Solar closets in a nutshell

To: london@sunsite.unc.edu
Subject: Solar closets in a nutshell
From: Nick Pine <nick@vu-vlsi.ee.vill.edu>
Date: 22 Dec 1995 15:34:45 -0500

Fred A <fabrams@fast.net> wrote in sci.engr.heat-vent-ac:
>amuller@dca.net (Alan Muller) writes:
>>I'm concerned about the electrical consumption of my oil
>>burner "gun," though I have yet to measure the consumption.

>Nothing is free. If you had a gas or electric hydronic system you would
>still have the circulator pump, and the zone valves. With gas you may
>still have the vent damper, burner motor; and, or other accessories.
>Electrical consumption for heating systems is a fact of life, and not
>a big deal...

It is for us energy misers :-) The sun is free, and plastic film backdraft
dampers use no electricity. If the only electrical power used in your
mostly passive solar heating system is to move two Honeywell MLS642LS
dampers and D6161A1001 actuator motors, and they only consume two watts
when they are moving, that's pretty close to free :-)

Important points:

o Glass is a very poor insulator, compared to an insulated wall.
o Trombe walls are very inefficient, because they store solar heat behind
  glass, and that heat leaks back out to the cold outdoors all night.
o Low-thermal-mass sunspaces, eg those made with thin polycarbonate glazing,
  make better solar heaters than Trombe walls. We want an insulated wall
  between the sunspace and the house, and dampers in about 5% of the insulated
  wall, or perhaps fans (1-2 cfm/ft^2 of glazing) that move warm air from the
  sunspace into the house on sunny days. The sunspace fan or motorized damper
  should be in series with a cooling thermostat in the sunspace and a heating
  thermostat in the house.  At night, the sunspace should get icy cold,
  leaving the heat stored inside the house, in the thermal mass of the house.
o Water stores 3 times more heat than masonry by volume, with lower thermal
  resistance, so a box full of water containers can have 1/3 the volume of a
  rock bed, and lower airflow resistance as well, so it can transfer heat
  better by natural convection, or with minimal fan power, vs a rock bed.
o It is good to have a separate heat battery, so we can charge it up to a
  high temperature on sunny days, and discharge it in a controllable way to
  heat the house to a constant temperature during a week of cloudy days.
  If we _live inside_ the heat battery, we cannot do that...
o The heat battery should have some sealed containers of water, and the
  total surface area of the water containers should be 5-10 times that
  of the glazing.
o Ohm's law for heatflow tells us how much heat we need for a house on
  an average day. U = hours x (Tin - Tout) (sum of A's over Rs) Beware
  of thermal bridges!
o This tells us how much low-thermal mass sunspace glazing we need,
  since each square foot of sunspace glazing gathers about 1000 Btu or
  300 watt-hours on an average day.
o The daily heat loss also tells us how much water we need in the heat
  battery--enough for 5 days without sun, say (this needs further study.)
  A pound of water raised 1 degree F stores 1 Btu.
o Solar closets can also heat water for houses, and serve as saunas or
  clothes-drying areas.

Other points:

