99 The equations for Ua and Us are simple and straightforward: ‘a
=
heat capacity of the annulus, Fig. 12.
A&, see Fig. 11, is the change in the average annulus temperature during time interval, t,.
-
Note that the peak temperature in the heat exchanger will be slightly above 3 because of the gradient in the annulus. With the annulus transferring heat at the generation rate existing lo4 sec after shutdown the increase is approximately 75°F. = heat capacity of the intermedi-
cis
ate shell.
A& = change in the average temperature of the intermediate shell.
The average temperature of the thick (2.5 in.) intermediate shell is, during the transient, appreciably dependent on both space and time. From Fig. 6 it is apparent that most of the gamma heat deposition takes place near the inside surface. The radiant heat received from the annulus will be deposited directly on the inner surface. The net effect, of course, i s to raise the temperature of the inner surface a substantial amount above the average value, &, that must be used to evaluate u6. However, the inner surface temperature, ea, is the effective heat sink temperature used in Eq. (1-1)when radiant transfer from the annulus is being calculated. This difference between the average and inner surface temperatures was not calculated directly as a function of elapsed time; instead, the approximate transit time for heat flow through the slab was estimated. Specifically, the case considered was an infinite slab, 2.5 in, thick, of Hastelloy N, with one face jnsulated. The uninsulated surface sees a step increase in temperature. From Fig. 10-2, p. 235, and related text material in reference 28, it was estimated that the average temperature will lag the inner surface temperature by approximately 1000 sec. This l o c a l transient effect in the intermediate shell was considered during the computations, The total heat transferred fram the annulus during any interval, (1-1).
- tl , is obtained by integrating Eq.