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re: what uses less energy?
17 feb 2001
harry opines:

>>...when using the dryer (gas, not electric), does it use less energy to
>>dry a load at a lower setting/longer time, or higher setting/shorter time?

>there isn't a single answer...

looks like harry is right. hotter is better, above about 110 f, but
cooler is better below that...

if l pounds of clothes have s ft^2 of surface and a fractional moisture
content m, with minimal water vapor flow resistance (unlike say, oranges),
they dry like a swimming pool, at a rate of 0.1s(pw-p) pounds of water
per hour, where pw (in inches of mercury) is the partial pressure of
water vapor near the clothes, inside the dryer, and pa is the partial
pressure in the rest of the dryer air.

pw only depends on the dryer temp t (f), but p also depends on the
intake airflow c (in cfm.) there's an optimal airflow for clothes drying
with minimum energy. too little airflow, eg c = 0 cfm, and the clothes
never dry, because the moisture never leaves the dryer, and the dryer heat
leaks out of the box through its insulation forever, as moisture builds up
until p = pw and the drying rate becomes zero. too much airflow, eg
infinite c, and the dryer wastes infinite energy heating an infinite
amount of air, even over a short time, while using infinite fanpower... 

if the room air has temperature tr and humidity ratio wr (pounds of
water per pound of dry air) and density d, then 60cdwr pounds of water
per hour enter the dryer via the room air. evaporation from clothes adds
0.1s(pw-p) pounds per hour to that, and the sum of these two incoming
water vapor flows equals the water vapor flow leaving via the dryer
exhaust air with greater humidity ratio w, which removes 60cdw pounds
of water per hour, ie 60cdwr+0.1s(pw-p) = 60cdw.

w = 0.62198/(29.921/p-1), which makes c = (fp^2+gp+h)/(j+kp), where
f= -0.1s and g = -f(pw+29.921) and h = 29.921fpw and j = 29.921(60)dwr
and k = -60d(wr+0.62198).

some dryers (asko) condense water out of moist dryer air while heating
room air with a heat exchanger. the calcs below assume the back of a dryer
closet contains an 8'x8' plastic film counterflow heat exchanger which
reduces the energy needed for drying and water vapor released to the room. 

seems like 100 f would be nice, with a 1.3 hour drying time and a pair of 
h&r's $5 humidistats at the top of the closet that turn on a 1500 w heater
below (maybe a quartz lamp or two) when the closet rh exceeds 53% (138%
at 70 f, so it will never turn on without wet clothes inside.) 

at 33.5 cfm, the outgoing air from the heat exchanger would enter the 
closet at 70+(100-70)(64ft^2x1.5btu/h-f-ft^2/(96+33.5)) = 92 f, and
the hot air would leave the exchanger at 78 f, so the air in the upgoing 
heat exchange chimney would have an average temp of 89 f and the air in
the downgoing chimney would average 81 f, and 33.5 cfm would naturally
flow when 16.6asqrt(8x(89-81)) = 33.5, with an a = 0.25 ft^2 vent at
the top and the bottom, eg 6"x6" holes, with a damper at the top.

with the damper closed, the temp could rise to 70+1500x3.41/17btu/h-f
= 371 f for a sauna. we could limit the temp to 200 f with thermostats.

h&r (800) 848-8001 sells navy surplus hair element
humidistats in 1x2x5" solid brass boxes full of holes, with a 20-80% range
and 3-6% differential and a spdt 7.5 a 125 vac switch that can be wired
to open or close on rising humidity. their catalog number is tm89hvc5203,
at $4.95 each. their catalog number tm92hvc2293 is a $2.50 8 a thermostat
with a range of 110 to 250 f +/-5%, normally closed. contacts open on
temperature rise and stay open until the temperature drops about 25 f. 


10 w=4:l=8:h=8'dimensions of dryer closet (feet)
20 s=2*(w*l+h*(w+l))'exterior closet surface (ft^2)
30 rv=15'us r-value of closet (ft^2-f-h/btu)
40 u=s/rv'thermal conductance of closet (btu/h-f)
50 tr=70'room temp (f)
60 rh=50'room rh (%)
70 pr=rh/100*exp(17.863-9621/(tr+459.57))'room air vapor pressure ("hg)
80 wr=.62198/(29.921/pr-1)'room air humidity ratio (water/dry air by wt)
90 d=.075'room air density (lb/ft^3)
100 cload=12'dry weight of clothes (lb)
110 cmoisture=50'moisture content after spin (%)
120 cw=cload*cmoisture/100'water weight (lb)
130 csurf=50'surface area of clothes (ft^2)
140 aq=.1*csurf
150 for td=70 to 180 step 10'closet temp (f)
160 pw=exp(17.863-9621/(td+459.57))'saturation pressure ("hg)
170 if td=70 then c=100:p=pr:drytime=cw/(aq*(pw-pr)):dryen=cw*1000:goto 270
180 ll=pr:ul=pw'initial range for closet partial pressure p ("hg)
190 s=(ul-ll)/3'optimize p for min energy
200 p=ll+s
210 gosub 360
220 dryenl=dryen
230 p=p+s
240 gosub 360
250 if dryen>dryenl then ul=ul-s: else ll=ll+s
260 if s>.01 goto 190'iterate to 0.01 step size
270 pwr=dryen/drytime/3.412'closet power (w)
280 c=int(10*c+.5)/10'round c (cfm)
290 drytime=int(100*drytime+.5)/100'drying time (h)
300 dryen=int(100*dryen/3412+.5)/100'drying energy (kwh)
310 pwr=int(pwr+.5)
320 rh=int(100*p/pw+.5)
330 print td;tab(6);c;tab(12);rh;tab(17);drytime;tab(23);dryen;tab(29);pwr
340 next
350 end
360 num=aq*p^2-aq*(29.921+pw)*p+aq*29.921*pw
370 c=num/(60*d*((wr+.62198)*p+29.921*wr))'optimum closet airflow (cfm)
380 dryrate=aq*(pw-p)'drying rate (lb h2o/h)
390 drytime=cw/dryrate
400 eff=96/(96+c)'condensing counterflow heat exchanger effectiveness
410 tco=tr+eff*(td-tr)'air temp entering closet from heat exchanger
420 dryen=cw*1000+drytime*(c*(td-tco)+u*(td-tr))'drying energy (btu)
430 return


temp  air   rh   time  energy power 
(f)   (cfm) (%)  (h)   (kwh)  (w)

 70   100   50   3.25  1.76   540 <--this power all comes from the
 80   33.4  47   2.19  1.92   879         home heating system...
 90   33.8  50   1.68  2.01   1196
 100  33.5  53   1.30  2.05   1576
 110  33.3  55   1.00  2.06   2059
 120  32.8  56    .77  2.05   2656
 130  32.5  57    .59  2.02   3429
 140  31.9  57    .45  1.99   4391
 150  31.3  57    .35  1.96   5626
 160  30.3  57    .27  1.93   7170
 170  29.1  56    .21  1.90   9120
 180  27.6  56    .16  1.88   11598

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