Abstract

Although the theory of partially enclosed, cavity-type sources of radiant energy, with a few clarifications and corrections, has reached an apparent fruition, surface characteristics and practical construction problems will still limit the closeness to which these sources can he made to approach blackbodies. This paper gives results, which agree with prior published data, of a new computation for cylinders and shows the ray-trace analysis of cones to be unacceptable.

© 1969 Optical Society of America

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References

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  1. S. H. Lin and E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
    [CrossRef]
  2. S. C. Jain, Indian J. Pure Appl. Phys. 1, 7 (1963).
  3. K. S. Krishnan, Nature 187, 135 (1960).
    [CrossRef]
  4. R. Berman, F. E. Simon, and J. M. Ziman, Proc. Roy. Soc. (London) A220, 176 (1953).
  5. C. S. Williams, J. Opt. Soc. Am. 51, 564 (1961).
    [CrossRef]
  6. K. S. Krishnan and R. Sundaram, Proc. Roy. Soc. (London) A256, 302 (1960).
  7. A. J. Lichtenberg and S. Sesnic, J. Opt. Soc. Am. 56, 75 (1966).
    [CrossRef]
  8. W. L. Eisenman, R. L. Bates, and J. D. Merriam, J. Opt. Soc. Am. 53, 729 (1963).
    [CrossRef]
  9. M. A. Bramson, Infrared Radiation (Plenum Press, New York, 1968), p. 265.
  10. A. G. Blokh, Fundamentals of Radiative Heat Exchange (in Russian) (Power Engng. Press, Moscow and Leningrad, 1962).
  11. André Gouffé, Rev. Opt. 24, No. 1–3 (1945).
  12. E. M. Sparrow and V. K. Jonsson, J. Heat Transfer 84C, 188 (1962).
    [CrossRef]
  13. H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).
  14. Z. Yamauti, Procés-Verbaux des Séances du Comité Internanational de Poids et Mesures (Gauthier–Villards, Editeur–Imprimeur–Libraire, Paris), (2nd Ser.) 16, 243 (1933).
  15. Y. Nakaji, Procés-Verbaux des Séances du Comité International de Poids et Mesures (Gauthier–Villards, Editeur–Imprimeur–Libraire, Paris), (2nd Ser.) 26B, Annex P61 (1958).
  16. D. E. Williamson, J. Opt. Soc. Am. 42, 712 (1952).
    [CrossRef]
  17. E. M. Sparrow, L. U. Albers, and E. R. G. Eckert, J. Heat Transfer 84C, 73 (1962).
    [CrossRef]
  18. E. M. Sparrow and V. K. Jonsson, J. Opt. Soc. Am. 53, 816 (1963).
    [CrossRef]
  19. M. L. Fecteau, Appl. Optics,  7, 1363 (1968).
    [CrossRef]
  20. J. C. De Vos, Physica 20, 669 (1954).
    [CrossRef]

1968 (1)

M. L. Fecteau, Appl. Optics,  7, 1363 (1968).
[CrossRef]

1966 (1)

1965 (1)

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

1963 (3)

1962 (2)

E. M. Sparrow and V. K. Jonsson, J. Heat Transfer 84C, 188 (1962).
[CrossRef]

E. M. Sparrow, L. U. Albers, and E. R. G. Eckert, J. Heat Transfer 84C, 73 (1962).
[CrossRef]

1961 (1)

1960 (2)

K. S. Krishnan and R. Sundaram, Proc. Roy. Soc. (London) A256, 302 (1960).

K. S. Krishnan, Nature 187, 135 (1960).
[CrossRef]

1954 (1)

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

1953 (1)

R. Berman, F. E. Simon, and J. M. Ziman, Proc. Roy. Soc. (London) A220, 176 (1953).

1952 (1)

1945 (1)

André Gouffé, Rev. Opt. 24, No. 1–3 (1945).

1927 (1)

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

Albers, L. U.

E. M. Sparrow, L. U. Albers, and E. R. G. Eckert, J. Heat Transfer 84C, 73 (1962).
[CrossRef]

Bates, R. L.

Berman, R.

R. Berman, F. E. Simon, and J. M. Ziman, Proc. Roy. Soc. (London) A220, 176 (1953).

Blokh, A. G.

A. G. Blokh, Fundamentals of Radiative Heat Exchange (in Russian) (Power Engng. Press, Moscow and Leningrad, 1962).

Bramson, M. A.

M. A. Bramson, Infrared Radiation (Plenum Press, New York, 1968), p. 265.

Buckley, H.

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

De Vos, J. C.

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

Eckert, E. R. G.

E. M. Sparrow, L. U. Albers, and E. R. G. Eckert, J. Heat Transfer 84C, 73 (1962).
[CrossRef]

Eisenman, W. L.

Fecteau, M. L.

M. L. Fecteau, Appl. Optics,  7, 1363 (1968).
[CrossRef]

Gouffé, André

André Gouffé, Rev. Opt. 24, No. 1–3 (1945).

Jain, S. C.

S. C. Jain, Indian J. Pure Appl. Phys. 1, 7 (1963).

Jonsson, V. K.

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

E. M. Sparrow and V. K. Jonsson, J. Heat Transfer 84C, 188 (1962).
[CrossRef]

Krishnan, K. S.

K. S. Krishnan and R. Sundaram, Proc. Roy. Soc. (London) A256, 302 (1960).

K. S. Krishnan, Nature 187, 135 (1960).
[CrossRef]

Lichtenberg, A. J.

