Abstract

Local effective spectral and total emissivities of nonisothermal cavities having diffuse surfaces are evaluated. The effective emissivity of the cavity wall around the half-depth of a cylinder is little affected by a linear decrease or increase of temperature along the cavity axis because of a compensation effect. The nonisothermal effect on the integrated cavity emissivity changes considerably with cavity geometry for a given temperature distribution.

© 1983 Optical Society of America

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References

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  1. R. E. Bedford, C. K. Ma, J. Opt. Soc. Am. 64, 339 (1974).
    [CrossRef]
  2. R. E. Bedford, C. K. Ma, J. Opt. Soc. Am. 65, 565 (1975).
    [CrossRef]
  3. R. E. Bedford, C. K. Ma, J. Opt. Soc. Am. 66, 724 (1976).
    [CrossRef]
  4. Y. Ohwada, J. Opt. Soc. Am. 71, 106 (1981).
    [CrossRef]
  5. Equation (2) in the text is identical to the following summation derived in Refs. 1–3: Mn(Q)=ε+ρ∑P=1NMn−1(P)⋅df(Q,P) (see Ref. 4).
  6. E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Brooks/Cole, Belmont, Calif., 1966).
  7. The quantity α in Refs. 8 and 9 is the angle between the cavity axis and the line where a plane containing the cavity axis intersects dQ and related to β in the text by α = π/2 − β.
  8. Y. Ohwada, Appl.Opt. 20, 3332 (1981).
    [CrossRef] [PubMed]
  9. Y. Ohwada, Temperature, Its Measurement and Control in Science and Industry (American Institute of Physics, New York, 1982), Vol. 5, Part 1, p. 517.
  10. C. Shouren, C. Zaixiang, C. Hongpan, Metrologia 16, 69 (1980).
    [CrossRef]

1981

1980

C. Shouren, C. Zaixiang, C. Hongpan, Metrologia 16, 69 (1980).
[CrossRef]

1976

1975

1974

Bedford, R. E.

Cess, R. D.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Brooks/Cole, Belmont, Calif., 1966).

Hongpan, C.

C. Shouren, C. Zaixiang, C. Hongpan, Metrologia 16, 69 (1980).
[CrossRef]

Ma, C. K.

Ohwada, Y.

Y. Ohwada, J. Opt. Soc. Am. 71, 106 (1981).
[CrossRef]

Y. Ohwada, Appl.Opt. 20, 3332 (1981).
[CrossRef] [PubMed]

Y. Ohwada, Temperature, Its Measurement and Control in Science and Industry (American Institute of Physics, New York, 1982), Vol. 5, Part 1, p. 517.

Shouren, C.

C. Shouren, C. Zaixiang, C. Hongpan, Metrologia 16, 69 (1980).
[CrossRef]

Sparrow, E. M.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Brooks/Cole, Belmont, Calif., 1966).

Zaixiang, C.

C. Shouren, C. Zaixiang, C. Hongpan, Metrologia 16, 69 (1980).
[CrossRef]

Appl.Opt.

Y. Ohwada, Appl.Opt. 20, 3332 (1981).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

Metrologia

C. Shouren, C. Zaixiang, C. Hongpan, Metrologia 16, 69 (1980).
[CrossRef]

Other

Y. Ohwada, Temperature, Its Measurement and Control in Science and Industry (American Institute of Physics, New York, 1982), Vol. 5, Part 1, p. 517.

Equation (2) in the text is identical to the following summation derived in Refs. 1–3: Mn(Q)=ε+ρ∑P=1NMn−1(P)⋅df(Q,P) (see Ref. 4).

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Brooks/Cole, Belmont, Calif., 1966).

The quantity α in Refs. 8 and 9 is the angle between the cavity axis and the line where a plane containing the cavity axis intersects dQ and related to β in the text by α = π/2 − β.

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Figures (4)

Fig. 1
Fig. 1

Schematic drawing of the cavities.

Fig. 2
Fig. 2

Temperature distribution along the cavity axis.

Fig. 3
Fig. 3

Deviation of the effective total emissivity for L = 2, ε = 0.5: ---, T(Q) = T1(l); —, T(Q) = T2(l); ▲, Cy, R = 1.0; ●, Cy, R = 0.5; △, Cy, R = 0.1; ○, Co, R = 0.5; □, Co, R = 0.5; ■, DoCo, R = 0.5, K = 0.7L.

Fig. 4
Fig. 4

Deviation of the effective spectral emissivity for L = 2, ε = 0.5: ---, T(Q) = T1(l); —, T(Q) = T2(l); ▲, Cy, R = 1.0; ●, Cy, R = 0.5; △, Cy, R = 0.1; ○, Co, R = 0.5; □, Co, R = 0.5; ■, DoCo, R = 0.5, K = 0.7L.

Tables (2)

Tables Icon

Table I Temperature T(A) for the Weighted Average Radiant Exitance; Tot, Total radiant Exitance; Spe, Spectral Radiant Exitance

Tables Icon

Table II Integrated Total Emissivity for R = 0.5

Equations (15)

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E ( V ) = M ( V ) / M b ( V ) ,
M n ( Q ) = M n 1 ( Q ) + ρ P = 1 N [ M n 1 ( P ) M n 2 ( P ) ] d f ( Q , P ) ,
d f ( Q , P ) = | f ( Q , P ) ± f ( Q , P 1 ) | ,
f ( Q , P ) = | sin β f 1 ( Q , P ) ± cos β f 2 ( Q , P ) | { + for X Q < X P for X Q > X P
E I = P = 1 K M ( P ) Δ f ( P , D ) / P = 1 K M b ( P ) Δ f ( P , D ) ,
M b ( A ) = P = 1 K M b ( P ) Δ f ( P , D ) / P = 1 K Δ f ( P , D ) ,
M b ( A ) P = 1 K Δ f ( P , D )
M b ( Q ) = { C 1 / [ ( exp { C 2 / [ λ T ( Q ) ] } 1 ) λ 5 ] for the spectral radiant exitance , σ T ( Q ) 4 for the total radiant exitance ,
T 1 ( l ) = T 0 ( 1 0.01 l / L ) ,
T 2 ( l ) = T 0 [ 1 0.04 ( l L / 2 ) 2 / L 2 ] ,
Δ T ( Q ) = { T 1 ( l ) T 0 , or T 2 ( l ) T 0 .
Δ E = E 1 E 0 or E 2 E 0 ,
T ( A ) = { C 2 / ( λ log e { C 1 / [ λ 5 M b ( A ) ] + 1 } ) for the spectral radiant exitance , [ M b ( A ) / σ ] 1 / 4 for the total radiant exitance .
Δ E ( T 1 ) = E I ( T 1 ) E I ( T 0 ) ,
Δ E ( T 2 ) = E I ( T 2 ) E I ( T 0 ) .

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