Abstract

A numerical solution is given for the radiation intensity from a spherical cavity whose spatial temperature and emissivity are both arbitrary. This simplifies and clarifies previous research. A numerical example with large axial temperature gradient is given, and it is suggested that this analysis could help establish the spherical cavity as a radiation standard.

© 2001 Optical Society of America

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References

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  1. H. H. Jensen, “Some notes on heat transfer by radiation,” Kgl. Danske Videnskab. Selskab. Mat.-Fys. Medd. 24, 1–26 (1948).
  2. M. Jakob, Heat Transfer (Wiley, New York, 1957), Vol. 2.
  3. E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Hemisphere, Washington, D.C., 1978).
  4. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).
  5. E. M. Sparrow, V. K. Jonsson, “Absorption and emission characteristics of diffuse spherical enclosures,” (NASA, Washington, D.C., 1962).
  6. R. E. Bedford, in The Theory and Practice of Radiation Thermometry, D. P. DeWitt, G. D. Nutter, eds. (Wiley, New York, 1988), Chap. 12.
  7. R. E. Bedford, C. K. Ma, Z. Chu, Y. Sun, S. Chen, “Emissivities of diffuse cavities. 4. Isothermal and nonisothermal cylindro-inner-cones,” Appl. Opt. 24, 2971–2980 (1985).
    [CrossRef]

1985 (1)

1948 (1)

H. H. Jensen, “Some notes on heat transfer by radiation,” Kgl. Danske Videnskab. Selskab. Mat.-Fys. Medd. 24, 1–26 (1948).

Bedford, R. E.

R. E. Bedford, C. K. Ma, Z. Chu, Y. Sun, S. Chen, “Emissivities of diffuse cavities. 4. Isothermal and nonisothermal cylindro-inner-cones,” Appl. Opt. 24, 2971–2980 (1985).
[CrossRef]

R. E. Bedford, in The Theory and Practice of Radiation Thermometry, D. P. DeWitt, G. D. Nutter, eds. (Wiley, New York, 1988), Chap. 12.

Cess, R. D.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Hemisphere, Washington, D.C., 1978).

Chen, S.

Chu, Z.

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).

Jakob, M.

M. Jakob, Heat Transfer (Wiley, New York, 1957), Vol. 2.

Jensen, H. H.

H. H. Jensen, “Some notes on heat transfer by radiation,” Kgl. Danske Videnskab. Selskab. Mat.-Fys. Medd. 24, 1–26 (1948).

Jonsson, V. K.

E. M. Sparrow, V. K. Jonsson, “Absorption and emission characteristics of diffuse spherical enclosures,” (NASA, Washington, D.C., 1962).

Ma, C. K.

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).

Sparrow, E. M.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Hemisphere, Washington, D.C., 1978).

E. M. Sparrow, V. K. Jonsson, “Absorption and emission characteristics of diffuse spherical enclosures,” (NASA, Washington, D.C., 1962).

Sun, Y.

Appl. Opt. (1)

Kgl. Danske Videnskab. Selskab. Mat.-Fys. Medd. (1)

H. H. Jensen, “Some notes on heat transfer by radiation,” Kgl. Danske Videnskab. Selskab. Mat.-Fys. Medd. 24, 1–26 (1948).

Other (5)

M. Jakob, Heat Transfer (Wiley, New York, 1957), Vol. 2.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Hemisphere, Washington, D.C., 1978).

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Hemisphere, Washington, D.C., 1981).

E. M. Sparrow, V. K. Jonsson, “Absorption and emission characteristics of diffuse spherical enclosures,” (NASA, Washington, D.C., 1962).

R. E. Bedford, in The Theory and Practice of Radiation Thermometry, D. P. DeWitt, G. D. Nutter, eds. (Wiley, New York, 1988), Chap. 12.

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Figures (2)

Fig. 1
Fig. 1

Geometry of a spherical cavity with arbitrary temperature and emissivity.

Fig. 2
Fig. 2

Exact spectral radiance from a nonisothermal diffuse spherical cavity.

Equations (11)

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Is, λ=s, λBs, λ+1-s, λcav Is, λFs, sds.
Fs, s=14πR21Asph,
Is, λ=s, λBs, λ+ρs, λAsph-1cav Is, λds.
Acav=2πRx0,
Bs, λ=c1λ-5expc2/λTs-1
 Is, λds= s, λBs, λds+Asph-1  ρs, λds  Is, λds,
 Is, λds= s, λBs, λds1-Asph-1  ρs, λds.
Is, λ=s, λBs, λ+ρs, λcav s, λBs, λdsAsph-cav ρs, λds,
aλ=λ1-1-λAcav/Asph.
Ix, λ=x, λBx, λ+ρx, λ0x0 x, λBx, λdx2R-0x0 ρx, λdx.
Ts=Tx=T0-x/x0T0-Tx0,

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