Abstract

Similarities between various cavity emissivity theories have been examined. It is shown here that, for the special case of the (isothermal) diffuse spherical cavity, the closed form emissivity expressions obtainable from the work of Gouffé, DeVos, and Sparrow and Jonsson agree exactly. Further, this result is not limited by the size of the opening in the cavity.

© 1968 Optical Society of America

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References

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  1. P. Campanaro, T. Ricolfi, Appl. Opt. 5, 929 (1966).
    [CrossRef] [PubMed]
  2. J. C. DeVos, Physica 20, 669 (1954).
    [CrossRef]
  3. A. Gouffé, Rev. Opt. 24, 1 (1945).
  4. C. S. Williams, Appl. Opt. 1, 564 (1961).
  5. E. M. Sparrow, V. K. Jonsson, J. Heat Transfer 84, 188 (1962); NASA Tech. Note TN–D–1289 (1962).
    [CrossRef]
  6. J. W. T. Walsh, Photometry (Constable and Company, Ltd., London, 1958), pp. 140–141.
  7. W. E. Sumpner, Proc. Phys. Soc. (London) 12, 10 (1892). Pertinent portions of Sumpner’s derivation will be found in the paper by F. E. Nicodemus in this issue: Appl. Opt. 7, 1359 (1968).
    [CrossRef] [PubMed]
  8. M. L. Fecteau, Progress of Cavity Emissivity Studies, Rep. No. 8416–6–T, The University of Michigan, Institute of Science and Technology, Willow Run Laboratories, Ann Arbor, Mich. (in publication).

1966 (1)

1962 (1)

E. M. Sparrow, V. K. Jonsson, J. Heat Transfer 84, 188 (1962); NASA Tech. Note TN–D–1289 (1962).
[CrossRef]

1961 (1)

C. S. Williams, Appl. Opt. 1, 564 (1961).

1954 (1)

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

1945 (1)

A. Gouffé, Rev. Opt. 24, 1 (1945).

1892 (1)

W. E. Sumpner, Proc. Phys. Soc. (London) 12, 10 (1892). Pertinent portions of Sumpner’s derivation will be found in the paper by F. E. Nicodemus in this issue: Appl. Opt. 7, 1359 (1968).
[CrossRef] [PubMed]

Campanaro, P.

DeVos, J. C.

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

Fecteau, M. L.

M. L. Fecteau, Progress of Cavity Emissivity Studies, Rep. No. 8416–6–T, The University of Michigan, Institute of Science and Technology, Willow Run Laboratories, Ann Arbor, Mich. (in publication).

Gouffé, A.

A. Gouffé, Rev. Opt. 24, 1 (1945).

Jonsson, V. K.

E. M. Sparrow, V. K. Jonsson, J. Heat Transfer 84, 188 (1962); NASA Tech. Note TN–D–1289 (1962).
[CrossRef]

Ricolfi, T.

Sparrow, E. M.

E. M. Sparrow, V. K. Jonsson, J. Heat Transfer 84, 188 (1962); NASA Tech. Note TN–D–1289 (1962).
[CrossRef]

Sumpner, W. E.

W. E. Sumpner, Proc. Phys. Soc. (London) 12, 10 (1892). Pertinent portions of Sumpner’s derivation will be found in the paper by F. E. Nicodemus in this issue: Appl. Opt. 7, 1359 (1968).
[CrossRef] [PubMed]

Walsh, J. W. T.

J. W. T. Walsh, Photometry (Constable and Company, Ltd., London, 1958), pp. 140–141.

Williams, C. S.

C. S. Williams, Appl. Opt. 1, 564 (1961).

Appl. Opt. (2)

J. Heat Transfer (1)

E. M. Sparrow, V. K. Jonsson, J. Heat Transfer 84, 188 (1962); NASA Tech. Note TN–D–1289 (1962).
[CrossRef]

Physica (1)

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

Proc. Phys. Soc. (London) (1)

W. E. Sumpner, Proc. Phys. Soc. (London) 12, 10 (1892). Pertinent portions of Sumpner’s derivation will be found in the paper by F. E. Nicodemus in this issue: Appl. Opt. 7, 1359 (1968).
[CrossRef] [PubMed]

Rev. Opt. (1)

A. Gouffé, Rev. Opt. 24, 1 (1945).

Other (2)

J. W. T. Walsh, Photometry (Constable and Company, Ltd., London, 1958), pp. 140–141.

M. L. Fecteau, Progress of Cavity Emissivity Studies, Rep. No. 8416–6–T, The University of Michigan, Institute of Science and Technology, Willow Run Laboratories, Ann Arbor, Mich. (in publication).

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Figures (1)

Fig. 1
Fig. 1

(a) Spherical blackbody illustrating some of the angles and solid angles. R0 is radius of the sphere, L is depth of the hole, R is radius of the hole (shaded area), dn is an arbitrary elemental area on the sphere’s surface, do is an elemental area of the hole. (b) Same sphere, but isolating the differential solid angle dΩno = dΩns. Note that θno = θsn, do is an element of the hole o; ds is an element of the surface s removed from total surface S = 4πR02.

Equations (8)

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0 ( w ) = 1 - [ ρ ( 1 π hole cos θ w 0 d Ω w 0 ) + ( ρ ) 2 1 π all n but hole cos θ w n d Ω w n ( 1 π hole cos θ n 0 d Ω n 0 ) + ( ρ ) 3 1 π n cos θ w n d Ω w n 1 π m cos θ n m d Ω n m × ( 1 π hole cos θ n 0 d Ω m 0 ) + ] ,
1 π hole cos θ n 0 d Ω n 0 = 1 π hole cos θ n 0 d s cos θ s n ( 2 R 0 cos θ n 0 ) 2 = s / S ,
1 π hole cos θ w 0 d Ω w 0 = 1 π hole cos θ n 0 d Ω n 0 = = s / S .
1 π n cos θ w n d Ω w n = 1 π m cos θ n m d Ω n m = = 1 - s / S .
0 = - ρ s / S [ 1 + ρ ( 1 - s / S ) + ρ 2 ( 1 - s / S ) 2 + ] ,
0 = 1 - ρ s / S 1 - ρ ( 1 - s / S ) ;
s / S = 1 4 π R 0 2 · 2 π R 0 2 0 2 θ 0 sin θ d θ = sin 2 θ 0 = 1 1 + ( L / R ) 2 ,
0 = [ 1 - 1 - 2 ( 1 + cos 2 θ 0 ) ] ,

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