Page 523 - Bird R.B. Transport phenomena

§16.5 Radiation Between Nonblack Bodies at Different Temperatures 503

Fig. 16.5-1. Radiation between two infinite, parallel gray
Surface 2 at surfaces.
temperature T 2 —
with emissivity e 2

Surface 1 at
— temperature 7^
with emissivity e }

Fig. 16.5-2. Equivalent cir-
|i cuit for system shown in
Fig. 16.5-1.
Radiation potential: crT-f

1
Radiation resistance:
A,F 1 2
1
A 2 F 2 1

Equations analogous to Eqs. 16.5-4, 7, and 8 arise in the analysis of direct-current cir-
cuits, from Ohm's law of conduction and Kirchhoff s law of charge conservation. Hence
we have the following analogies:

Electrical Radiative
Current Q
Voltage J or aT 4
Resistance (1 - е,)/еД or \/Af Vj
This analogy allows easy diagramming of equivalent circuits for visualization of simple
enclosure radiation problems. For example, the system in Fig. 16.5-1 gives the equivalent
circuit shown in Fig. 16.5-2 so that the net radiant heat transfer rate is
(T{T\ -
Qu = (16.5-9)
1 -e, 1
• + • • +
e \A\ A M : e 2 A 2
The shortcut solution summarized in Eq. 16.4-15 has been similarly generalized to
non-black-walled enclosures giving
Ql2 = (16.5-10)
in place of Eq. 16.5-8, for an enclosure with Q,•, = 0 for / = 2, ,..., n. The result is like
3
that in Eq. 16.5-9, except that F u must be used instead of F to include indirect paths
12
from A to A , thus giving a larger heat transfer rate.
A 2
EXAMPLE 16.5-1 Develop an expression for the reduction in radiant heat transfer between two infinite parallel
gray planes having the same area, A, when a thin parallel gray sheet of very high thermal
Radiation Shields conductivity is placed between them as shown in Fig. 16.5-3.