[Greenbuilding] Solar air heater efficiency vs absorber area and airflow

[nick pine]

Modeling an air heater with R1 single glazing with a nominal R2/3
inside air film resistance and an R1/3 outdoor film and 90% solar
transmission in 250 Btu/h-ft^2 sun on a 30 F day with 70 F inlet air
in a fixed font (can we fix this group to allow that?)...

  225 Btu/h 
     ---   Tp  Ra/AP  Ta   1/cfm
|---|-->|-------www---------www--- 70 F
     ---    |         |    ----->
            |         |     Uhg
         I| w      I| w
         g| w Rr   g| w Ra
         r| w      c| w
          v |       v |
            |         |     1/3   
             ---------------www--- 30 F  
                      Tg   ----->
                            Iga
 
Assuming Tg = 70 F to start makes the glazing loss to outdoor air
Iga = (70-30)3 = 120 Btu/h, which makes the useful heat gain
Uhg = 225-120 = 105 Btu/h, which makes the air temp Ta = 70+105/10
= 80.5 F with 10 cfm of airflow, which makes the convective glazing
gain Igc = (80.5-60)/R2/3 = 30.8 Btu/h, approximately, which makes
the absorber plate temp Tp = 80.5+(30.8+105)/R2/3/1ft^2 = 284 F, with
1ft^2 of plate area, which makes the average absolute plate-glazing
temp Tavg = 460+(284+60)/2 = 632 R, which makes the linearized
plate-glazing radiation resistance Rr = 1/(4x1.714E-9x632^3)
= 0.58 ft^2-F-h/Btu, which makes the radiative glazing heat gain
Igr = (284-60)/0.58 = 388 Btu/h (wow), which makes Tg = 0.9x70
+0.1(30+(388+30.8)/3) = 80 F, and so on...
     
10 D=6/12'collector depth (feet)
20 FOR AP = 1 TO 5'absorber plate area (ft^2)
30 FOR CFM=5 TO 20 STEP 5'collector airflow
40 V=CFM/D/88'air velocity (mph)
50 RA=1/(1.5+V/5)'airfilm resistance (ft^2-F-h/Btu)
60 TG=60'initial glazing temp (F)
70 FOR I=1 TO 100'relaxation iterations
80 IGA=(TG-30)*3'glazing loss (Btu/h)
90 UHG=225-IGA'useful heat gain (Btu/h)
100 TA=70+UHG/CFM'collector air temp (F)
110 IGC=(TA-TG)/RA'convective glazing gain
120 TP=TA+(IGC+UHG)*RA/AP'plate temp (F)
130 TAVG=460+(TP+TG)/2'average plate-glazing temp (R)
140 RR=1/(4*1.714E-09*TAVG^3)'radiation resistance
150 IGR=(TP-TG)/RR'radiative glazing gain (Btu/h)
160 TG=.9*TG+.1*(30+(IGR+IGC)/3)'new glazing temp (F)
170 NEXT
180 EFF=100*UHG/250'efficiency
190 PRINT 1000*AP+CFM;"'";TG,TA,TP,EFF
200 NEXT CFM
210 NEXT AP

AP  cfm   Tg (F)     Ta (F)     Tp (F)      Efficiency
  
1   05    74.78818   88.12709   160.9878    36.25419%
1   10    71.01676   80.19498   155.3407    40.7799
1   15    69.4577    77.10846   152.7532    42.65077
1   20    68.55936   75.4661    151.0895    43.72877

2   05    69.2611    91.44334   137.74      42.88668
2   10    64.71699   82.0849    129.8671    48.33962
2   15    62.89892   78.42022   126.4515    50.5213
2   20    61.89681   76.46548   124.39      51.72383

3   05    66.82973   92.90216   126.66      45.80433
3   10    61.9705    82.90885   117.7309    51.63541
3   15    60.05735   78.98853   113.958     53.93118
3   20    59.02503   76.89625   111.7519    55.16997

4   05    65.47826   93.71304   120.2377    47.4261
4   10    60.45372   83.36388   110.7095    53.45554
4   15    58.49396   79.30121   106.745     55.80725
4   20    57.44931   77.13261   104.4702    57.06084

5   05    64.62126   94.22724   116.0589    48.45449
5   10    59.4962    83.65114   106.1483    54.60457
5   15    57.50936   79.49813   102.0662    56.98878
5   20    56.45863   77.28121   99.75274    58.24965

The glazing and plate temps fall and solar collection
efficiency rises with more plate area and airflow.

A mesh plate can further improve efficiency
by keeping cooler inlet air near the glazing and
blocking some radiation from a back wall to the glazing.

Nick
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