nick pine
unread,Sep 6, 2011, 4:51:13 PM9/6/11Sign in to reply to author
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to sunspace
At 85 F, 60% of the sugar in sweet corn turns to starch in 1 day, vs
6% at 32. And the sugar-to-starch conversion process generates heat.
If my farmer friend Barry throws 50 well-spaced 40-lb bags of corn
into our 42 F 13'x14' walk-in cooler with its 24K Btu/h compressor,
modeled as a 42 F battery in series with an 800 Btu/h-F conductor
with RC = 2000Btu/F/(800Btu/h-F) = 2.5 hours, the corn might cool
to 50 F in -2.5ln((50-42)/(90-42)) = 4.5 hours.
With 30 4"x10' thinwall PVC pipes with endcaps containing 1650 pounds
of 42 F water with an airfilm conductance of about 450 Btu/h-F hanging
on 2 inside walls of the cooler and no help from the compressor,
the final corn and water temps would be (90x2000+42x1650)/(2000+1650)
= 68 F. The combined series capacitance would be 2000x1650/3650 = 900
Btu/F. With lots of corn airfilm conductance, RC = 900/450 = 2 hours,
so the corn would be 68+(90-68)e^(-t/2) after t hours, eg 81 F after
1 hour, 76 after 2 hours, and so on.
With help from the compressor, the corn would be about 73 F after
1 hour, 62 after 2 hours, and so on...
10 TC=90'initial corn temp (F)
20 CC=2000'corn capacitance (Btu/F)
30 GC=800'cooler conductance (Btu/h-F)
40 TW=42'initial water temp (F)
50 CW=1650'water capacitance (Btu/F)
60 GW=450'pipe airfilm conductance (Btu/h-F)
70 FOR T = 0 TO 12.01 STEP .1
80 QC=.1*(TC-42)*GC'heatflow from corn to air (Btu/h)
90 QW=.1*(TW-TC)*GW'heatflow from water to air (Btu/h)
100 TC=TC-QC/CC'new corn temp
110 TW=TW-QW/CW'new water temp
120 IF ABS(T-INT(T+9.000001E-02))>.03 GOTO 140
130 PRINT T,TC,TW
140 NEXT T
hours corn temp water temp
0 88.08 43.30909
1 72.63548 52.23412
2 62.36746 55.90568
3 55.54095 56.63104
4 51.00246 55.81211
5 47.98513 54.28084
6 45.9791 52.51436
7 44.64543 50.77232
8 43.75876 49.18365
9 43.16928 47.80095
10 42.77737 46.63406
11 42.51682 45.67047
12 42.3436 44.88741
Nick