Abstract

An analysis is made of large aperture parabolic reflectors as solar furnaces to determine the most effective areas and estimate maximum attainable temperatures for two types of radiation targets. The maximum attainable temperature calculated is 5200°K.

© 1957 Optical Society of America

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References

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  1. Trombe, Foex, and LaBlanchetais, Ann. chim. et phys. 2, 385 (1947).
  2. G. P. Kuiper, Temperature—Its Measurement and Control in Science and Industry (Rheinhold Publishing Corporation, New York, 1941), p. 395.
  3. J. A. Hynek, Ohio J. Sci. 53, 314 (1953).
  4. W. M. Conn, Z. angew. Phys. 6, 284 (1954).
  5. M. Jakob, Heat Transfer (John Wiley and Sons, Inc., New York, 1949), Vol. I.

1954 (1)

W. M. Conn, Z. angew. Phys. 6, 284 (1954).

1953 (1)

J. A. Hynek, Ohio J. Sci. 53, 314 (1953).

1947 (1)

Trombe, Foex, and LaBlanchetais, Ann. chim. et phys. 2, 385 (1947).

Conn, W. M.

W. M. Conn, Z. angew. Phys. 6, 284 (1954).

Foex,

Trombe, Foex, and LaBlanchetais, Ann. chim. et phys. 2, 385 (1947).

Hynek, J. A.

J. A. Hynek, Ohio J. Sci. 53, 314 (1953).

Jakob, M.

M. Jakob, Heat Transfer (John Wiley and Sons, Inc., New York, 1949), Vol. I.

Kuiper, G. P.

G. P. Kuiper, Temperature—Its Measurement and Control in Science and Industry (Rheinhold Publishing Corporation, New York, 1941), p. 395.

LaBlanchetais,

Trombe, Foex, and LaBlanchetais, Ann. chim. et phys. 2, 385 (1947).

Trombe,

Trombe, Foex, and LaBlanchetais, Ann. chim. et phys. 2, 385 (1947).

Ann. chim. et phys. (1)

Trombe, Foex, and LaBlanchetais, Ann. chim. et phys. 2, 385 (1947).

Ohio J. Sci. (1)

J. A. Hynek, Ohio J. Sci. 53, 314 (1953).

Z. angew. Phys. (1)

W. M. Conn, Z. angew. Phys. 6, 284 (1954).

Other (2)

M. Jakob, Heat Transfer (John Wiley and Sons, Inc., New York, 1949), Vol. I.

G. P. Kuiper, Temperature—Its Measurement and Control in Science and Industry (Rheinhold Publishing Corporation, New York, 1941), p. 395.

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Figures (9)

Fig. 1
Fig. 1

Large aperture parabolic mirror.

Fig. 2
Fig. 2

Radiation received by a hemispherical target.

Fig. 3
Fig. 3

Variation of average absorptivity of a blackbody hemispherical target with mirror angle.

Fig. 4
Fig. 4

Variation of flux on flat plate target from a parabolic mirror element with angle.

Fig. 5
Fig. 5

Total flux from a parabolic mirror to a flat plate target.

Fig. 6
Fig. 6

Variation of flux on a hemispherical target from a parabolic mirror element with angle.

Fig. 7
Fig. 7

Total flux from a parabolic mirror to a hemispherical target.

Fig. 8
Fig. 8

Variation of flux at a “hole” target from a parabolic mirror element with angle.

Fig. 9
Fig. 9

Total flux from a parabolic mirror to al “hole” target.

Equations (20)

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ρ = a sec 2 θ / 2 ,             y 2 = 4 a ( x + a ) ,
q = q 0 cos ( θ / 2 ) ,
R = 1 - ( 1 - R n ) cos ( θ / 2 ) ,
d = ρ α / cos θ
B = a 2 cos θ / ρ 2
A = = n cos θ .
B = a 2 ( cos θ + 1 ) / 2 ρ 2
Ā = s n cos φ d s s d s = π 4 n ( 1 + cos θ ) π - θ .
d q / d s = 4 π q 0 n a cos 2 θ cos 4 θ / 2 sin θ / 2 × [ 1 - ( 1 - R n ) cos ( θ / 2 ) ] .
d q / d s = 4 π a q 0 R n sin ( θ / 2 ) .
Q = 4 π n a 2 q 0 θ 1 θ 2 cos 2 θ sin θ 2 cos θ 2 [ 1 - ( 1 - R n ) cos θ 2 ] d θ = - 8 π n a 2 q 0 [ 2 3 cos 6 θ 2 - cos 4 θ 2 + 1 2 cos 2 θ 2 - ( 1 - R n ) ( 4 7 cos 7 θ 2 - 4 5 cos 5 θ 2 + 1 3 cos 3 θ 2 ] θ 1 θ 2 .
Q = 8 π a 2 R n q 0 θ 1 θ 2 sin θ 2 sec 3 θ 2 · 1 2 d θ = 8 π a 2 R n q 0 [ 1 2 tan 2 θ 2 2 - 1 2 tan 2 θ 1 2 ] .
d q d s = 2 π 2 a n q 0 π - θ cos 8 θ 2 sin θ 2 [ 1 - ( 1 - R n ) cos θ 2 ] .
Q = - 8 π a 2 Ā 0 q 0 cos 4 θ 2 [ 1 4 - 1 5 ( 1 - R n ) cos θ 2 ] θ 1 θ 2 .
d q / d s = 4 π a q 0 cos 4 θ / 2 cos θ × [ 1 - ( 1 - R n ) cos θ / 2 ] sin θ / 2.
Q = - 8 π a 2 q 0 [ - 2 / 5 cos 5 θ / 2 + 1 / 2 cos 4 θ / 2 + 1 / 3 cos 3 θ / 2 - 1 / 2 cos 2 θ / 2 + ( 2 / 5 cos 5 θ / 2 - 1 / 3 cos 3 θ / 2 ) R n ] θ 1 θ 2 .
Q A = π a 2 q 0 π ( a α / 2 ) 2 = 4 q 0 / α 2 .
q = σ T 4 ,
q = - 8 π n a 2 q 0 π / 4 ( a α ) 2 [ 2 3 cos 6 θ 2 - cos 4 θ 2 + 1 2 cos 2 θ 2 - ( 1 - R n ) ( 4 7 cos 7 θ 2 - 4 5 cos 5 θ 2 + 1 3 cos 3 θ 2 ] 0 π / 2 .
T max = 4650 ° K .