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<DIV><STRONG><FONT face=Courier>Modeling an air heater with R1 single glazing
with a nominal R2/3<BR>inside air film resistance and an R1/3 outdoor film and
90% solar<BR>transmission in 250 Btu/h-ft^2 sun on a 30 F day with 70 F inlet
air<BR>in a fixed font (can we fix this group to allow
that?)...</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier> 225 Btu/h <BR>
--- Tp Ra/AP Ta
1/cfm<BR>|---|-->|-------www---------www--- 70 F<BR>
--- |
|
-----><BR>
| |
Uhg<BR> I|
w I|
w<BR> g| w Rr g| w
Ra<BR> r|
w c|
w<BR> v
| v
|<BR>
| |
1/3
<BR>
---------------www--- 30 F
<BR>
Tg
-----><BR>
Iga<BR> <BR>Assuming Tg = 70 F to start makes the glazing loss to outdoor
air<BR>Iga = (70-30)3 = 120 Btu/h, which makes the useful heat gain<BR>Uhg =
225-120 = 105 Btu/h, which makes the air temp Ta = 70+105/10<BR>= 80.5 F with 10
cfm of airflow, which makes the convective glazing<BR>gain Igc = (80.5-60)/R2/3
= 30.8 Btu/h, approximately, which makes<BR>the absorber plate temp Tp =
80.5+(30.8+105)/R2/3/1ft^2 = 284 F, with<BR>1ft^2 of plate area, which makes the
average absolute plate-glazing<BR>temp Tavg = 460+(284+60)/2 = 632 R, which
makes the linearized<BR>plate-glazing radiation resistance Rr =
1/(4x1.714E-9x632^3)<BR>= 0.58 ft^2-F-h/Btu, which makes the radiative glazing
heat gain<BR>Igr = (284-60)/0.58 = 388 Btu/h (wow), which makes Tg =
0.9x70<BR>+0.1(30+(388+30.8)/3) = 80 F, and so on...<BR>
<BR>10 D=6/12'collector depth (feet)<BR>20 FOR AP = 1 TO 5'absorber plate area
(ft^2)<BR>30 FOR CFM=5 TO 20 STEP 5'collector airflow<BR>40 V=CFM/D/88'air
velocity (mph)<BR>50 RA=1/(1.5+V/5)'airfilm resistance (ft^2-F-h/Btu)<BR>60
TG=60'initial glazing temp (F)<BR>70 FOR I=1 TO 100'relaxation iterations<BR>80
IGA=(TG-30)*3'glazing loss (Btu/h)<BR>90 UHG=225-IGA'useful heat gain
(Btu/h)<BR>100 TA=70+UHG/CFM'collector air temp (F)<BR>110
IGC=(TA-TG)/RA'convective glazing gain<BR>120 TP=TA+(IGC+UHG)*RA/AP'plate temp
(F)<BR>130 TAVG=460+(TP+TG)/2'average plate-glazing temp (R)<BR>140
RR=1/(4*1.714E-09*TAVG^3)'radiation resistance<BR>150 IGR=(TP-TG)/RR'radiative
glazing gain (Btu/h)<BR>160 TG=.9*TG+.1*(30+(IGR+IGC)/3)'new glazing temp
(F)<BR>170 NEXT<BR>180 EFF=100*UHG/250'efficiency<BR>190 PRINT
1000*AP+CFM;"'";TG,TA,TP,EFF<BR>200 NEXT CFM<BR>210 NEXT
AP</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier>AP cfm Tg
(F) Ta (F) Tp
(F) Efficiency<BR> <BR>1
05 74.78818 88.12709
160.9878 36.25419%<BR>1 10
71.01676 80.19498 155.3407
40.7799<BR>1 15 69.4577
77.10846 152.7532 42.65077<BR>1
20 68.55936 75.4661
151.0895 43.72877</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier>2 05
69.2611 91.44334
137.74 42.88668<BR>2
10 64.71699 82.0849
129.8671 48.33962<BR>2 15
62.89892 78.42022 126.4515
50.5213<BR>2 20 61.89681
76.46548 124.39
51.72383</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier>3 05
66.82973 92.90216 126.66
45.80433<BR>3 10 61.9705
82.90885 117.7309 51.63541<BR>3
15 60.05735 78.98853
113.958 53.93118<BR>3 20
59.02503 76.89625 111.7519
55.16997</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier>4 05
65.47826 93.71304 120.2377
47.4261<BR>4 10 60.45372
83.36388 110.7095 53.45554<BR>4
15 58.49396 79.30121
106.745 55.80725<BR>4 20
57.44931 77.13261 104.4702
57.06084</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier>5 05
64.62126 94.22724 116.0589
48.45449<BR>5 10 59.4962
83.65114 106.1483 54.60457<BR>5
15 57.50936 79.49813
102.0662 56.98878<BR>5 20
56.45863 77.28121 99.75274
58.24965</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier>The glazing and plate temps fall and solar
collection<BR>efficiency rises with more plate area and
airflow.</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier>A mesh plate can further improve
efficiency<BR>by keeping cooler inlet air near the glazing and<BR>blocking some
radiation from a back wall to the glazing.</FONT></STRONG></DIV>
<DIV><STRONG><FONT face=Courier></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Courier>Nick</FONT></STRONG></DIV></BODY></HTML>