Lin, S. H.

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

Merriam, J. D.

Nakaji, Y.

Y. Nakaji, Procés-Verbaux des Séances du Comité International de Poids et Mesures (Gauthier–Villards, Editeur–Imprimeur–Libraire, Paris), (2nd Ser.) 26B, Annex P61 (1958).

Sesnic, S.

Simon, F. E.

R. Berman, F. E. Simon, and J. M. Ziman, Proc. Roy. Soc. (London) A220, 176 (1953).

Sparrow, E. M.

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

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

E. M. Sparrow and V. K. Jonsson, J. Heat Transfer 84C, 188 (1962).
[CrossRef]

E. M. Sparrow, L. U. Albers, and E. R. G. Eckert, J. Heat Transfer 84C, 73 (1962).
[CrossRef]

Sundaram, R.

K. S. Krishnan and R. Sundaram, Proc. Roy. Soc. (London) A256, 302 (1960).

Williams, C. S.

Williamson, D. E.

Yamauti, Z.

Z. Yamauti, Procés-Verbaux des Séances du Comité Internanational de Poids et Mesures (Gauthier–Villards, Editeur–Imprimeur–Libraire, Paris), (2nd Ser.) 16, 243 (1933).

Ziman, J. M.

R. Berman, F. E. Simon, and J. M. Ziman, Proc. Roy. Soc. (London) A220, 176 (1953).

Appl. Optics (1)

M. L. Fecteau, Appl. Optics,  7, 1363 (1968).
[CrossRef]

Indian J. Pure Appl. Phys. (1)

S. C. Jain, Indian J. Pure Appl. Phys. 1, 7 (1963).

J. Heat Transfer (3)

E. M. Sparrow and V. K. Jonsson, J. Heat Transfer 84C, 188 (1962).
[CrossRef]

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

E. M. Sparrow, L. U. Albers, and E. R. G. Eckert, J. Heat Transfer 84C, 73 (1962).
[CrossRef]

J. Opt. Soc. Am. (5)

Nature (1)

K. S. Krishnan, Nature 187, 135 (1960).
[CrossRef]

Phil. Mag. (1)

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

Physica (1)

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

Proc. Roy. Soc. (London) (2)

R. Berman, F. E. Simon, and J. M. Ziman, Proc. Roy. Soc. (London) A220, 176 (1953).

K. S. Krishnan and R. Sundaram, Proc. Roy. Soc. (London) A256, 302 (1960).

Rev. Opt. (1)

André Gouffé, Rev. Opt. 24, No. 1–3 (1945).

Other (4)

Z. Yamauti, Procés-Verbaux des Séances du Comité Internanational de Poids et Mesures (Gauthier–Villards, Editeur–Imprimeur–Libraire, Paris), (2nd Ser.) 16, 243 (1933).

Y. Nakaji, Procés-Verbaux des Séances du Comité International de Poids et Mesures (Gauthier–Villards, Editeur–Imprimeur–Libraire, Paris), (2nd Ser.) 26B, Annex P61 (1958).

M. A. Bramson, Infrared Radiation (Plenum Press, New York, 1968), p. 265.

A. G. Blokh, Fundamentals of Radiative Heat Exchange (in Russian) (Power Engng. Press, Moscow and Leningrad, 1962).

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Figures (3)

Fig. 1
Fig. 1

Effective emissivities of cylinders open at both ends having walls that radiate diffusely and reflect specularly.

Fig. 2
Fig. 2

Effective emissivities of cylinders closed at one end having walls that radiate diffusely and reflect specularly.

Fig. 3
Fig. 3

Method for tracing a ray into and out of a cone using the construction described by Williamson.16

Equations (17)

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P L = σ T 4 2 r = 0 ( 1 - ) r 0 L f [ h / ( r + 1 ) ] d h .
f ( h ) = - d ξ / d h ,
ξ ( h ) = ( π / 4 ) [ 2 h 2 + D 2 - 2 h ( h 2 + D 2 ) 1 2 ] .
P L = σ T 4 2 r = 0 ( 1 - ) r ( r + 1 ) 0 L / ( r + 1 ) f ( h ) d h
P L = ( σ T 4 A ) [ - 2 q 2 2 r = 0 [ ( 1 - ) r / ( r + 1 ) ] × { 1 - [ 1 + ( r + 1 q ) 2 ] 1 2 } ]
P L = σ T 4 A [ 2 φ 1 ( ) - 2 φ 3 ( ) / 4 q 2 + 2 φ 5 ( ) / 8 q 4 - 5 2 φ 7 ( ) / 64 q 6 + ] .
φ m ( ) = r = 0 ( 1 - ) r ( r + 1 ) m ,
φ m + 1 ( ) = φ m ( ) - ( 1 - ) ( d φ m / d ) .
o c = - 8 q 2 2 r = 0 ( 1 - ) r + 1 ( r + 1 ) { 1 - [ 1 + ( r + 1 2 q ) 2 ] 1 2 } .
φ n = φ 0 + 2 n θ .
1 - ( 1 - ) n .
2 n θ + φ 1 + φ 2 = π .
n = ( π - 2 φ ) / 2 θ .
d φ 1 = - d φ 2 .
2 n θ + 2 φ 21 = π 2 ( n + 1 ) θ + 2 φ 22 = π .
2 θ + 2 ( φ 22 - φ 21 ) = 0
Δ φ 2 max θ .