o What's wrong with Trombe walls?
  (They are 25 times less efficient than low-thermal-mass sunspaces.)
o What's wrong with direct gain houses?
  (Large temperature swings from day to night, steadily decreasing
  temperatures over a few days without sun, large backup heat requirement
  in cloudy climates, lack of privacy, excessive glare, can't put rugs on
  the floor, expensive masonry construction, no solar water heating,
  "optimal ratio of glass to floorspace" dilemma, etc.)
o Temperature swings in a solar house
  (U delta t = C delta T, RC time constant)
o What's wrong with "solar panels"?
  (Expensive, need pumps, antifreeze, heat exchangers, roof climbing-->
  broken bones, roof mounting-->inefficient, surrounded by cold air
  and wind, with back losses lost to ambient, vs back losses that heat
  the house, roof mounting-->leaks in roof penetrations and reroofing
  difficulties, roof mounting-->expensive rigid framework and installation
  labor, etc, etc.)
o Efficiency vs. cost-effectiveness
  (Do you want a Mercedes or do you want transportation?)
o What's wrong with PV? :-)
  (100 times less cost-effective than passive solar)
o Ohm's law for heatflow
  (U = (hours)(Tin-Tout) x area/R-value)
o Heat capacity and storage
  (Rocks, 22 Btu/ft^3/degree F
  Water, 62 Btu/ft^3/degree F
  Air, 0.02 Btu/ft^3/degree F
  A cubical solar closet L feet on a side has a time constant of L^2 days.)
o Why water vs. rocks?
  (Cheaper, easier to move, lower thermal resistance, 3 times more heat
  capacity, lower airflow resistance.)
o Why fans vs. blowers?
  (Blowers use hundreds of watts. Fans use 10s of watts.)
o Is it wrong to waste solar energy?
  (No, if using a bit more sunspace glazing and a hotter sunspace lets one
  use a damper instead of a fan, and no, if it costs less to underinsulate
  the sunspace wall and open a house cooling damper during the day.)
o Why dampers vs. fans?
  (Some motorized dampers only use 2 watts when moving, and zero watts in a
  fixed position. Using these with thermostats allows very accurate room temp
  control, with very little electrical power consumption.)
o Convective loop heat flow
  (The amount of air in cfm that flows through a damper in an unrestricted
  chimney with height h feet and openings of Ad ft^2 at the top and bottom
  and a temperature difference of delta T from top to bottom is approximately
  Q=16.6 Ad sqrt(h*delta T). The amount of heat that moves through the dampers
  in Btu/hour is approximately U = Q delta t.)

An example:

10 'ball park solar closet house design
20 TA=32'average December ambient temp
30 TCOLD=-10'coldest December ambient temp
40 SUN=1000'average amount of sun falling on sunspace glazing (Btu/ft^2/day)
50 DL=6'average number of hours of sun per day
60 TR=68'room temp
70 L=12'house length
80 W=8'house width
90 H=8'house height
100 AW=2*(L*W+L*H+W*H)'outside surface area
110 RW=23'R-value of outside surface of house
120 DHL=24*(TR-TA)*AW/RW'daily heat loss
130 DHLC=24*(TR-TCOLD)*AW/RW'heat loss on coldest day
140 AV=8*8/144'damper area (ft^2)
150 DF=AV*161.6*SQR(H)'damper factor
160 TSS=TR+(DHL/6/DF)^(2/3)'minimum ss temp to supply average daily heat
170 PRINT TSS;"F, minimum sunspace temp to supply average daily house heat
180 C=4000'pounds of water in solar closet
190 ATM=200'thermal mass surface area
200 RM=2/3'thermal mass surface R-value
210 LC=4'closet length
220 WC=4'closet width
230 HC=8'closet height
240 RC=20'R-value of solar closet surface
250 'find min solar closet temp ness to heat house on an average day w/o sun
260 TCM=TR+(DHL/24/DF)^(2/3)
270 PRINT TCM;"F, closet temp ness to heat house on an average day w/o sun"
280 'find min ss solar closet temp to provide heat for 5 days w/o sun
290 TCS=TCM+5*DHL/C
300 PRINT TCS;"F, min steady state solar closet temp for 5 day heat storage
310 'find avg closet cfm to keep house warm on coldest day w/o sun"
320 CFM=DHLC/24/(TCS-TR)
330 PRINT CFM;"cfm, avg closet airflow to heat house on coldest day w/o sun
340 'find average daily solar closet loss at that steady state temp
350 DCL=24*((TCS-TR)*(HC*WC+HC*LC)/RC+(TCS-TA)*(HC*WC+HC*LC)/RW)
360 AC=2*2'solar closet damper area
370 DFC=16.6*AC*SQR(H)'solar closet damper factor
380 TCP=TCS+(DCL/6/DFC)^(2/3)
390 PRINT TCP;"F, sunspace temp ness to make 5 day closet air temp"
400 'find min glazed area to make tcp, while providing heat and closet heat
410 AG=(DHL+DCL)/(SUN-DL*(TCP-TA))
420 PRINT AG;"ft^2, min glazed area to make 5 day closet air temp"

RUN

 74.29121 F, minimum sunspace temp to supply average daily house heat
 70.49667 F, closet temp ness to heat house on an average day w/o sun
 94.53841 F, min steady state solar closet temp for 5 day heat storage
 65.42774 cfm, avg closet airflow to heat house on coldest day w/o sun
 97.65994 F, sunspace temp ness to make 5 day closet air temp
 41.99063 ft^2, min glazed area to make 5 day closet air temp