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# SHW201 Solar Hot Water Controller

The SHW201 is based on the DAS201 MiniDAS. Its block diagram is shown below.

### Solar Collector D*T*

The solar collectors raise the temperature, *T*_{L},
of inlet fluid,* *assumed here to be
water, by transferring solar heat, *Q*_{l},
to the fluid, resulting in an exit temperature of *T*_{H}. The temperature difference is D*T* = *T*_{H} – T_{L}. The relationship between
change in heat, D*Q*,
and D*T* 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, *c*_{p}. The total heat capacity (not per-mass) is *C*_{p}.
(In thermodynamics, lower-case quantities are per-mass). Then

D*Q* = *C*_{p}×D*T*

A water use of 50 l/day requires 97 W average over
the day. With a daily average solar heating flux of 212 W/m^{2},
including losses for an easily obtained efficiency of 46 %, the rule of thumb
for sizing collector panel area is: 1 m^{2} 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.

### Pump Sizing

For *T*_{L} = 25 °C
(slightly warmer than ambient) and a desired *T*_{H} of 65 °C
(149 °F),

D*T* = 65 °C
– 45 °C = 40 °C = 40 K

The choice of *T*_{H}
is based on a desired *T*_{o} = *T*_{H} = 65 °C = 149 °F,
a typical hot-water setting. Equating *T*_{o}
and *T*_{H} assumes no heat loss
in the pipe from collector exit to hot-water tank, and if the loss is
significant, *T*_{H} 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.