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re: spa heating
6 jun 2001
brian craft  wrote:

>i'm considering trying to solar heat my hot tub. the heating requirements
>are a bit odd. it needs to reach about 101f for perhaps 20 or 30 minutes a
>day, usually after dusk. the rest of the time it doesn't really matter
>what the temperature is. it's about 500 gallons of water.

but fairly useless for thermal storage, since people find 105 f too hot
and 103 too cold :-( a 104 f florida tub used 1.5 hours per day lost 20k
btu/day (180 kwh/mo) over average 73 f days in 1995, but some tubs live
in 30 f air... a better cover and fewer bubbles would help. 

>with these parameters, it seems like conventional pool and spa heaters
>don't really do the job. they might keep the tub warm all day, rather than
>reaching a high temperature for a short period of time. i'd still need to
>fire up the gas heater to get to operating temperature.

you might solar heat the tub to 104 f max, and let the temp fall at night,
so you don't use much gas on an average day...

>i'm thinking perhaps the thing to do is use a themosiphon to heat some
>water to above the operating temperature, and pump it into the tub just
>prior to use.

that's a lot of water, as you say, and modern hot tubs seem very well
insulated, except for the cover. some have 6 or 8 inches of foam under
the shell. you might make a 4' foam cube to hold 500 gallons of hot
water, and move the water into the tub before use and back to the cube
afterwards, but the cube would lose heat as well. with 96 ft^2 of 6"
styrofoam walls, the conductance would be 96ft^2/(r5x6) = 3.2 btu/h-f,
so it would lose about 24h(104-73)3.2 = 2.4k btu/day.

or make the cube the tub, eg a 6'x6'x 3' tall box (id) with 1' styrofoam
walls and a 1' thick hinged lid, and about 210 ft^2 of average wall area 
and 210ft^2/(r5x12) = 3.5 btu/h-f of conductance and 24h(104-73)3.5
= 2604 btu/day of heat loss, with the lid closed. but styrofoam costs
about $4/ft^3 ($16/4'x8'x1.5" sheet, where i live), and that tub would
need 212 ft^3, and it wouldn't be as nice as a commercial tub...

i like the idea of improving the lid and disconnecting the blower and
heating a commercial tub with solar heated water, vs electricity.

we might make a better lid with bolts and deck screws and multiple
layers of styrofoam with latex paint or plywood on the outside,
and lift it with a large tripod and pulley and counterweight.

the tub thermostat might turn on a small pump instead of a heater and
circulate warmer water through a hose coiled up in the bottom. people
say hot tub heaters can be unreliable. they scale up and burn out, and
cost $200 or so to replace. and some of the chemicals used in tubs are
there to prevent that scaling. i'd vote for fewer chemicals. just ozone 
and copper ions (5 parts per billion :-) from a sponge in the filter.

we might supply 20k btu/day (833 btu/h) with 100' of 5/8" reinforced 
garden hose, about 5 turns around a 6' tub. a heat exchange calc: if
c lb/h of water moves through the hose, ntu = 16ft^2x10btu/h-f-ft^2/c,
approximately, and e = 1-exp(-ntu), with a 0 capacity rate ratio (the
tub temp change is small compared to the hose temp change)... 120 f
water leaves the hose at t = 120-e(120-104), and 833 = c(120-t)
= 16c(1-exp(-160/c)), so c = 52/(1-exp(-160/c)). starting with c = 52
pounds per hour on the right hand side makes c = 54.5 on the left.
plugging that back in makes c 54.9, 54.98, and 54.99, so c is about
55, ie 0.11 gpm, and e = 0.945, and the water goes back in to the
central water heater at t = 104.9 f via the drain hose fitting.

we might use grainger's $118 4pc86 6 gpm pump to circulate hot water.
it draws about 40 watts, ie 40x0.11/6 = 1w running 2% of the time.
to change the tub water, we could turn off the tub heat and close
a valve to the cold water input of the water heater and let the cold
water bypass the pump and enter the hose for preheating household
water and cooling the tub water, then drain the tub after it's cold
(how long would it take, with typical family hot water consumption?),
and refill it via the hose with a mix of fresh hot and cold water. 


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