Page 204 - Mechanical Engineers' Handbook (Volume 4)

3 Radiation Heat Transfer 193

Table 21 Values of X for Radiative Shields
Geometry X
1 1 Infinitely long parallel plates
1
s1 s2
1 1
1
1 2

2 1 1 1 n 1 for infinitely long concentric cylinders
r 1
2
r 2 s1 s2 n 2 for concentric spheres
1 1 1 r 1
1 2 r 2

q h A (T T )
2
1
r
is the radiation heat-transfer coefficient or radiation film coefficient. For the case
where h r
of radiation between two large parallel plates with emissivities, respectively, of and ,
1 2
4
4
T T 1 1 1
2
1
h (T T )
r
1
2

1 2
3.5 Thermal Radiation Properties of Gases
All of the previous expressions assumed that the medium present between the surfaces did
not affect the radiation exchange. In reality, gases such as air, oxygen (O ), hydrogen (H ),
2
2
and nitrogen (N ) have a symmetrical molecular structure and neither emit nor absorb ra-
2
diation at low to moderate temperatures. Hence, for most engineering applications, such
nonparticipating gases can be ignored. However, polyatomic gases such as water vapor
(H O), carbon dioxide (CO ), carbon monoxide (CO), sulfur dioxide (SO ), and various
2
2
2
hydrocarbons, emit and absorb significant amounts of radiation. These participating gases
absorb and emit radiation in limited spectral ranges, referred to as spectral bands. In cal-
culating the emitted or absorbed radiation for a gas layer, its thickness, shape, surface area,
pressure, and temperature distribution must be considered. Although a precise method for
calculating the effect of these participating media is quite complex, an approximate method
21
developed by Hottel will yield results that are reasonably accurate.
The effective total emissivities of carbon dioxide and water vapor are a function of the
temperature and the product of the partial pressure and the mean beam length of the sub-
stance as indicated in Figs. 25 and 26, respectively. The mean beam length, L , is the char-
e
acteristic length that corresponds to the radius of a hemisphere of gas, such that the energy
flux radiated to the center of the base is equal to the average flux radiated to the area of
interest by the actual gas volume. Table 22 lists the mean beam lengths of several simple