. Res. Inst., Rept. No. 2144–105-T.

Gouffé, A.

A. Gouffé, Rev. Opt. 24, 1 (1945).

Jonsson, V. K.

Lin, S. H.

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
[CrossRef]

Moon, P.

Ricolfi, T.

P. Campanaro, T. Ricolfi, “Calcolo e realizzazione di simulatori del radiatore integrate”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).

Rosso, A.

P. Campanaro, A. Cibrario, A. Rosso, G. Ruffino, “Simulatore di corpo nero con regolazione au omatica della temperatura”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).

Ruffino, G.

P. Campanaro, A. Cibrario, A. Rosso, G. Ruffino, “Simulatore di corpo nero con regolazione au omatica della temperatura”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).

Sanders, C. L.

C. L. Sanders, B. A. Stevens, Rev. Opt. 33, 179 (1954).

Sparrow, E. M.

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
[CrossRef]

E. M. Sparrow, V. K. Jonsson, J. Opt. Soc. Am. 53, 816 (1963).
[CrossRef]

Stevens, B. A.

C. L. Sanders, B. A. Stevens, Rev. Opt. 33, 179 (1954).

Williams, C. S.

C. S. Williams, J. Opt. Soc. Am. 51, 566 (1961).

J. Heat Transfer (1)

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
[CrossRef]

J. Opt. Soc. Am. (3)

Phil. Mag. (3)

H. Buckley, Phil. Mag. 4, 753 (1927).

H. Buckley, Phil. Mag. 6, 447 (1928).

H. Buckley, Phil. Mag. 17, 576 (1934).

Physica (1)

J. C. DeVos, Physica 20, 669 (1954).
[CrossRef]

Rev. Opt. (2)

A. Gouffé, Rev. Opt. 24, 1 (1945).

C. L. Sanders, B. A. Stevens, Rev. Opt. 33, 179 (1954).

Other (3)

D. E. Edwards, Univ. Mich. Res. Inst., Rept. No. 2144–105-T.

P. Campanaro, A. Cibrario, A. Rosso, G. Ruffino, “Simulatore di corpo nero con regolazione au omatica della temperatura”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).

P. Campanaro, T. Ricolfi, “Calcolo e realizzazione di simulatori del radiatore integrate”, presented at the Congresso ATI, Genova (22–25 Sept. 1965).

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 (8)

Fig. 1
Fig. 1

Geometrical factors used in the analysis of a spherical cavity.

Fig. 2
Fig. 2

Comparison between Eq. (15) and Gouffé’s formula for the sphere. The walls are assumed to be diffusing perfectly. α = D/r. ao-5-6-929-i001 left ordinate. = = = right ordinate.

Fig. 3
Fig. 3

Distribution curves for a moderately rough surface.

Fig. 4
Fig. 4

Distribution curves for a surface intermediate to those shown in Figs. 3 and 5.

Fig. 5
Fig. 5

Distribution curves for a moderately smooth surface.

Fig. 6
Fig. 6

Nomograph for computing rAAA as a function of α.

Fig. 7
Fig. 7

Emissivity results for a spherical cavity. α = D/r. a, diffusely reflecting walls; b–d, partially specular reflecting walls according to Figs. 35.

Fig. 8
Fig. 8

Distribution of the energy entering from A′ and reaching dA2 after two reflections.

Tables (3)

Tables Icon

Table I Emissivity Values Assuming Perfectly Diffuse Reflection: Data Are Given for ϑA < π/4

Tables Icon

Table II Value of K of Eq. (8) as Function of α

Tables Icon

Table III Emissivity Values from Eq. (6) in the Third Approximation. Results Compared with Those of Edwards in Second Approximation

Equations (20)

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

c = 1 - r A A A d Ω A A - r A A A 1 r A 1 A A d Ω A A 1 d Ω A 1 A
c = 1 - r A A A π α 2 - 2 π 2 α 2 0 π / 2 r A A A 1 r A 1 A A d ϑ A 1 ,
- r A A A = ρ A / π - r A A A = ρ ( A / π ) cos ϑ A 1 - r A 1 A A = ( ρ A / π ) sin ϑ A 1
c = 1 - ρ A ( α 2 ) - 1 - ρ A 2 ( α 2 ) - 1 .
ɛ c = 1 - 0.96 ( α 2 ) - 1 .
c = 1 - π r A A A ( 1 - 2 E α ) - 2 π 2 α 2 ϑ A π / 2 r A A A 1 r A 1 A A d ϑ A 1 - 2 π 3 α 2 0 π r A 1 A A 2 r A 2 A 1 A sin φ A 2 d φ A 2 ϑ A π / 2 r A A A 1 × sin ϑ A 1 d ϑ A 1 cos ( ϑ A 1 - φ A 2 ) ,
E α = ϑ A π / 2 sin ϑ cos ϑ d ϑ = 1 + cos 2 ϑ A 4 .
c = 1 - π r A A A ( 1 - 2 E α ) - ( K / α 2 ) ,
c = [ 1 + ( 1 - ) ( A A S - Ω A A π ) ] ( 1 - A A S ) + A A S
d W A 1 A 2 = A S r A A A 1 r A 1 A A 2 d Ω A A 1 d Ω A 1 A 2 ,
r A A A 1 = ρ A / π cos ϑ A 1 ; r A 1 A A 2 = ρ A / π sin ( ϑ A 1 + ϑ 0 ) ; d Ω A A 1 = sin ϑ A 1 d ϑ A 1 d φ ; d Ω A 1 A 2 = d ϑ A 2 d φ / 2 sin ( ϑ A 1 + ϑ 0 ) .
d W A 1 A 2 = ρ A 2 / 2 π ) d ϑ A 2 d φ
ρ A 2 ( d A 2 / A S ) = ρ A 2 ( d ϑ A 2 d φ / 2 π ) .
c = 1 - r A A A d Ω A A - r A A A 1 r A 1 A A d Ω A A 1 d Ω A 1 A - r A A A 1 r A 1 A A 2 r A 2 A 1 A d Ω A A 1 d Ω A 1 A 2 d Ω A 2 A
c = 1 - ρ A sin 2 ϑ A 1 - 2 ρ A 2 α 2 ϑ A π / 2 sin ϑ A 1 cos ϑ A 1 d ϑ A 1 - 4 ρ A 3 α 2 ϑ A π / 2 cos ϑ A 1 sin ϑ A 1 d ϑ A 1 ϑ A π / 2 cos φ A 2 sin φ A 2 d φ A 2
c = + 2 ρ A E α - ( 2 ρ A 2 / α 2 ) E α - ( 4 ρ A 3 / α 2 ) E α 2 ,
E α = ϑ A π / 2 sin ϑ cos ϑ d ϑ = 1 + cos 2 ϑ A 4
α = 2 / sin 2 ϑ A .
c = + 2 ρ A E α - ( 2 A ρ 2 / α 2 ) ( E α / 1 - 2 ρ A E α ) .
c = / [ ( 1 - A / A S ) + A / A S ] .

Metrics