Abstract

The emissivity c of cylindrical cavities with different bases (flat, perpendicular to the axis; flat, inclined to the axis; conical) is derived from measurements of the cavity reflectance ρc. A general formula for the calclation of ρc = 1 − c is given, which holds for high values of the ratio length L of the cylinder to radius R of the cylinder. For a flat base perpendicular to the axis only the value of the reflectance ρ0 of the wall material is needed; in both other cases one must refer to the measurements.

© 1971 Optical Society of America

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References

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  1. E. M. Sparrow, L. U. Albers, E. R. G. Eckert, J. Heat Transf. 84, 73 (1962).
    [CrossRef]
  2. G. Bauer, Optik 28, 177 (1968).
  3. G. Bauer, Optik 18, 603 (1961).
  4. F. J. Kelly, D. G. Moore, Appl. Opt. 4, 31 (1965).
    [CrossRef]
  5. G. Bauer, K. Bischoff, Optik 31, 507 (1970).
  6. K. C. Lapworth, T. J. Quinn, L. A. Allnut, J. Phys. E 3, 116 (1970).
    [CrossRef]
  7. F. J. Kelly, Appl. Opt. 5, 925 (1966).
    [CrossRef] [PubMed]

1970 (2)

G. Bauer, K. Bischoff, Optik 31, 507 (1970).

K. C. Lapworth, T. J. Quinn, L. A. Allnut, J. Phys. E 3, 116 (1970).
[CrossRef]

1968 (1)

G. Bauer, Optik 28, 177 (1968).

1966 (1)

1965 (1)

1962 (1)

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

1961 (1)

G. Bauer, Optik 18, 603 (1961).

Albers, L. U.

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

Allnut, L. A.

K. C. Lapworth, T. J. Quinn, L. A. Allnut, J. Phys. E 3, 116 (1970).
[CrossRef]

Bauer, G.

G. Bauer, K. Bischoff, Optik 31, 507 (1970).

G. Bauer, Optik 28, 177 (1968).

G. Bauer, Optik 18, 603 (1961).

Bischoff, K.

G. Bauer, K. Bischoff, Optik 31, 507 (1970).

Eckert, E. R. G.

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

Kelly, F. J.

Lapworth, K. C.

K. C. Lapworth, T. J. Quinn, L. A. Allnut, J. Phys. E 3, 116 (1970).
[CrossRef]

Moore, D. G.

Quinn, T. J.

K. C. Lapworth, T. J. Quinn, L. A. Allnut, J. Phys. E 3, 116 (1970).
[CrossRef]

Sparrow, E. M.

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

Appl. Opt. (2)

J. Heat Transf. (1)

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

J. Phys. E (1)

K. C. Lapworth, T. J. Quinn, L. A. Allnut, J. Phys. E 3, 116 (1970).
[CrossRef]

Optik (3)

G. Bauer, Optik 28, 177 (1968).

G. Bauer, Optik 18, 603 (1961).

G. Bauer, K. Bischoff, Optik 31, 507 (1970).

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Figures (6)

Fig. 1
Fig. 1

Apparatus for measurement of cavity reflectance. C, cavity under test; U, Ulbricht sphere with circular ports H1, H2; M, semitransparent mirror; S1, S2 sources; F, filter for matching source S2 with respect to color and brightness combined with a ground glass; L1, L2 lenses; D1, D2, D3 diaphragms; P, photomultiplier; L1 images the aperture H2 of the Ulbricht sphere onto diaphragm D3; L2 images D3 onto a ground glass in front of the multiplier P; f number 250.

Fig. 2
Fig. 2

Cylindrical cavity with a plane bottom perpendicular to the axis. The radiation leaving the cavity from the bottom without reflection on the walls is limited by the angle 2 φ. sin2φ = [1 + (L/R)2]−1.

Fig. 3
Fig. 3

Cylindrical cavity with a plane bottom perpendicular to the axis. Cavity reflectance ρc = f[1/(L/R)2] for various reflectances ρ0 of the wall material.

Fig. 4
Fig. 4

Function ρ0* = ρ0/(1 − ρ0). The additional values ρ0* are extrapolated from the curves ρc = f[1 + (L/R)2]. See Fig. 3 and Table I.

Fig. 5
Fig. 5

Cylindrical cavity with a plane bottom inclined to the axis. Cavity reflectance ρc = f[1/(L/R)2] for various reflectances ρ0 of the wall material.

Fig. 6
Fig. 6

Cyclindrical cavity with a cone-shaped end. Cavity reflectance ρc = f[1 + (L/R)2] for various reflectances ρ0 of the wall material.

Tables (1)

Tables Icon

Table I Fictive Reflectances ρ0* of Cylindrical Cavities with Bottoms of Different Shapesa

Equations (4)

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

ρ c = ( i 1 · ρ s ) / i 2 .
ρ c = ρ 0 * sin 2 φ = ρ 0 * / [ 1 + ( L / R ) 2 ] ,
ρ 0 * = ρ 0 / ( 1 - ρ 0 ) .
ρ c = [ ρ 0 / ( 1 - ρ 0 ) ] · { 1 / [ 1 + ( L / R ) 2 ] } .

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