Page 202 - Mechanical Engineers' Handbook (Volume 4)

3 Radiation Heat Transfer 191

4
J T (1 )G
For an enclosure consisting of N surfaces, the irradiation on a given surface i can be
expressed as
G JF
N
i
j 1 j i j
and the net radiative heat-transfer rate at given surface i is
A
q A (J G ) i i ( T J )
4
i
i
i
i
1 i i i
For every surface in the enclosure, a uniform temperature or a constant heat transfer rate
can be specified. If the surface temperature is given, the heat-transfer rate can be determined
for that surface and vice versa. Shown below, are several specific cases that are commonly
encountered.
Case I. The temperatures of the surfaces, T (i 1, 2, . . . , N), are known for each
i
of the N surfaces and the values of the radiocity, J , are solved from the
i
expression
{
(1 )F }J T , 1 i N
N
4
j 1 ij i i j i i i
The net heat-transfer rate to surface i can then be determined from the fun-
damental relationship

q A i i ( T J ), 1 i N
4
i
i
i
1 i
where
0 for i j and
1 for i j.
ij ij
Case II. The heat-transfer rates, q (i 1, 2,..., N), to each of the N surfaces are
i
known and the values of the radiocity, J , are determined from
i
{
F }J q /A 1 i N
N
j 1 ij i j j i i
The surface temperature can then be determined from
T i i J 1/4
11 q
i
i A i i 1 i N
Case III. The temperatures, T (i 1,..., N ), for N surfaces and heat-transfer rates
i 1 i
q (i N 1,..., N) for (N N ) surfaces are known and the radiocities
i 1 i
are determined by
{
(1 )F }J T 4 1 i N
N
j 1 ij i i j j i i 1
{
F }J q i N 1 i N
N
j 1 ij i j j A i 1
The net heat-transfer rates and temperatures van be found as