The SHW201 is based on the DAS201 MiniDAS. Its block diagram is shown below.
The solar collectors raise the temperature, TL, of inlet fluid, assumed here to be water, by transferring solar heat, Ql, to the fluid, resulting in an exit temperature of TH. The temperature difference is DT = TH – TL. The relationship between change in heat, DQ, and DT is a thermodynamic quantity called the heat capacity. The per-mass (or specific) heat capacity is called the specific heat. In this case, the inlet and exit pressures are equal, and the quantity of relevance is the constant-pressure specific heat, cp. The total heat capacity (not per-mass) is Cp. (In thermodynamics, lower-case quantities are per-mass). Then
DQ = Cp×DT
A water use of 50 l/day requires 97 W average over the day. With a daily average solar heating flux of 212 W/m2, including losses for an easily obtained efficiency of 46 %, the rule of thumb for sizing collector panel area is: 1 m2 of panel per person. This rule of thumb assumes the sun will shine everyday for at least 8 hours. For high-availability hot water at the commanded temperature, cloudy days must be accounted for by adding additional capability. Under better than minimum insolation, the warm tank water receives the excess heat so that less heating is required under less favorable conditions. Consequently, the warm tank is a buffer which reduces the amount of collector area required to cover the worst case of minimum insolation. Tank sizing accounts for these dynamic variations, including variations in hot-water use.
For TL = 25 °C (slightly warmer than ambient) and a desired TH of 65 °C (149 °F),
DT = 65 °C – 45 °C = 40 °C = 40 K
The choice of TH is based on a desired To = TH = 65 °C = 149 °F, a typical hot-water setting. Equating To and TH assumes no heat loss in the pipe from collector exit to hot-water tank, and if the loss is significant, TH must be raised to account for it.
The required pumping power, with pump efficiency included is miniscule. An aquarium pump would suffice. The small size of the pumps makes it more cost-effective to use two pumps in the system instead of a single pump and an electrically-actuated three-way valve.
The check valve at the collector exit prevents back-flow from the hot tank into the collector when the collector cools at night.
The non-controller system design equations, except for tank sizing, are worked out in more detail in the documentation for Assistants. System design is completed by considering its dynamics; random variations in user flow rate and in solar heating rate over wide ranges leads to imprecision in design relative to performance. The additional warm tank helps to average out these variations and keep design parameters within reasonable bounds.