An approximate analysis of multi-pass, closed-loop solar systems with well-mixed storage tanks is presented. The thermal coupling of the storage tank both to the collector-storage loop (“charging” cycle) and the load-storage loop (“discharging” cycle) is shown to reduce system performance by a penalty factor, called the partial depletion factor, when compared to one-pass, open-loop systems in which the storage fluid is completely consumed by the load by the end of each 24-hour day (total depletion). This penalty factor is typically around 20 percent for systems with a daytime-only load and 30 percent for systems with a nighttime-only load. Our analysis provides, for the first time, the explanation for the findings of various experiments and numerical simulations. We establish the approximate validity of a “quasi-steady state” approach, wherein actual system performance is approximated by a calculation based on the repetition of one representative day. The approach is general in that it is applicable to all solar collector types.

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