Abstract

Effective emissivities of conical cavities having diffuse surfaces are computed by an iterative procedure and effective reflectances from series that involve powers of the reflectance of the wall material. If reflections after the nth are neglected in the computation, an upper bound for the truncation error in the effective reflectance is 1.2ρn+1In+1/(1 − ρ) for cone half-angles between 3.75 and 60° and for 5 ≤ n, where ρ is the surface reflectance and In+1 is the (n + 1)th-order coefficient of the effective reflectance.

© 1981 Optical Society of America

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References

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1981 (1)

1980 (2)

1979 (1)

1976 (2)

1975 (1)

1974 (2)

1969 (1)

1968 (2)

1967 (2)

S. Takata, J. Illum. Eng. Inst. Jpn. 51, 702 (1967).
[CrossRef]

T. J. Quinn, Br. J. Appl. Phys. 18, 1105 (1967).
[CrossRef]

1966 (3)

1963 (2)

1962 (1)

E. M. Sparrow, L. U. Albers, E. R. G. Eckert, J. Heat Transfer C84, 73 (1962).
[CrossRef]

1954 (1)

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

Albers, L. U.

E. M. Sparrow, L. U. Albers, E. R. G. Eckert, J. Heat Transfer C84, 73 (1962).
[CrossRef]

Bartell, F. O.

Bedford, R. E.

Campanaro, P.

Cess, R. D.

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

Chandos, R. E.

Chandos, R. J.

De Vos, J. C.

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

Eberly, J. H.

Eckert, E. R. G.

E. M. Sparrow, L. U. Albers, E. R. G. Eckert, J. Heat Transfer C84, 73 (1962).
[CrossRef]

Fecteau, M. L.

Hongpan, C.

Jonsson, V. K.

Kelly, F. J.

Ma, C. K.

Nicodemus, F. E.

Ohno, A.

Ohwada, Y.

Peavy, B. A.

B. A. Peavy, J. Res. Nat. Bur. Stand. Sect. C 70, 139 (1966).

Quinn, T. J.

T. J. Quinn, Br. J. Appl. Phys. 18, 1105 (1967).
[CrossRef]

T. J. Quinn, Comité Consultatif de Thermometrie 13e session (Juin 1980), CCT/80-45.

Ricolfi, T.

Shirley, J. H.

Souren, C.

Sparrow, E. M.

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

E. M. Sparrow, L. U. Albers, E. R. G. Eckert, J. Heat Transfer C84, 73 (1962).
[CrossRef]

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

Sydnor, C. L.

Takata, S.

S. Takata, J. Illum. Eng. Inst. Jpn. 51, 702 (1967).
[CrossRef]

Treuenfels, E. W.

Wolfe, W. L.

Zaixiang, C.

Appl. Opt. (7)

Br. J. Appl. Phys. (1)

T. J. Quinn, Br. J. Appl. Phys. 18, 1105 (1967).
[CrossRef]

J. Heat Transfer (1)

E. M. Sparrow, L. U. Albers, E. R. G. Eckert, J. Heat Transfer C84, 73 (1962).
[CrossRef]

J. Illum. Eng. Inst. Jpn. (1)

S. Takata, J. Illum. Eng. Inst. Jpn. 51, 702 (1967).
[CrossRef]

J. Opt. Soc. Am. (9)

J. Res. Nat. Bur. Stand. Sect. C (1)

B. A. Peavy, J. Res. Nat. Bur. Stand. Sect. C 70, 139 (1966).

Physica Utrecht (1)

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

Other (2)

T. J. Quinn, Comité Consultatif de Thermometrie 13e session (Juin 1980), CCT/80-45.

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

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Figures (3)

Fig. 1
Fig. 1

Schematic drawing of a conical cavity.

Fig. 2
Fig. 2

Computed values of the effective emissivity plotted as a difference ΔE from 0.99210: H, bandwidth; YQ, Y coordinate of the representative points; Y0, Y coordinate of the centers of the bands.

Fig. 3
Fig. 3

Effective emissivity in the vicinity of the apex plotted as the difference from the effective emissivity at the apex.

Tables (3)

Tables Icon

Table I Effective Emissivities of Conical Cavities

Tables Icon

Table II Coefficients Ik(X) of the Effective Reflectance (R = 1.0)

Tables Icon

Table III Coefficients Ik(X) of the Effective Reflectance (R = 0.5)

Equations (10)

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E n ( Q ) = E n - 1 ( Q ) + ρ P = 1 N [ E n - 1 ( P ) - E n - 2 ( P ) ] · Δ f ( Q , P ) ,
Δ f ( Q , P ) = f ( Q , P ) - f ( Q , P - 1 ) ,
f ( Q , P ) = cos α · f 1 ( Q , P ) + sin α · f 2 ( Q , P ) ,
f 1 ( Q , P ) = Y Q - Y P · { [ X Q 2 + X P 2 + ( Y Q - Y P ) 2 ] / { [ X Q 2 + X P 2 + ( Y Q - Y p ) 2 ] 2 - 4 X Q 2 X p 2 } 1 / 2 - 1 } / ( 2 X Q ) , f 2 ( Q , P ) = ± { 1 - [ X Q 2 + ( Y Q - Y p ) 2 - X p 2 ] / { [ X Q 2 + ( Y Q - Y P ) 2 + X p 2 ] 2 - 4 X p 2 X Q 2 } 1 / 2 } / 2 , { + ( Y Q < Y p ) , - ( Y Q > Y p ) ,
E ( 0 ) = / [ + ( 1 - ) sin 3 θ ]
R n ( X ) = R n - 1 ( X ) + ρ X 1 X 2 Δ F ( X , X 2 n - 1 , X 1 ) · Δ f ( X 1 , A ) ,
Δ F ( X , X 2 n , X 1 ) = ρ X 3 Δ F ( X , X 3 n - 1 , X 2 ) · Δ f ( X 2 , X 1 )             for n 2.
ρ X 1 X 2 Δ F ( X , X 2 n - 1 , X 1 ) · Δ f ( X 1 , A ) = ρ n [ G n - 1 ( X ) - G n ( X ) ] ,
R n ( X ) = k = 1 n ρ k · I k ( X ) ,
k = n + 1 ρ k I k ( X ) ρ n + 1 I n + 1 ( X ) / ( 1 - ρ ) .

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