Several companies make ventless dryers that condense water vapor from dryer air with a dehumidifier or cool water which gets discarded or a large fan and an air-air heat exchanger, but they are expensive and often waste sensible heat, and people complain they are noisy and use more energy and take longer than conventional dryers...
It looks like most of the sensible heat can be recovered by heating an incoming airstream (Tlo and Wlo below), with a dryer output (Tdo and Wdo), but it seems hard to reduce the latent heat. Maybe the best we can do is to run the dryer output into one side of an air-air heat exchanger with condensation on the dryer air side, then run the (Tao, Wao) airstream past some cool water pipes, then run the (Tlo, Wlo) airstream into the other side of the air-air hx, like this, viewed in a fixed-font:
125 0.08 -------------- 113 0.07 ---------------------- ------- Tdo, Wdo | | Tao, Wao | | | |----->----------->------------->------water containers->- | | | | condensation | | condensation | | | dryer | |--------------| |------------------- | | | |-----<-----------<-------------<------water containers-<- | ------- Tdi, Wdi | | Tlo, Wlo | condensation | 117 0.01 -------------- 67 0.01 ---------------------- air-air hx condensing hx
This requires finding the dryer air inlet and adding a hose for that...
The air-air hx could be 32 2'x4' vertical plastic film layers on 3/4" centers inside half of a 4'x4'x2'-tall box. The condensing hx could be
16 4"x4' thinwall PVC pipes in the other half of the box, plumbed close in a 4x4 array with 3/4" PVC male adapters as bulkhead fittings, with
96' of 4" pipe above the box in 2 2'4x4' pipe shelves with 4 pipe posts and a back to add more thermal mass and act as a passive radiator with
160' of pipe containing 870 pounds of water with a 5.8 hour external time constant. The box would contain enough pipe surface (about 70 ft^2) to make its condensing heat exchange effectiveness close to 100%. If one load of laundry per day adds 12K Btu, it might warm from 60.26 to 12K/870 = 74.05 by the end of the load and cool back to 60.26 23 hours later...
20 DRYPOW=5000'dryer power (W)
30 DRYHEAT=3.412*DRYPOW'dryer heat (Btu/h)
40 CFM=60'dryer airflow (cfm)
50 AC=200'clothing area (ft^2, both sides)
60 TDI=116.842'initial dryer inlet temp est. (F)
70 WDI=.01443'initial dryer inlet hum rat est.
80 PRINT "Tdi =";TDI,"Wdi =";WDI
90 ALPHA=.62198
*4.5*CFM'terms
100 BETA=4.5
*CFM*WDI
110 GAMMA=.1
*AC
120 TERM1=(DRYHEAT+TDI*CFM)/(100*AC)
130 TERM2=CFM/(100*AC)
140 TDO=120'initial dryer temp est (F)
150 PW=EXP(17.863-9621/(460+TDO))'vapor pressure near clothes ("Hg)
160 A=GAMMA
170 B=-(ALPHA+BETA+GAMMA
*(29.921+PW))'quadratic term
180 C=29.921*(BETA+GAMMA*PW)'quadratic term
190 PAO=(-B-SQR(B^2-4
*A*C))/(2*A)'vapor pressure in dryer air ("Hg)
200 TDOH=9621/(17.863-LOG(TERM1+PAO-TERM2*TDO))-460'new dryer temp est (F)
210 IF ABS(TDOH-TDO)/TDO>.0001 THEN TDO=TDOH:GOTO 150'iterate to 0.01%
220 LHEAT=100
*AC*(PW-PAO)'latent heat removal rate (Btu/h)
230 DRYTIME=12000/LHEAT'drying time (hours)
240 DRYENERGY=5*DRYTIME'drying energy (kWh)
250 WDO=.62198/(29.921/PAO-1)'dryer output humidity ratio
260 PRINT "Tdo =";TDO,"Wdo =";WDO
270 TROOM=60'basement air temp (F)
280 LIPIPE=4
*16'length of 4" pipe inside box (feet)
290 LEPIPE=96'length of 4" pipe outside box (feet)
300 CCHX=62.33*3.14159*(4/12/2)^2*(LIPIPE+LEPIPE)'heat cap (Btu/F)
310 SPIPE=3.14159*4/12*LEPIPE'exposed pipe surface (ft^2)
320 RC=CCHX/(1.5*SPIPE)'condensing hx time constant (hours)
330 DT=12000/CCHX'temp rise during drying (F)
340 TMIN=(TROOM+(DT-TROOM)*EXP(-23/RC))/(1-EXP(-23/RC))'min cond hx temp (F)
350 TLO=TMIN+DT/2'average condensing hx output temp (F)
360 PLO=EXP(17.863-9621/(460+TLO))'vapor pressure after cond hx ("Hg)
370 WLO=.62198/(29.921/PLO-1)'hum rat after cond hx
380 N=24/.75'number of films in air-air hx
390 A=N
*2*4'air-air hx area (ft^2)
400 NTU=1.5*A/CFM'air-air hx NTU
410 E=NTU/(NTU+1)'air-air hx effectiveness
420 TDI=TLO+E
*(TDO-TLO)'dryer input air temp (F)
430 AAHEAT=CFM*(TDI-TLO)'air-air hx heat (Btu/h)
440 TMX=TDO+1000
*60*.075*WDO-AAHEAT/CFM'terms
450 TMY=TMX+4500*.62198
460 TERM3=17.863-LOG(29.921)
470 TAO=110'initial Tao est (F)
480 TAOH=9621/(TERM3-LOG((TMX-TAO)/(TMY-TAO)))-460
490 IF ABS(TAOH-TAO)/TAO > .0001 THEN TAO=TAOH: GOTO 480
500 WAO=(TMX-TAO)/4500'hum rat
510 PRINT "Tao =";TAO,"Wao =";WAO
520 PRINT "Tlo =";TLO,"Wlo =";WLO
530 WDI=WLO'no condensation in cold stream of air-air hx
540 PRINT "Tdi =";TDI,"Wdi =";WDI
550 PRINT "Troom =";TROOM,,"Tmin =";TMIN
560 PRINT"Drytime =";DRYTIME,"Dryenergy =",DRYENERGY
Tdi = 116.842 F Wdi = .01443 humidity ratio Tdo = 124.6056 Wdo = 7.579565E-02 Tao = 113.006 Wao = 6.733185E-02 Tlo = 67.15541 Wlo = 1.443278E-02 Tdi = 116.8421 Wdi = 1.443278E-02
Troom = 60 Tmin = 60.26116
Drytime = .7242576 hours Dryenergy = 3.621288 kWh
We can simulate the dryer alone by changing line 60 above to
60 TDI=60'initial dryer inlet temp est. (F)
Drytime = .8868306 hours Dryenergy = 4.434153
So this box might save 60(0.887-0.724) = 10 minutes of drying time and put 3.62x3412 = 12350 Btu of heat (but no water vapor) into the house, vs exhausting 4.43x3412 = 15115 Btu of warm moist air from the house with the dryer alone.
At today's energy prices, this might save 2(4.43-3.62)10 = 16 cents/day :-)
Nick