An analytic model for the long-term performance of solar thermal systems with well-mixed storage

A simple analytic method is presented for predicting the long-term performance of solar thermal systems with well-mixed storage and loads that do not vary significantly from day to day. Recognizing that most conventionally designed systems have effective relaxation times that are long relative to the time scale of variations in insolation, but short compared to the time scale for day-to-day variations in insolation, we invoke a constant radiation model and solve the problem within that framework. The results of the analytic method are simple closed-form expressions which enable the user to understand clearly the dependence of system performance on the physically important variables. Good agreement is found between the predictions of the analytic method and the corresponding results of the F-f-chart method and computer simulations. The analytic method is furthermore applicable to all collector types and storage fluids and is not restricted to flat plates and hot water storage. The limitations of the analytic method are discussed and found not to introduce a serious restriction for commonly designed conventional systems.