Abstract

An analysis was performed to determine the radiation transmitting characteristics of a circularly reflecting duct with a collimated beam of rays entering at one end. Data were obtained for various angles of beam incidence, duct included angle, and ratios of the radii of the two walls. Both the over-all energy transmitting characteristics and the local energy absorption distribution were determined.

© 1967 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. R. G. Eckert, E. M. Sparrow, Intern. J. Heat Mass Transfer 3, 42 (1961).
    [CrossRef]
  2. M. Perlmutter, R. Siegel, J. Heat Transfer 85, 55 (1963).
    [CrossRef]
  3. S. H. Lin, E. M. Sparrow, Appl. Opt. 4, 277 (1965).
    [CrossRef]
  4. S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
    [CrossRef]

1965 (2)

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
[CrossRef]

S. H. Lin, E. M. Sparrow, Appl. Opt. 4, 277 (1965).
[CrossRef]

1963 (1)

M. Perlmutter, R. Siegel, J. Heat Transfer 85, 55 (1963).
[CrossRef]

1961 (1)

E. R. G. Eckert, E. M. Sparrow, Intern. J. Heat Mass Transfer 3, 42 (1961).
[CrossRef]

Eckert, E. R. G.

E. R. G. Eckert, E. M. Sparrow, Intern. J. Heat Mass Transfer 3, 42 (1961).
[CrossRef]

Lin, S. H.

S. H. Lin, E. M. Sparrow, Appl. Opt. 4, 277 (1965).
[CrossRef]

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
[CrossRef]

Perlmutter, M.

M. Perlmutter, R. Siegel, J. Heat Transfer 85, 55 (1963).
[CrossRef]

Siegel, R.

M. Perlmutter, R. Siegel, J. Heat Transfer 85, 55 (1963).
[CrossRef]

Sparrow, E. M.

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
[CrossRef]

S. H. Lin, E. M. Sparrow, Appl. Opt. 4, 277 (1965).
[CrossRef]

E. R. G. Eckert, E. M. Sparrow, Intern. J. Heat Mass Transfer 3, 42 (1961).
[CrossRef]

Appl. Opt. (1)

Intern. J. Heat Mass Transfer (1)

E. R. G. Eckert, E. M. Sparrow, Intern. J. Heat Mass Transfer 3, 42 (1961).
[CrossRef]

J. Heat Transfer (2)

M. Perlmutter, R. Siegel, J. Heat Transfer 85, 55 (1963).
[CrossRef]

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87, 299 (1965).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Two dimensional curved duct.

Fig. 2
Fig. 2

Two reflection patterns, reflections occur only on outer surface in upper figure and reflections alternate between inner and outer surfaces in lower figure.

Fig. 3
Fig. 3

Number of reflections experienced by the rays for positive angles of inclination.

Fig. 4
Fig. 4

Number of reflections experienced by the rays for negative angles of inclination.

Fig. 5
Fig. 5

Energy transmission and function of incidence angle.

Fig. 6
Fig. 6

Energy transmission as a function of duct width.

Fig. 7
Fig. 7

Local energy absorption characteristics of duct with a large angle of incidence.

Fig. 8
Fig. 8

Local energy absorption characteristics of duct with zero angle of incidence.

Equations (26)

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

θ 1 = - ϕ + arccos ( R cos ϕ )
Δ θ = arccos ( R cos ϕ ) - arccos [ ( R / R 1 ) cos ϕ ] ,
θ 1 = - ϕ - arccos [ ( R / R 1 ) cos ϕ ] .
Δ θ = 2 arccos ( R cos ϕ ) .
θ = θ 1 + ( n - 1 ) Δ θ .
R c = R 1 / cos ϕ
ψ = θ 1 + n Δ θ .
ψ + ϕ = ( n i + 1 ) arccos ( ξ i cos ϕ ) - n i arccos [ ( ξ i / R 1 ) cos ϕ ] .
ψ + ϕ = n i arccos ( ξ i cos ϕ ) - ( n i + 1 ) arccos [ ( ξ i / R 1 ) cos ϕ ] .
n i = ( 1 / cos ϕ ) cos [ ( ψ + ϕ ) / ( 2 m i + 1 ) ] .
n 1 = integral part of { ψ - ϕ + arccos ( R 1 cos ϕ ) } ,
n 1 = integral part of { 1 + ψ ϕ + arccos ( R 1 cos ϕ ) } .
m 1 = integral part of { ψ + ϕ + arccos ( R 1 ) 2 arccos ( R 1 ) } .
a i = α + α ρ + α ρ 2 + α ρ 3 + + α ρ n i - 1 ,
a i = 1 - ρ n i .
t i = ρ n i .
Q i = ρ n i Δ ξ i S 0 cos ϕ .
Q / ( 1 - R 1 ) S 0 cos ϕ = [ 1 / ( 1 - R 1 ) ] ( i = 1 i = N ρ n i Δ ξ i + i = 1 i = M ρ m i Δ η i ) ,
θ = - ϕ + n arccos ( R cos ϕ ) - ( n - 1 ) arccos ( R cos ϕ / R 1 ) .
R = ( 1 / cos ϕ ) cos [ ( θ + ϕ ) / ( 2 m - 1 ) ] .
θ = - ϕ + ( n - 1 ) arccos ( R cos ϕ ) - n arccos ( R cos ϕ / R 1 )
E = S 0 ρ n - 1 cos ϕ d R / d θ .
E = S 0 ρ n - 1 cos ϕ d R / d θ / R 1 .
q ( θ ) / S 0 = J ( 1 - ρ ) ρ n - 1 n / ( 1 - R 2 cos 2 ϕ ) 1 2 - ( n - 1 ) / ( R 1 2 - R 2 cos 2 ϕ ) 1 2 + K ( 1 - ρ ) ρ m - 1 [ ( 2 m - 1 ) / ( 1 - R 2 cos 2 ϕ ) 1 2 ] ,
( n - 1 ) / ( 1 - R 2 cos 2 ϕ ) 1 2 - n / ( R 1 2 - R 2 cos 2 ϕ ) 1 2 .
q ( θ ) / S 0 = ( 1 / R 1 ) J ( 1 - ρ ) ρ n - 1 n / ( 1 - R 2 cos 2 ϕ ) 1 2 - ( n - 1 ) / ( R 1 2 - R 2 cos 2 ) 1 2 ,

Metrics