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re: modeling an air heater with a massy ceiling
5 jan 2005
>we might store overnight heat for an 8' r10 cube near phila with a 4'x8'
>air heater that keeps 70 f air near the glazing using 16' of fin-tube
>under the ceiling...

>the tank must be larger for 5 cloudy days in a row. more insulation (r10
>isn't much) or an 8'x8' vs 4'x8' air heater would raise the water temp and
>reduce the tank size...
looks like a 4.2'x8' air heater will do, with half the previous water flow,
ie 0.05 gpm during the day and 0.02 (from thermosyphoning) at night.

10 rv=10'wall and ceiling us r-value (ft^2-h-f/btu)
20 gc=5*8*8/rv'cube to outdoor conductance (btu/h-f)
30 ta=30'outdoor temp (f)
40 ts=50'setback temp (f)
50 eds=2*(70-ta)*gc+16*(ts-ta)*gc'daily heat storage requirement (btu)
60 edsh=eds/6'daily heat storage rate (btu/h)
70 ssun=1000'daily sun on south wall (btu/ft^2)
80 aha=4.2*8'air heater area (ft^2)
90 nahg=.9*ssun*aha-6*(70-ta)*aha/1'net air heater gain (btu/day)
100 edw=6*(70-ta)*(4*64-aha)/rv'6-hour heat loss from walls (btu)
110 tc=ta+(nahg-eds-edw)/(6*64/rv)'average daytime air temp under ceiling (f)
120 lu=16'ceiling fin-tube length (feet)
130 gu=5*lu'ceiling fin-tube to air conductance (btu/h-f)
140 qd=26.5'daytime water flow rate (btu/h-f)
150 tind=tc-edsh/(qd*(1-exp(-gu/qd)))'required daytime input temp (f)
160 toud=tind+edsh/qd'daytime output and nighttime input temp (f)
170 dawnheat=(ts-ta)*gc'heat requirement at dawn (btu/h)
180 qn=dawnheat/(toud-tind)'nighttime water flow rate (btu/h-f)
190 ll=-(log(1-((dawnheat/qn)/(toud-ts)))*qn)/5'floor fin-tube length (feet)
200 print ts,tind,toud,tc'ts,tcold,thot,tc (f)
210 print qd,qn'day and night water flow rates (lb/hour)
220 print lu,ll,lu+ll'upper, lower, total fin tube length (feet)
230 ecs=8*(70-ta)*gc+16*(50-ta)*gc'cloudy day heat requirement (btu)
240 ctank=(eds+5*ecs)/(toud-tind)'stratified tank volume (pounds of water)
250 print ctank,ctank/8.33,ctank/(8.33*8)

setback       tcold         thot          tceiling
50            50.52835      131.0315      135.1666 f

daytime       nighttime
water flow    water flow
26.5          7.95 lb/hour

ceiling       floor         total 
fin-tube      fin-tube      fin-tube
16            8.002228      24.00223 feet

stratified tank size
1431 lb       171.7887 gal  21.47359 ft^3.


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