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re: sizing a heating system
17 jun 2000
news  wrote:

>would double glazing, maybe low "e" glass, on a sunspace affect the
>performance of a air heater behind it?
sure, with lower solar transmission and higher thermal resistance,
say 50% and metric r1 vs 90% and r0.2 (u5), collecting 1 kwh/day of
sun requires more air heater glazing in the first case, although
less sunspace glazing is needed. we can reduce the air heater (closet)
glazing area by turning the sunspace into a solar sauna.

for example, suppose it's 0 c outdoors and 3 kwh/m^2 of sun falls on
a south wall on an average january day over 6 hours, and we want to
collect 1 kwh of 60 c air in a sunspace at temperature ts with 90%
r0.2 air heater glazing.

in the first case, with 50% r1 sunspace glazing, a m^2 of air heater
glazing gains 3kwhx0.5x0.9a = 1350a wh of sun and loses 6h(60c-ts)/r0.2 
= 1800a-30tsa wh of heat per day to the sunspace on average, so we need 
a = 1000/(30ts-450) m^2 of air heater glazing to collect 1 kwh/day.

the air heater removes 1000 wh of useful heat from the sunspace, and
its glazing heat loss is sunspace gain. s m^2 of sunspace glazing gains
3kx0.5 = 1500s wh of solar heat and loses 6h(ts-0c)s/r1 = 6tss wh per day
to the outdoors. keeping the sunspace ts (c) with energy inflow equal
to outflow over a day makes 1500s = 6tss + 1000, so s = 1000/(1500-6ts). 

the sunspace glazing needs to be at least as large as the air heater
glazing, if sun shines through both. if a = s, ts = 54 c and a = 0.85
m^2, in this linear model. making ts = 20 c makes a 6.7 m^2. making the
sunspace glazing 6.7 m^2 means dumping lots of heat by ventilation to
the outdoors (or the house, which needs lots of thermal mass and mass
surface to store it overnight, with a reasonable day-night temp swing.)

in the second case, with 90% r0.2 sunspace glazing, a m^2 of air heater
glazing gains 3kx0.9x0.9a = 2.43a kwh and loses 1800a-30tsa, so we only
need a = 1000/(30ts+630) m^2 of air heater glazing. 

s m^2 of sunspace glazing gains 3kx0.9 = 2700s wh of sun and loses
6h(ts-0c)s/r0.2 = 30tss wh-day to the outdoors. equal daily energy
inflow and outflow makes 2700s = 30tss + 1000, so s = 1000/(2700-30ts).
s = a makes ts = 34.5 c and s = 0.6 m^2, less than in the first case,
because the sunspace is cooler, with less heat loss to the outdoors,
but the sunspace is still warm enough to provide some useful heat for
the house during the day, which makes it even cooler, ie more efficient
and comfortable. 

>would a wide sunspace with an air heater on the wall, with about
>6 to 10 foot gap from the sunspace glass to the air heater, work
>any better than having one a foot or two away?

the wider sunspace is more useful to people, at the expense of a little
more heat loss to the outdoors, which could be overcome by making it
longer to gather more solar energy or putting a dark mesh curtain
inside near the south wall. a wider sunspace would also have less air
velocity near the glazing, which reduces the heat loss, other things
being equal.

putting the air heater farther away from the sunspace glazing makes
the space between the air heater and glazing less useful for people,
since they has to avoid shading the air heater. it also makes it harder
to shade the sunspace with an overhang without shading the air heater
in summertime, something people might want to do if the air heater
makes domestic hot water.

otoh, one might make the floor in front of the air heater reflective
or use a reflective surface in front of the sunspace to increase the
amount of sun that falls on the air heater by about 30%.


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