[Greenbuilding] A Solar Hot Tub

[Nick Pine]

Dan writes:

> Like any storage system, inluding the most expensive double insulated solar storage tanks, there is a temperature loss. But even with this loss a hot tub "stores hot water. 

But a hot tub can't store any heat if its temperature never changes...

>A typical hot tub use pattern is to set a heater on a timer. At our house, the timer is set from 6-8 pm. At six the pump and heater turn on at it only takes about twenty minutes to bring the hot tub temperature up to 104, after which the heater turns off and the pump circulates the water through the filter.

Perhaps you mean the heater initially turns off after the tub reaches 104, then cycles as needed to maintain 104 F until 8 PM. 
 
> Some people might set their hot tubs on 24/7, but it's unusual and makes no sense.

That would seem to make sense for people who like to jump into the tub at any time, without waiting for it to reheat.

> But with solar, the energy is free so all day long when the sun shines the tub will be maintained at 104. Nothing wrong with that.

That kind of solar heating doesn't seem to save much energy. Consider 4 scenarios:

1. "100% solar heat" with a secondary storage tank.
2. solar heat for 6 hours per day, with a constant 104 F tub temp
3. solar heat for 6 hours per day, with electric reheat on a sunny day
4. electric reheat on a cloudy day.

   Eon        Eoff          Esun          Elec          Delay
   (Btu/day)  (Btu/day)     (kWh/day)     (kWh/day)     (minutes)

1  5409.405   7496.244      3.782429      0             0
2  5409.405   7496.244      .4323834      3.350046      0
3  5390.759   7496.244      1.364025      2.41294       8.636646
4  5358.812   7496.244      0             3.767602      62.82312

In scenario 1 the sun provides all the heat for up to 5 cloudy days in a row. No electricity is used for heat. 
In scenario 2 the sun only provides 13% of the heat, keeping the tub 104 F with no reheat delay.
In scenario 3 the sun provides 56% of the heat, like a very good direct gain house, with a small delay.
In scenario 4 the sun provides no heat, with a very large inconvenient reheat delay.

The biggest heat loss (Eoff) happens with the cover off, and scenarios 2-4 don't help at all with that.

If cloudy days are like coin flips, averaging scenarios 3 and 4, this "solar heated" tub would only be 18% solar heated on an average day, using 3.1 kWh/day of electric heat with an average wait time of 36 minutes. Extremely lame, IMO.

> If you can afford a secondary storage tank to be the secondary heat source, great, but it's a much larger and more expensive system.

I disagree. A 170 F tank with some evacuated tubes could 100% solar heat this tub for 5 cloudy days with 5x3.76x3412/(170-110) = 1069 pounds of water cooling from 170 to 110 F. That's 17.2 ft^2, eg a 2' tall x 3.3' diameter well-insulated unpressurized tank.

>If you don't have a conventional heater in a lot of climates you'll simply not have a hot tub for many cold days when soaking is at a premium, no matter how large your thermal system is and how much storage you have.

Au contraire. If cloudy days are like coin flips, you'll have a hot tub 100(1-2^-5) = 97% of the time, without using the electric heater.

Nick

20 PI=4*ATN(1)
30 D=5'tub diameter (feet)
40 H=4'tub depth (feet)
50 ALID=PI*(D/2)^2'lid area (ft^2)
60 ATUB=PI*D*H-ALID'tub area, without lid (ft^2)
70 RV=15'R-value of tub and lid (ft^2-F-h/Btu)
80 PRINT"    Eon        Eoff          Esun          Elec          Delay"
90 PRINT"    (Btu/day)  (Btu/day)     (kWh/day)     (kWh/day)     (minutes)
110 '1. 100% solar heat
120 EON=22*(104-45.3)*(ALID+ATUB)/RV'lid-on energy (Btu/day)
130 PW=EXP(17.863-9621/(460+104))'tub vapor pressure ("Hg)
140 PA=29.921/(1+.62198/.0087)'air vapor pressure ("Hg)
150 EOFF=2*((104-45.3)*ATUB/RV+100*ALID*(PW-PA))'lid-off energy (Btu/day)
160 SKWH1=(EON+EOFF)/3412'solar heat (kWh/day)
170 PRINT 1;EON,EOFF,SKWH1,EKWH,DELAY
180 '2. solar heat for 6 hours per day
190 ESUN=6*(104-45.3)*(ALID+ATUB)/RV/3412'solar energy (kWh/day)
200 PRINT 2;EON,EOFF,ESUN,SKWH1-ESUN,DELAY
210 '3. solar heat with delay, sunny day
220 G=(ALID+ATUB)/RV'tub conductance (Btu/h-F)
230 C=ALID*H*62.33'thermal capacitance (Btu/F)
240 RC=C/G'time constant (hours)
250 T6=45.3+(104-45.3)*EXP(-3/RC)'tub temp at 6 PM (F)
260 REHEAT=(104-T6)*C/3412'reheat energy (kWh/day)
270 PHEAT=1.5'heater power (kW)
280 DELAY=60*REHEAT/PHEAT'reheat delay (minutes)
290 T9=45.3+(104-45.3)*EXP(-13/RC)'tub temp at 9 AM (F)
300 EON=(104-T9)*C+6*(104-45.3)*G+REHEAT*3412
310 ESUN=((104-T9)*C+6*(104-45.3)*G)/3412
320 ELEC=REHEAT+EOFF/3412
330 PRINT 3;EON,EOFF,ESUN,ELEC,DELAY
340 '4. solar heat with delay, cloudy day
350 T6=45.3+(104-45.3)*EXP(-22/RC)'tub temp at 6 PM (F)
360 REHEAT=(104-T6)*C/3412'reheat energy (kWh/day)
370 DELAY=60*REHEAT/PHEAT'reheat delay (minutes)
380 ESUN=0
390 ELEC=REHEAT+EOFF/3412
400 PRINT 4;REHEAT*3412,EOFF,ESUN,ELEC,DELAY