Page 203 - Mechanical Engineers' Handbook (Volume 4)

192 Heat-Transfer Fundamentals

4
q A i i ( T J ) 1 i N 1
i
i
i
1 i
T i i J 1/4
11 q
1
i
i A i i N 1 i N
Two Diffuse-Gray Surfaces Forming an Enclosure
The net radiative exchange, q , for two diffuse-gray surfaces forming an enclosure are shown
12
in Table 20 for several simple geometries.
Radiation Shields
Often in practice, it is desirable to reduce the radiation heat transfer between two surfaces.
This can be accomplished by placing a highly reflective surface between the two surfaces.
For this configuration, the ratio of the net radiative exchange with the shield to that without
the shield can be expressed by the relationship
q 12 with shield 1
q 12 without shield 1
Values for this ratio, , for shields between parallel plates, concentric cylinders, and con-
centric spheres are summarized in Table 21. For the special case of parallel plates involving
more than one or N shields, where all of the emissivities are equal, the value of equals N.

Radiation Heat-Transfer Coefficient
The rate at which radiation heat transfer occurs can be expressed in a form similar to
Fourier’s law or Newton’s law of cooling, by expressing it in terms of the temperature
difference T T ,oras
2
1

Table 20 Net Radiative Exchange between Two Surfaces Forming an Enclosure
4
4
Large (infinite) parallel planes A 1 A 2 A A (T T )
2
1
q 12
1 1
1
1 2
4
Long (infinite) concentric cylinders A 1 r 1 A (T T )
4
1
1
2
q 12
1
A 2 r 2 1 2 r 1

1 2 r 2
4
4
Concentric sphere A 1 r 1 2 A (T T )
2
1
1
q 12
2 2
A 2 r 2 1 1 2 r 1

1 2 r 2
Small convex object in a large cavity A 1 q 12 A (T T )
4
4
1 1
1
2
0
A 2