ENGINEERING TREATMENT OF GAS RADIATION IN ENCLOSURES

1. ENGINEERING TREATMENT OF GAS RADIATION IN ENCLOSURES • net-radiation method for enclosure filled with isothermal gas: spectral relations • mean beam length for radiation from • an entire gas volume to all or part of its • boundary • exchange of total radiation in an • enclosure by application of mean • beam length • zonal method: non-isothermal gases

2. Net-Radiation Method for Enclosures Filled with Isothermal Gases Equation of Transfer in an absorbing and emitting medium in terms of optical thickness

3. formal solution in a given direction of propagation integrating factorexp(tl)

4. dAj qj ilo,dj dwk s qk ili,dj-dk dAk Spectral Geometric-Mean Transmission and Absorption Factors Aj, Tj Gl,k Jl,k Ak, Tk gas atTg Ak, Tk

5. for an isothermal gas ilb,g = constant, assume al = constant, then without scattering

6. Spectral transmittance : Spectral absorptance : For diffuse surface

7. or Irradiation

8. Geometric-mean transmittance: Geometric-mean absorptance:

9. Geometric transmission factor: Geometric absorption factor: Irradiation in terms of geometric factors

10. or or for an enclosure with n surfaces

11. hemisphere to differential area at the center of its base Ex Aj dAj Rsinqk qj = 0 qk s = R R dAk Evaluation of spectral geometric-mean transmittance and absorption factors

12. Aj dAj Rsinqk qj = 0 qk s = R R dAk but Thus,

13. entire sphere to any area on its surface or to its entire surface Ex dAj q Aj S q R dAk Aj: area of entire sphere

14. and dAj q Aj S q R dAk

16. Recall inside sphere method dAj q Aj S q R dAk

17. dAj Aj s q D Ak dAk or Ex infinite plate to any area on parallel plate Tg

18. exponential integral function

19. Ex 13-3 Te = 495 K, black 2 Tg = 550 K, non-gray absorbing, emitting D = 1.2 cm 1 heating element e1 = 0.65, T1 = 630 K, diffuse-gray

22. = 1 Mean Beam Length for Radiation from an Entire Gas Volume to All or Part of Its Boundary Definition When Jl,j is negligible, for a hemisphere of gas radiating to an area element dAk at the center of its base

23. el: spectral emittance of the gas mean beam lengthLefor an arbitrary geometry of gas

24. Ex mean beam length for gas between parallel plates radiating to area on plate

28. transmittance: Radiation from entire gas volume to its entire boundary in limit when gas is optically thin emitted energy per unit volume for entire radiating volume for uniform-temperature gas:

29. when Le is small, let Thus, average spectral flux received at the boundary:

30. a sphere of diameter D : infinitely long cylinder of diameter D: between two infinite parallel plates:

31. When C = 0.9 Ex between infinite plates Correction for mean beam length when gas is not optically thin for a thick gas: for a given alD, approximation:

35. Exchange of Total Radiation in an Enclosure by Application of Mean Beam Length Total radiation from entire gas volume to all or part of boundary total heat flux from the gas that is incident on a surface

36. gas total emittance radiation to area Akfrom the gas volume

37. : spectral overlap Hottel’s charts for gas total emittance for a mixture

43. Representation of total emittance in an analytical form Weighted sum of gray gases Gas is assumed to behave like a mixture of gray gases and a transparent (nonemitting) medium to account for the windows between the absorption bands when path length is long

44. Let for CO2 Table 13-5 for H2O Table 13-6

45. : black wall : evaluated at Tw, and high pressure and temperature Exchange between entire gas volume and emitting boundary

46. Ex 13-8 W = 1 m plate 2 T2 = 500 K, black CO2 Tg = 1000 K PCO2 = 1 atm Te << 500 K D = 1 m boundary 3 boundary 4 plate 1 T1 = 2000 K, black

48. c a b Let total transmittance and absorption factors

49. 1.34

50. Note: the radiation in the term is elb,1 and is coming from wall 1 : evaluated at Tw, and 0.22