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re: central heat
7 jan 2000
gskimin   wrote:

>thank you for this detailed analysis for se michigan, my home town.

you are welcome, in advance :-) you seem to have overlooked that that
detailed analysis was for seattle, but i've modified it for detroit,
which is a little cooler than seattle, but has about 50% more sun.
my brother lives near detroit too...

>...i do have some comments and questions:

i'll try to find some answers. 

>the 0.2 ach and the insulation values show your example is a very tight
>house. i would assume that this is new construction, with the r values
>shown. that's fine, but would be premium construction at extra first
>dollar costs.

i was thinking about a new house with sip walls (structural insulated
panels, ie glued osb/foamboard sandwiches.) these are manufactured by
about 100 companies in the us, and they are reasonably inexpensive,
with a materials cost of about $3/ft^2 for 6" walls with a real r-value
of about 24, including (minimal) thermal bridging. they also end up
with low air infiltration. one pa builder will guarantee 0.2 ach with
a blower door test. they go up quickly, with walls in large pieces up to
8'x20', screwed together with splines, with holes precut exactly for
windows and doors, which typically makes the total house cost (including
labor) less than average. 

>this should be considered in light of the average length
>of home ownership of less than five (or even ten) years.

seems to me a house like this would be more valuable than others, in
economic terms (heating bills), and also for people with a certain
environmental zeal or competitiveness. this would increase the resale
price, but i'm not sure a house like this would cost more to build.
for one thing, a polycarbonate roof is cheaper than shingles, etc.
for another, there's no furnace or water heater, and maybe no well,
if the heat storage tanks contain rainwater. fire insurance might be
$50/year cheaper with 3k gallons of water and an iso-approved or
dry hydrant. 

>...i can't picture your "32' long x 4' wide 30" diameter $20 polyethylene
>tube filled with 2" of water." is it round, a flattened tube, is there
>a picture of this? is it partly filled with water?

it's a flattened tube with a little water inside.

i can see how that could be unclear. a 30" diameter polyethylene film duct
as used for greenhouse air distribution collapses flat to about 48" wide. 
one local supplier sells these for 62 cents per linear foot, with a 4-year
guarantee. fill it with 2" of water when the sun is shining, and raise
both ends slightly to keep the water from running out. greek and israeli
greenhouses use these water-filled tubes between rows of plants to store
solar heat, with no concentration. i've boiled this poly with no loss of
strength. the duct would sit in an 30 cent/ft^2 epdm rubber-liner with
a lip to contain possible leaks. 

>does your heated attic have problems with ice dams?

no. then again, it's only heated for a few hours a day. and my attic has
no roof insulation or reflectors or concentrating trough. 

>not to pick a nit, but it looks like your calculation for attic air
>temperature may be a bit wishful.

my attic has been up to 130 f in december, and 143 in august, with lots
of windows and turbine vents open...

>i just can't imagine an attic, no matter how well insulated it was, attain
>a temperature of almost 120 f after six hours on a 34 f december "day"

the attic air would rise to 120 f very quickly a few minutes after it
starts getting sun, since air has so little thermal mass (my attic also
has two stone endwalls.) do you believe in ohm's law for heatflow?
if 250 btu/h of sun shines on a square foot of r1 surface with 90%
solar transmission and 34 f air on the other side, and the space behind
is perfectly insulated, the air inside would rise to 34+250x0.9 = 259 f,
using this linear model. fourth power radiation loss would make 250x0.9
= 0.174x10^-8((t+460)^4-(34+460)^4), so t = 200 f, still pretty hot.

if you don't believe that, try putting an oven thermometer on your lawn
in the sun some afternoon, with a storm window on top... it goes up to
300 or 400 f, and the grass quickly turns brown. 

>(...when its cloudy it never seems to get very bright).

>> nrel says a south wall in detroit gets an average daily dose of
>> 1.1 kwh/m^2 (417 btu/ft^2) of direct beam sun in december, when
>> the average outdoor temp is 28.3 f... 

they don't say whether this happens for 2 hours every day (unlikely)
or for 10 6 hour days in a row (also unlikely.) but it does happen,
as measured for 30 years, and the exact distribution in time makes
little difference if the house has enough thermal storage to keep
itself warm for say, 5 cloudy days in a row. a smart controller would
only fill or pump water through the solar trough during those short
times of direct beam sun, to minimize thermal loss over time.

>also, following your calculations, it looks like you start with the
>amount of heat withdrawn from the attic and use that to arrive at a
>required indoor temperature.

not exactly. i start by withdrawing a certain amount of energy and
then calculate what the attic temp would be in that case, given the
amount of solar energy that flows in. energy in = energy out, for the
attic, over an average day. useful energy flows out of the attic into
the house. withdrawing more and more useful heat up to the solar energy
inflow rate lowers the attic air temp to the outdoor temp. withdrawing
less raises it to the "stagnation point" where the amount of solar energy
that flows into the attic equals the amount of heat that flows out
to the outdoors, and the attic supplies no useful heat for the house.

>i believe a real simulation requires modeling the dyanmic system
>of heat gains, losses, storage and permeability/permitivity of
>each major component/system.

damn! one of my new year's resolutions was to stop arguing about
technical stuff with people who cannot spell :-) simulations are
capable of infinite elaboration, but one needn't consider these
electromagnetic and dielectric properties of a house unless
one is into the evils of metal bedsprings.

