Summary
The large path length limit is investigated for infrared gaseous radiation. This limit differs considerably, as the result of the wing regions of vibrationrotation bands, from the conventional Rosseland limit. For illustrative purposes, results are presented for a gas bounded by two parallel black plates and within which there is a uniform heat source. In order to demonstrate its range of applicability, the large path length limit is compared with numerical solutions for CO, CO2, H2O, and CH4. It is further shown that a gas such as CO2 is a very poor transmitter of radiant energy, relative to other absorbing-emitting gases, in the large path length limit, although just the opposite is true under optically thin conditions.
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Abbreviations
- A i :
-
total band absorptance of the ith band, cm−1
- A oi :
-
correlation quantity, cm−1
- Ā i :
-
dimensionless band absorptance, A i /A oi
- B 2 i :
-
correlation quantity
- B e,i :
-
rotational constant for the ith band, cm−1
- c :
-
speed of light
- C 2 oi :
-
correlation quantity, atm−1 cm−1
- e ω :
-
Planck's distribution function, (watt cm−2) cm−1
- e ωi :
-
Planck's function evaluated at the center of the ith band
- e 1ωwi :
-
Planck's function evaluated at the center of the ith band and at the temperature T 1
- h :
-
Planck's constant
- k :
-
Boltzmann's constant
- L :
-
distance between plates, cm
- P :
-
gas pressure, atm
- P ei :
-
equivalent broadening pressure of the ith band
- q R :
-
total radiation heat flux, watt/cm2
- q Ri :
-
radiation heat flux for ith band, watt/cm2
- Q :
-
heat source or sink, watt/cm3
- T :
-
temperature, °K
- T 1 :
-
wall temperature
- T c :
-
centerline temperature
- u i :
-
dimensionless coordinate, C 2 oi Py
- u oi :
-
dimensionless path length, C 2 oi PL
- y :
-
physical coordinate, cm
- ξ :
-
dimensionless coordinate, y/L
References
Cess, R. D., P. Mighdoll, and S. N. Tiwari, Int. J. Heat Mass Transfer 10 (1967) 1521.
Tien, C. L. and J. E. Lowder, Int. J. Heat Mass Transfer 9 (1966) 698.
Edwards, D. K. and W. A. Menard, Applied Optics 3 (1964) 621.
Edwards, D. K. and W. A. Menard, Applied Optics 3 (1964) 847.
Edwards, D. K. and W. Sun, Applied Optics 3 (1964) 1501.
Edwards, D. K., B. J. Flornes, L. K. Glassen, and W. Sun, Applied Optics 4 (1965) 715.
Edwards, D. K., Applied Optics 4 (1965) 1352.
Edwards, D. K., L. K. Glassen, W. C. Hauser, and J. S. Tuchscher, ASME J. Heat Transfer 89C (1967) 219.
Cess, R. D. and S. N. Tiwari, State University of New York at Stony Brook, College of Engineering Report No. 90, 1967.
Mikhlin, S. G., Integral Equations, p. 126, Pergamon Press, Oxford 1967.
Sparrow, E. M. and R. D. Cess, Radiation Heat Transfer, p. 212, Brooks/Cole, Belmont (Calif.) 1966.
Tien, C. L., Thermal Radiation Properties of Gases, in Advances in Heat Transfer, V, Academic Press, New York 1967.
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Cess, R.D., Tiwari, S.N. The large path length limit for infrared gaseous radiation. Appl. Sci. Res. 19, 439–449 (1968). https://doi.org/10.1007/BF00383938
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DOI: https://doi.org/10.1007/BF00383938