Page 505 - Mechanical Engineers' Handbook (Volume 4)

494 Cryogenic Systems

wrapped around the processing vessel within the vacuum space has been used for most
applications at temperatures approaching absolute zero.

4.1 Vacuum Insulation

Heat transfer occurs by convection, conduction, and radiation mechanisms. A vacuum space
ideally eliminates convective and conductive heat transfer but does not interrupt radiative
transfer. Thus heat transfer through a vacuum space can be calculated from the classic equa-
tion:
4
4
q AF (T T ) (10)
2
12
1
where q rate of heat transfer, J/sec
Stefan-Boltzmann constant, 5.73 10 8 J/sec m K
2
F 12 combined emissivity and geometry factor
T ,T temperature (K) of radiating and receiving body, respectively
2
1
In this formulation of the Stefan–Boltzmann equation it is assumed that both radiator and
receiver are gray bodies, that is, emissivity
and absorptivity are equal and independent of
temperature. It is also assumed that the radiating body loses energy to a totally uniform
surroundings and receives energy from this same environment.
The form of the Stefan–Boltzmann equation shows that the rate of radiant energy trans-
fer is controlled by the temperature of the hot surface. If the vacuum space is interrupted by
a shielding surface, the temperature of that surface will become T , so that
s
4
4
4
q/A F (T T ) F (T T ) (11)
4
1s
s2
s
1
2
s
Since q/A will be the same through each region of this vacuum space, and assuming F
1s
F F
s2 12
T T 2 4
4
4
1
T (12)
s 2
For two infinite parallel plates or concentric cylinders or spheres with diffuse radiation
transfer from one to the other,
1 1 1 1
F A 1 (13)
12

1 A 2
2
If A is a small body in a large enclosure, F 12
. If radiator or receiver has an emissivity
1
1
that varies with temperature, or if radiation is spectral, F 12 must be found from a detailed
statistical analysis of the various possible radiant beams. 30
Table 5 lists emissivities for several surfaces of low emissivity that are useful in vacuum
insulation. 31
It is often desirable to control the temperature of the shield. This may be done by
arranging for heat transfer between escaping vapors and the shield, or by using a double-
walled shield in which is contained a boiling cryogen.
It is possible to use more than one radiation shield in an evacuated space. The temper-
ature of intermediate streams can be determined as noted above, although the algebra
becomes clumsy. However, mechanical complexities usually outweigh the insulating advan-
tages.