>differential and integral analysis would be required.

i disagree. perhaps you were tortured this way as a youth... :-)

   when we play tennis or walk downstairs we are actually solving
   whole pages of differential equations, quickly, easily and without
   thinking about it, using the analogue computer which we keep in our
   minds. what we find difficult about mathematics is the formal,
   symbolic presentation of the subject by pedagogues with a taste for
   dogma, sadism and incomprehensible squiggles.

   from _structures: why things don't fall down_, by j. e. gordon

we only need a few monthly averages and back of the envelope calcs here. 

>also, i can't quite see how the the concentrated solar could raise the
>tube to over 200 f without enormous losses to the surrounding space.
>again, integral analysis of gains and losses would be needed, but
>without understanding the tube's geometry i can't even start a steady
>state analysis.
 
would you believe 150 f? :-)

well, take a look at the numbers again. lots of solar power concentrates
into a small area, with small thermal loss since it is a small area. and
the attic air temp is fairly high, which further lowers the loss from
the small area (which also increases the air temp, which in turn raises
the amount of energy that can be collected with an air-water heat exchanger
for heating the house on an average day, in a nice symbiosis.)

>finally, my guess is that cooling your thermal storage to 80 f, against
>a 70 f house temperature, would be difficult. you would need a very
>large (expensive) to get reasonably fast heat transfer out of a media dt
>of 10 f.

not with a hydronic floorslab in a well-insulated house--244k btu/day
is about 10k btu/h. a 32'x32' slab with 1500 btu/h-f of slab-air thermal
conductance can supply 10k btu/h of house heat with a 10k/1500 = 6.7 f
slab-air temperature difference. the slab would distribute and store
solar heat collected from attic air with an air-water heat exchanger
(like an auto radiator) on an average day, and the hot rainwater tanks
(heated with the concentrator) would only supply heat for cloudy days. 

here's the detroit rewrite:

a 32'x32'x16' tall house with real r24 6" sip walls and ceiling, 176 ft^2
of r4 windows with 50% solar transmission, and 0.2 house air volumes per
hour of air leaks has a thermal conductance of 176ft^2/r4 = 44 btu/h-f for
the windows plus 78 for the walls plus 85 for the ceiling. the air leakage
rate is 0.2achx32x32x16/60 = 109 cfm, which adds about 109 btu/h-f to the
conductance, making the total about 316 btu/h-f.

the house needs about 24h(70-28.3)316 = 316k btu to stay warm on an average
december day in detroit, when 410, 160, 270, 270 and 610 btu/ft^2 of sun
fall on a level surface and north, east, west, and south windows. if 10,
15, 25, and 50% of the windows face north, east, west, and south, they
will collect a total of 38k btu/day of sun (solar heating the house about
12%.) a frugal 300 kwh/month of internal electrical usage adds 34k btu/day
of heat, so the house needs an additional 316k-38k-34k = 244k btu/day
for 100% solar heating in december.
 
with a 4' stemwall above the attic floor and a 3:4 pitch roof with 90%
solar transmission, we can collect about 0.9x410x32'x16'= 189k btu of
overhead sun and about 0.9x610x32'x16' = 281k of sun from the south,
470k btu/day altogether. line the north wall with masonite covered with
nielsen's (www.snomo.com/mylar.html) 90% reflective 9 cent/ft^2 film and
collect about 0.9x0.9x0.9x417x16'x32'= 156k btu/day of south sun in a
32' long x 4' wide 30" diameter $20 polyethylene tube filled with 2" of
water along the base of the north wall. the reflector would focus at
y^2/(4x) = 16'^2/(4x16') = 4' from the north wall at dawn, and closer
during the day.

if we withdraw 244k btu/day of heat from the attic, some warm air as well
as heat from skylights and sun concentrated in water, and most of the attic
walls are well-insulated, with an average attic air temp t over a 6 hour
solar collection day in december, the r1 south attic roof will lose about
6h(t-32f)16'x20'/r1 btu/day = 470k - 244k, making t = 32 + 226k/(6x16x20)
= 150 f (which also lowers the daytime heat loss from the house ceiling.)

putting 156k btu/6h = 26k btu/h of sun into the 4'x32'/r0.67 = 192 btu/h-f
tube makes the water collection temp 150+26kbtu/h/192btu/h-f = 285 f,
which seems good enough :-) if the water turns out to be cooler, we might
raise that temp with a controller that only fills or pumps the trough
during times of direct beam sun.

the house needs 5d(316k-38k) = 1410k btu for 5 cloudy 28.3 f days in a row.
(are cloudy days warmer in detroit?) if this comes from g gallons of 150f
rainwater cooling to 80 f, (150f-80f)gx8btu/gal = 1410k, so g = 2518. we
might use a couple of $419.95 1500 gallon 84"dx60" tall polyethylene tanks
in/under the house, surrounded by insulation...

nick

nicholson l. pine                      system design and consulting
pine associates, ltd.                           (610) 489-1475/0545 
821 collegeville road                           fax: (610) 489-7057
collegeville, pa 19426                     email: nick@ece.vill.edu

computer simulation and modeling. high performance, low cost, solar heating
and cogeneration system design. bsee, msee. senior member, ieee. registered
us patent agent. web site: http://www.ece.vill.edu/~nick 




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