Gary improved his first solar stock tank
http://www.builditsolar.com/Experimental/StockTank/SolarStockTankProto.htm
in
http://www.motherearthnews.com/do-it-yourself/solar-stock-tank-z10m0gri.aspx?page=3#ixzz1Xl5V3nYP
This might work better with a 10" Jolly ball
http://www.valleyvet.biz/ct_detail.html?pgguid=30e0742c-7b6a-11d5-a192-00b0d0204ae5&ccd=IGO043&gclid=CMX97c7QnKsCFYpM4AodCDiCgA
or a 10" Styrofoam ball
http://www.plasteelcorp.com/foamshapes/smoothfoam_styrofoam/10071.html
under a round hole in the floating foamboard.
Where I live in PA, 1000 Btu/ft^2 of sun falls on a south wall on an
average 30 F January day, so a 2'x2'x4' galvanized metal 70 F tank
with 2'x4' of R2 twinwall polycarbonate glazing with 80% solar
transmission over the south side would gain would gain 0.8x1000x8ft^2
= 6.4K Btu and lose about 6h(70-30)8ft^2/R2 = 960 Btu during a 6 hour
solar collection day, for a net gain of 5440 Btu.
A tank that's 4' vs 2' above the ground could gather more sun and be
easier to drain and clean. If the lower 2' of 4'x4' of glazing
transmits I = 6.4K/6h = 1067 Btu/h to the airspace below a 70 F tank
with 32 ft^2 of surface completely surrounded by air (not packed with
insulation), with a glazing resistance Rg = R2/16ft^2 and an Ra =
R2/3/32ft^2 tank surface airfilm resistance and a Thevenin equivalent
sunspace temp Vt = 30+IRg = 163 F, the tank will gain 6.4K Btu
directly plus 6h(Vt-70)/(Rg+Ra) = 3826 Btu from 70+3652/6hRa = 83 F
air, for a 6-hour net gain of 10,226 Btu.
With a T (F) tank temp, the air temp surrounding the tank Td = 0.857T
+ 23.9 F during the day. With Rv insulation (eg 2" Styrofoam walls and
cover), 12.8K Btu = 6h(Td-34)(16ft^2/R2+32ft^2/Rv)+18h(T-30)(8ft^2/
R2+24ft^2/Rv)+24h(T-30)8ft^2/Rv, so T = (2574Rv-3443)/(12.9Rv+131), if
I did that right. Rv = 10 makes T = 86 F.
On a cloudy day, with a tank thermal conductance G = 8ft^2/R2+32ft^2/
R10 = 7.2 Btu/h F and capacitance C = 100galx8.33Btu/F/gal = 833 Btu/
F, time constant RC = C/G = 116 hours, so the tank would cool to 35 F
in -116ln((35-30)/(86-30)) = 280 hours, after about 12 cloudy 30 F
days.
Nick