John Siegenthaler kindly supplied an equation for the heat output Q of 1' of

baseboard radiator fin tube with a low water-air temperature difference:

Q=G^.04*Nom*9.6865E-04*(Tw-Ta)^1.4172 Btu/h-ft,

where G is the flow rate in gpm, Nom is the nominal heat output in Btu/h-ft

with 200 F water and 65 F air, and Tw and Ta (F) are water and air temps.

I used this backwards in line 100 below to estimate the air-water conductance

of 64' (about $28) of Argo Technology Lo Trim fin tube containing 100 F water

near the top of an air heater on an average 32 F December day in Rochester NY,

to compare its output with 4 10'x21" homebrew collectors made with 40' x 2' of

0.018" Amerimax Home Products brown aluminum flashing silicone-caulked to 12

10' x 1/2" copper pipes (about $34.)

The air heater modeled had 144 ft^2 of single-layer Dynaglas US R1 corrugated

polycarbonate ("solar siding") with 90% light transmission inside 144 ft^2 of

U0.58 Thermaglas Plus twinwall polycarbonate with 80% light transmission.

The fin tube won in this case, with less labor and more confidence in

the output estimate.

20 SUN=.8*.9*560/6'solar gain (Btu/h-ft^2)

30 GG4/(1+1/.58)'glazing conductance (Btu/h-F)

40 TT2+144*SUN/GG'Thevenin equivalent temp (F)

50 NFT=8'number of 8' fin tubes

60 FTL=8*NFT'total fin tube length (ft)

70 GF=FTL*5'initial air-fin conductance (Btu/h-F)

80 FINGAIN=(TT-100)/(1/GG+1/GF)'useful heat output (Btu/h)

90 TA0+FINGAIN/GF'air heater temp (F)

100 GF=FTL*5^.04*690*9.6865E-04*(TA-100)^0.4172'adj fin conductance (Btu/h-F)

110 IF ABS(TA-TAL)>0.1 THEN TAL=TA: GOTO 80'iterate

120 PRINT NFT,TA,FINGAIN

130 BFU=4'number of 3-pipe Big Fin units

140 AU*17.55'Big Fin area (ft^2)

150 AC=1.75/6'half-fin area for conductance calc (ft^2)

160 GSF=2*.535'half-fin metal conductance (Btu/h-F)

170 GFP=2.35'half-fin to pipe conductance (Btu/h-F)

180 RC=1/GSF+1/GFP'sun-fin + fin-pipe resistance (F-h/Btu)

190 GSWF=A/(AC*RC)'sun-water fin conductance (Btu/h-F)

200 TTF0+SUN*A/GSWF'Thevenin equivalent temp (F)

210 GFA=1.5'fin-air conductance (Btu/h-F-ft^2)

220 TTG2+SUN*(144-A)/GG'glazing Thev equivalent temp (F)

230 FINLOSS=(TTF-TTG)/(1/GSWF+1/(3*A)+1/GG)'heat loss from fin to air (Btu/h)

240 FINGAIN=SUN*A-FINLOSS'useful heat output (Btu/h)

250 TA2+(144*SUN-FINGAIN)/GG'air heater temp (F)

260 PRINT BFU,TA,FINGAIN

units air temp (F) output (Btu/h)

8 126.2808 4693.044

4 126.7552 4667.969

Nick

nicksanspam@ece.villanova.edu wrote:

*> John Siegenthaler kindly supplied an equation for the heat output Q of 1' of*

*> baseboard radiator fin tube with a low water-air temperature difference: *

*> *

*> Q=G^.04*Nom*9.6865E-04*(Tw-Ta)^1.4172 Btu/h-ft,*

*> *

*> where G is the flow rate in gpm, Nom is the nominal heat output in Btu/h-ft*

*> with 200 F water and 65 F air, and Tw and Ta (F) are water and air temps.*

*> *

*> I used this backwards in line 100 below to estimate the air-water conductance*

*> of 64' (about $28) of Argo Technology Lo Trim fin tube containing 100 F water *

*> near the top of an air heater on an average 32 F December day in Rochester NY,*

*> to compare its output with 4 10'x21" homebrew collectors made with 40' x 2' of*

*> 0.018" Amerimax Home Products brown aluminum flashing silicone-caulked to 12*

*> 10' x 1/2" copper pipes (about $34.)*

*> *

*> The air heater modeled had 144 ft^2 of single-layer Dynaglas US R1 corrugated*

*> polycarbonate ("solar siding") with 90% light transmission inside 144 ft^2 of*

*> U0.58 Thermaglas Plus twinwall polycarbonate with 80% light transmission.*

*> The fin tube won in this case, with less labor and more confidence in*

*> the output estimate.*

*> *

*> 20 SUN=.8*.9*560/6'solar gain (Btu/h-ft^2)*

*> 30 GG4/(1+1/.58)'glazing conductance (Btu/h-F)*

*> 40 TT2+144*SUN/GG'Thevenin equivalent temp (F)*

*> 50 NFT=8'number of 8' fin tubes*

*> 60 FTL=8*NFT'total fin tube length (ft)*

*> 70 GF=FTL*5'initial air-fin conductance (Btu/h-F)*

*> 80 FINGAIN=(TT-100)/(1/GG+1/GF)'useful heat output (Btu/h)*

*> 90 TA0+FINGAIN/GF'air heater temp (F)*

*> 100 GF=FTL*5^.04*690*9.6865E-04*(TA-100)^0.4172'adj fin conductance (Btu/h-F)*

