storing solar heat SOLAR.KnowledgePublications.com

storing solar heat
13 feb 1997
a friend from frozen milwaukee writes:

>...solar will never really amount to a lot in the future, until we can
>discover some storage medium that can maintain gains for longer than 48
>hours. if we had materials or techniques that could store energy for periods
>of say, 240 hours, we'd be getting closer.

a cube of water surrounded by insulation with a dimension of l feet can have
a time constant of about l squared days. consider a box made with plywood and
2x6's, say an 8x8x8' cube, with r20 insulation (6" of fiberglass) and 6x8x8
= 384 ft^2 of surface area, and a thermal resistance of r20/384 ft^2-f-hr/btu.
line it with epdm rubber, fill it with 7x7x7' = 343 cubic feet or about 22k
pounds of water and the natural time constant rc = r20/384x22k = 1143 hours
or 48 days, so if it starts out at say, 120 f in a 70 f house, after 240 hours
it will have a temperature of 70+(120-70)exp(-240/1143) = 111 f. if it's
sitting outside at 18.9 f (the average january temperature in milwaukee),
after 240 hours it will have a temperature of 18.9+(120-18.9)exp(-240/1143)
= 101 f. still reasonably warm...

i like the idea of using sealed containers of water inside a small insulated
room instead of a big tank like that, so sun-warmed air can heat the water
perhaps with the help of a few low-power fans, instead of using hydronic solar
collectors, plumbing, freezing, pumps, corrosion, antifreeze, heat exchangers,
etc. an 8x8x8' room might contain 32 plastic 55 gallon drums full of water,
ie about 16k vs 32k pounds of water, with a time constant of 853 vs 1143 hr,
35 days vs 48 days. still not bad. when the house needs heat, open a damper or
turn on a small fan to this solar closet to allow cooler house air to flow in
at the bottom and warmer closet air to flow back into the house from the top.  

concrete isn't so bad. a 16x16x16' house with 8" solid concrete walls and 3"
of foam on the outside has a surface area of 6x16x16 = 1,536 square feet,
a thermal resistance of r15/1536 and a thermal capacitance c=1,536x8/12x22  
= 22,528 btu/f and a time constant rc = r15/1536x22,528 = 220 hours. adding a
foot of water in the attic raises this to r15/1536x38,912 = 380 hours if the
walls and water have the same temperature, or more if the water starts out
warmer than the walls...  

how warm can we make the water in the attic, over a long string of average
winter days? this 16 foot cubical house has a thermal conductance of
1,536/r15 = 100 btu/hr-f, so it needs 24(68-18.9)100 = 118k btu to stay warm
on an average january day in milwaukee. suppose we put a lean-to sunspace
over the south side, 16' wide, 16' tall, and say 8' wide at the bottom, say
a single layer of 49" wide $1.25/ft^2 polycarbonate plastic over some 2x6s.
the average daytime high in january in milwaukee is 26.1 f. on average, 950
btu/ft^2/day of sun falls on a south wall, and the polycarbonate transmits
about 90% of this. let's say this 950 btu arrives over a 6 hour day. then the
sunspace gains 256ft^2x950x90% = 219k btu/day of which 118k is needed to keep
the house warm, leaving about 100k, which means the sunspace can have an
average temperature t that results in about 100k of thermal loss over the
6 hour day, so if the endwalls are reasonably good insulators, we have
6(t-26.1)(256/r1) = 100k, or t = 26.1+100k/(6x256) = 91 f...

putting a shallow frozen reflecting pond to the south of the sunspace would
raise the solar input by about 20% to 263k btu/day, increasing the net gain
to 144k btu/day and raising the sunspace temperature to 26.1+144k/(6x256)
= 120 f. (we measured a sunspace temp of 157 f in our little solar structure
near philadelphia last winter.) adding another layer of glazing or some dark
shadecloth inside the sunspace near the house wall would lower reradiation
losses and keep the solar warmed air near the house wall, making the air next
to the outer glazing closer to 70 f, so the sunspace glazing loss might
decrease to about 6(70-26.1)256/r1 = 67k btu per day, leaving 263k-118k-67k
= 78k to warm the water in the attic or room full of drums. if 78k btu/day
flows into the attic warmstore with r15 insulation above it, it wants to have
a temperature t where 24(t-18.9)256/r15 = 78k, so t = 18.9+78k/(24x256/15)
= 209 f :-) adding more attic or house insulation tends to further increase
the storage temperature...

norman saunders, pe, has been building houses with "attic warmstores" in cold
cloudy new england since 1944. some of them have long track records from his
electronic data logger/controllers, and some of them have no backup heating
systems at all... 

>i've seen an 80% solar dependant home. used for air conditioning, both
>hot and cold, as well as water and electricity. it's located in sun valley, 
>idaho, built by a boeing engineer and cost about $11m to complete, with only
>6,000 useable square feet. this is hardly a practical solution.

agreed, but bad examples don't necessarily prove something can't be done well.

nick