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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
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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
Net-Radiation Method for Enclosures Filled with Isothermal Gases Equation of Transfer in an absorbing and emitting medium in terms of optical thickness
formal solution in a given direction of propagation integrating factorexp(tl)
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
for an isothermal gas ilb,g = constant, assume al = constant, then without scattering
Spectral transmittance : Spectral absorptance : For diffuse surface
or Irradiation
Geometric-mean transmittance: Geometric-mean absorptance:
Geometric transmission factor: Geometric absorption factor: Irradiation in terms of geometric factors
or or for an enclosure with n surfaces
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
Aj dAj Rsinqk qj = 0 qk s = R R dAk but Thus,
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
and dAj q Aj S q R dAk
Recall inside sphere method dAj q Aj S q R dAk
dAj Aj s q D Ak dAk or Ex infinite plate to any area on parallel plate Tg
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
= 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
el: spectral emittance of the gas mean beam lengthLefor an arbitrary geometry of gas
Ex mean beam length for gas between parallel plates radiating to area on plate
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:
when Le is small, let Thus, average spectral flux received at the boundary:
a sphere of diameter D : infinitely long cylinder of diameter D: between two infinite parallel plates:
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:
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
gas total emittance radiation to area Akfrom the gas volume
: spectral overlap Hottel’s charts for gas total emittance for a mixture
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
Let for CO2 Table 13-5 for H2O Table 13-6
: black wall : evaluated at Tw, and high pressure and temperature Exchange between entire gas volume and emitting boundary
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
c a b Let total transmittance and absorption factors
Note: the radiation in the term is elb,1 and is coming from wall 1 : evaluated at Tw, and 0.22