*> 110 IF ABS(TA-TAL)>0.1 THEN TAL=TA: GOTO 80'iterate*

*> 120 PRINT NFT,TA,FINGAIN*

*> 130 BFU=4'number of 3-pipe Big Fin units*

*> 140 AU*17.55'Big Fin area (ft^2)*

*> 150 AC=1.75/6'half-fin area for conductance calc (ft^2)*

*> 160 GSF=2*.535'half-fin metal conductance (Btu/h-F)*

*> 170 GFP=2.35'half-fin to pipe conductance (Btu/h-F)*

*> 180 RC=1/GSF+1/GFP'sun-fin + fin-pipe resistance (F-h/Btu)*

*> 190 GSWF=A/(AC*RC)'sun-water fin conductance (Btu/h-F)*

*> 200 TTF0+SUN*A/GSWF'Thevenin equivalent temp (F)*

*> 210 GFA=1.5'fin-air conductance (Btu/h-F-ft^2)*

*> 220 TTG2+SUN*(144-A)/GG'glazing Thev equivalent temp (F)*

*> 230 FINLOSS=(TTF-TTG)/(1/GSWF+1/(3*A)+1/GG)'heat loss from fin to air (Btu/h)*

*> 240 FINGAIN=SUN*A-FINLOSS'useful heat output (Btu/h)*

*> 250 TA2+(144*SUN-FINGAIN)/GG'air heater temp (F)*

*> 260 PRINT BFU,TA,FINGAIN*

*> *

*> units air temp (F) output (Btu/h)*

*> *

*> 8 126.2808 4693.044*

*> 4 126.7552 4667.969*

*> *

*> Nick*

*> *

seems like it wouldnt be that big a deal to get up to 171deg F. for a

solar ethanol still.

> John Siegenthaler kindly supplied an equation for the heat output Q of 1' of> baseboard radiator fin tube with a low water-air temperature difference:>> Q=G^.04*Nom*9.6865E-04*(Tw-Ta)^1.4172 Btu/h-ft,>> where G is the flow rate in gpm, Nom is the nominal heat output in Btu/h-ft> with 200 F water and 65 F air, and Tw and Ta (F) are water and air temps.>> I used this backwards in line 100 below to estimate the air-water conductance> of 64' (about $28) of Argo Technology Lo Trim fin tube containing 100 F water> near the top of an air heater on an average 32 F December day in Rochester NY,> to compare its output with 4 10'x21" homebrew collectors made with 40' x 2' of> 0.018" Amerimax Home Products brown aluminum flashing silicone-caulked to 12> 10' x 1/2" copper pipes (about $34.)>> The air heater modeled had 144 ft^2 of single-layer Dynaglas US R1 corrugated> polycarbonate ("solar siding") with 90% light transmission inside 144 ft^2 of> U0.58 Thermaglas Plus twinwall polycarbonate with 80% light transmission.> The fin tube won in this case, with less labor and more confidence in> the output estimate.>> 20 SUN=.8*.9*560/6'solar gain (Btu/h-ft^2)> 30 GG4/(1+1/.58)'glazing conductance (Btu/h-F)> 40 TT2+144*SUN/GG'Thevenin equivalent temp (F)> 50 NFT=8'number of 8' fin tubes> 60 FTL=8*NFT'total fin tube length (ft)> 70 GF=FTL*5'initial air-fin conductance (Btu/h-F)> 80 FINGAIN=(TT-100)/(1/GG+1/GF)'useful heat output (Btu/h)> 90 TA0+FINGAIN/GF'air heater temp (F)> 100 GF=FTL*5^.04*690*9.6865E-04*(TA-100)^0.4172'adj fin conductance (Btu/h-F)> 110 IF ABS(TA-TAL)>0.1 THEN TAL=TA: GOTO 80'iterate> 120 PRINT NFT,TA,FINGAIN> 130 BFU=4'number of 3-pipe Big Fin units> 140 AU*17.55'Big Fin area (ft^2)> 150 AC=1.75/6'half-fin area for conductance calc (ft^2)> 160 GSF=2*.535'half-fin metal conductance (Btu/h-F)> 170 GFP=2.35'half-fin to pipe conductance (Btu/h-F)> 180 RC=1/GSF+1/GFP'sun-fin + fin-pipe resistance (F-h/Btu)> 190 GSWF=A/(AC*RC)'sun-water fin conductance (Btu/h-F)> 200 TTF0+SUN*A/GSWF'Thevenin equivalent temp (F)> 210 GFA=1.5'fin-air conductance (Btu/h-F-ft^2)> 220 TTG2+SUN*(144-A)/GG'glazing Thev equivalent temp (F)> 230 FINLOSS=(TTF-TTG)/(1/GSWF+1/(3*A)+1/GG)'heat loss from fin to air (Btu/h)> 240 FINGAIN=SUN*A-FINLOSS'useful heat output (Btu/h)> 250 TA2+(144*SUN-FINGAIN)/GG'air heater temp (F)> 260 PRINT BFU,TA,FINGAIN>> units air temp (F) output (Btu/h)>> 8 126.2808 4693.044> 4 126.7552 4667.969>> Nick>