Page 207 - Mechanical Engineers' Handbook (Volume 4)

196 Heat-Transfer Fundamentals

Table 22 Mean Beam Length a
Geometry of Gas Volume Characteristic Length L e
Hemisphere radiating to element at Radius R R
center of base
Sphere radiating to its surface Diameter D 0.65D
Circular cylinder of infinite height Diameter D 0.95D
radiating to concave bounding
surface
Circular cylinder of semi-infinite
height radiating to:
Element at center of base Diameter D 0.90D
Entire base Diameter D 0.65D
Circular cylinder of height equal to
diameter radiating to:
Element at center of base Diameter D 0.71D
Entire surface Diameter D 0.60D
Circular cylinder of height equal to
two diameters radiating to:
Plane end Diameter D 0.60D
Concave surface Diameter D 0.76D
Entire surface Diameter D 0.73D
Infinite slab of gas radiating to:
Element on one face Slab thickness D 1.8D
Both bounding planes Slab thickness D 1.8D
Cube radiating to a face Edge X 0.6X
Gas volume surrounding an infinite
tube bundle and radiating to a
single tube:
Equilateral triangular array:
S 2D Tube diameter D and 3.0(S - D)
S 3D spacing between 3.8(S - D)
tube centers, S
Square array: 3.5(S - D)
S 2D
a Adapted from Ref. 19.

In this expression, the values of and can be found from Figs. 25 and 26 using
CO 2 H O
2
an abscissa of T , but substituting the parameters p L T /T and p L T /T for p L
w CO 2 e w g H O e w g CO 2 e
2
and p L , respectively.
HO e
2
Radiative Exchange between a Gray Enclosure and a Gas Volume
When the emissivity of the enclosure, , is larger than 0.8, the rate of heat transfer may be
w
approximated by
q 1
w

gray
2 q black
where q gray is the heat-transfer rate for gray enclosure and q black is that for black enclosure.
For values of 0.8, the band structures of the participating gas must be taken into account
w
for heat-transfer calculations.