K'Al thermal conductivity (Btu/h-F-ft)
T=.018/12'Al coil stock thickness (feet) = 0.0015
D=2'Al coil stock width (feet)
OD=5/8/12'Cu pipe OD (feet) = 0.0521
L=D/6-PI*OD/4-OD/2'half-fin width (feet) = 0.266
If the half-fin Al conductance is kT/L = 0.535 Btu/h-F, ie 0.282 W/K,
and 225Btu/h-ft^2x0.266ft^2 = 60 Btu/h ie 17.5 watts of sun falls on
a 1'x0.266' half-fin with no heat loss to the surroundings, the temp
rise from the fin to the pipe might be about 17.5/0.282/2 = 33 K.
IIRC, RTV (eg GE silicone II caulk) has about 0.2 W/mK, so a 1 m cube
would have a face-face conductance of 0.2 W/K, or 200 W/K, if it were
only 1 mm thick, or 200x0.00622 = 1.24 W/K, if the faces were only
0.00622 m^2 (the half-fin to pipe contact area), so it looks like
the caulk would not be the bottleneck, with about 1.24/0.282 = 4.4X
the thermal conductance of the half-fin, if I did that right.
This really seems like quite a temperature "loss". That and the
thermal radiation is linked to the 4th power, seems like a lot of loss.
Or have I misread this.
Oops, yes. It's a rise from the pipe to the fin.
Glass and polycarbonate block that.
That may be unimportant for Big Fins in a sunspace, where the fin heat loss
ends up in sunspace air which heats a house. Even a perfectly-conducting
fin will lose heat to the surroundings. Foamboard on the back can help...
30 K'Al thermal conductivity (Btu/h-F-ft)
40 T=.018/12'Al coil stock thickness (feet)
50 D=2'Al coil stock width (feet)
60 OD=5/8/12'Cu pipe OD (feet)
70 L=D/6-PI*OD/4-OD/2'half-fin width (feet)
80 HB=1.5/2'one-sided airfilm conductance (Btu/h-F-ft^2)
90 NL=SQR(2*HB/(K*T))*L'fin efficiency term
110 FEFF0*TANHNL/NL'fin efficiency (%)
120 Wr*(L+OD/2)'tip-to-tip fin width (inches)
130 PRINT W,FEFF'fin width (in) and efficiency (%)
140 AC=2*W/12*10'collector area (ft^2)
150 ACEFF*FEFF/100'effective collector area (ft^2)
160 AGH'total glazed area (ft^2)
170 SUNPOWER=.9*250'full-sun heat into box (Btu/h-ft^2)
180 FINPOWEREFF*SUNPOWER'full-sun into fins (Btu/h)
190 BOXPOWER=AG*SUNPOWER'full-sun heat into box (Btu/h)
200 TA4'average daytime outdoor temp in Phila in January (F)
210 BOXNET=BOXPOWER-FINPOWER'net global sun into box (Btu/h)
220 BOXTT=TA+BOXNET/AG'Thevenin equivalent box temp (F)
230 DHWTEMP0'average collector water temp (F)
240 DHWPOWER=FINPOWER+(BOXTT-DHWTEMP)*1.5*ACEFF'water heating (Btu/h)
250 BOXTEMP=TA+(BOXPOWER-DHWPOWER)*1/AG'air temp in box (F)
260 SUNHOURS=4'full-sun hours in January in Phila
270 DHWENERGY=SUNHOURS*DHWPOWER'dhw energy (Btu/day)
280 COST=2*AG+2*AC'water heater materials cost ($)
290 PRINT AC,BOXTEMP,DHWENERGY,COST
fin width efficiency
fin area box air daily heat cost
35.09126ft^2 102.9664F 29958.45Btu $66.1825