## FrUlT Ta

The useful energy gain can thus be written in terms of critical radiation level as:

The plus superscript in Eqs. (11.35) and (11.37) and in the following equations indicates that only positive values of Itc are considered. If the critical radiation level is constant for a particular hour of the month having N days, then the monthly average hourly output for this hour is a - ^N^ £(i. - ite)+ (11.38)

Because the monthly average radiation for this particular hour is It, the average useful output can be expressed by

where $ is given by Eq. (11.22). This can be estimated from the generalized $ curves or Eq. (11.26), given earlier for the dimensionless critical radiation level, Xc, given by Eq. (11.23), which can now be written in terms of the collector parameters, using Eq. (11.36), as x = = frul (ti ta ) (11.40)

(Ta)n where (ra)/(Ta)n can be determined for the mean day of the month, shown in Table 2.1, and the appropriate hour angle and can be estimated with the incidence angle modifier constant, bo, from Eq. (4.25).

With $ known, the utilizable energy is It The main use of hourly utiliz-ability is to estimate the output of processes that have a critical radiation level, Xc, that changes considerably during the day, which can be due to collector inlet temperature variation.

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