The fundamental nonlinear heat-transfer equations that appear in a steady-state energy balance on a collector absorber plate are presented and solved for nonsolar (nighttime) periods. Solutions are presented for two cases: first, where the plate temperatures are held constant and the heat loss varies with the ambient temperature; and, second, where the net heat transfer to the plate is zero and the plate temperature varies with outdoor air temperature. The solutions were obtained using steady simulation techniques based upon the Newton Raphson methods.

The solutions are then applied to a number of collector, freeze-up situations: first, determination of ambient temperatures at which collectors will freeze; second, the nighttime thermal loss from a pumped recirculation freeze-protection system; third, the prospects of a collector freezing at night with an inlet fluid temperature of 32°F (0°C); finally, estimation of the minimum volume of thermal storage to be sacrificed in open systems to prevent collector freeze-ups.