Refined poly mesh efficiency calc

[nick pine]

20 S=1.714E-09'Stefan-Boltzmann constant
30 DIM E(5,5)'combined emittance matrix
40 DATA 0,0,70,70,0,1,70,70,0,1,70,70
50 DATA 0.5,0.5,70,70,0.5,0.5,70,70
60 DATA 1,1,70,70
70 'above: solar absorption, IR absorption,
80 ' screen temp, air temp south of screen
90 TAUCUM=1'initialize cumulative layer transmission fraction
100 FOR I=0 TO 5'find each layer's solar absorption fraction
110 READ ASUN(I),AIR(I),TS(I),TE(I)
120 TAUCUML=TAUCUM
130 TAUCUM=TAUCUM*(1-ASUN(I))'cumulative layer transmission
140 ASUN(I)=ASUN(I)*TAUCUML'absorption fraction for layer I
150 NEXT I
160 FOR I=1 TO 4'find IR emittance fraction
170 FOR K=I+1 TO 5'for each pair of layers
180 E=AIR(I)
190 FOR J=I+1 TO K-1
200 E=E*(1-AIR(J))
210 NEXT J
220 E(I,K)=E*AIR(K)
230 E(K,I)=E(I,K)
240 NEXT K
250 NEXT I
260 TA=34'ambient temp (F)
270 SUN=.91^2*1000/6'sun through glazing (Btu/ft^2-h)
280 TR=70'air heater inlet temp (F)
290 CFM=1.2'airflow/ft^2
300 C=10'relaxation damping cap
310 FOR I=1 TO 499'relaxation iterations
320 FOR L=1 TO 5'mesh layer
330 GA=(TE(L-1)-TS(L))/(2/3+1/CFM)'layer air gain
340 GR=0'initialize rad gain
350 FOR K=1 TO 5
360 GR=GR+E(K,L)*S*((TS(K)+460)^4-(TS(L)+460)^4)
370 NEXT K
380 IF L=1 THEN GFLOW=(TA-TS(1))/1 ELSE GFLOW = 0
390 GFLOW=GFLOW+ASUN(L)*SUN+GA+GR'heatflow into layer
400 TS(L)=TS(L)+GFLOW/C'new layer temp
410 TE(L)=TE(L-1)-GA/CFM'air temp leaving layer
420 NEXT L
430 NEXT I
440 PRINT"998'";
450 FOR L=1 TO 4
460 PRINT INT(TS(L)+.5);INT(TE(L)+.5);
470 NEXT L
480 PRINT INT(TS(5)+.5);INT(TE(5)+.5)
490 EFF=100*6*(TE(5)-TR)*CFM*60/55/1000'solar collection efficiency
(%)
500 LEFF=100*(1000-6*(TS(1)-TA))/1000'glazing loss-based efficiency
510 PRINT "999'";EFF;LEFF

T1 air T2 air Ts1 air Ts2 air Tb air

73 72 109 93 154 127 156 143 160 152

64.62651 76.43108

This looks good to me now, with 2 layers of IR greenhouse film and 2
layers of 50% black greenhouse shadecloth. A single layer of R1 film
with 70 F air indoors and 34 F air outdoors and no radiation loss
would have a collector efficiency of 100(1000-6h(70-34))/1000 = 78.4%.

I suspect the 2 efficiencies above don't match because I approximated
the heat capacity of a C cfm airstream as C Btu/h-F when it's really
closer to 1.08C, but I'm inclined to believe the 2nd efficiency, which
is nicely close to an ideal 78.4% with no radiation loss.

Nick

PS: I can post, but I still can't see full text in this group. I
wonder why...

[Loren Bittner]

That Afib Protocol is called CHADS2.