Subject: Re: aquarium, on limited energy

From: [email-masked] (Nick Pine)
Date: 26 Nov 1996 06:13:54 -0500

Harvey White <[email-masked]> wrote:
>>[email-masked] (Nick Pine) wrote:

>>>...A 110 VAC heater attached to a 12 VDC source might work fine with an
>>> aquarium with some added insulation.

>>I think I will try insulating it.

Good. Double glass on the front and 4" of styrofoam or some foil-faced
foamboard all round a 1x2x2' aquarium gives it a thermal conductance of about
4ft^2/R2 + 14ft^2/R20 = 2.7 Btu/hr-F, so keeping it 80 F in a 68 F room would
require an average of about (80-68)x2.7/3.41 = 9.5 watts, plus a little more
for the heat that leaves via the moist air bubbling through the water.

>>Do you mean, an AC heater attached directly to a 12V source...

Sure.

>>Will it work at a much lower voltage?

I would guess so.

>Why?

Aquarium heaters I've seen have wires glowing red, something like an
incandescent lamp. The resistance of a lamp filament decreases a lot with
decreasing temperature (and voltage) so the power dissipated (V^2/R) does not
drop nearly so much as in a linear resistor, with lower-than-normal voltage, as
R decreases with temperature. Heaters with red nichrome wires change resistance
less than lamps with incandescent tungsten filaments, but it's change in the
same direction. And you might only need 10% of the nominal power. 

>...the contacts might arc a bit more

That may or may not be a problem. 

>(resistor and capacitor in series, across contacts, might work well...

I don't think that snubber circuit would help. More mechanical hysteresis
might, but that would also increase the dead band.  
 
>The problem is the voltage.  Assuming that the resistance of a heater
>is linear (and it isn't!), then running a 100 watt 120 volt heater on
>12 volts will only give you 10 watts...

Sounds like enough. Nichrome is more linear than copper or tungsten over
temperature. Is red-hot 1200 F? Nichrome wire resistance at 650 C is
(650-20)x0.00017 = 0.107 times more than at 20 C. Tungsten wire resistance
at 2600 C is (2600-20)0.0045 = 11.6 times more than at 20 C.
 
>You'd have to rewire a heater so it had about a tenth of the amount
>of wire in it...

Good idea. Short out part of the wire or wind more wire around it or shorten
it or add a center tap, if necessary. But that probably isn't necessary.

>Really, the resistance of a heater isn't linear with voltage, so how
>much you get, iirc, will be a bit less.

It seems to me that an incandescent light bulb is approximately a constant
power device, but a heater with a glowing nichrome wire is not. 

Now, if the back of the aqarium faced a south window, you could hinge the
foamboard on the back at the bottom, and tilt it back with something like
a string wound around Grainger's $31.05 2L009 reversible permanent magnet
1/125 HP gearmotor (1.4 A @ 12 VDC, 17 rpm, 30 in-lb), with one of their
$6.46 2E245 110 F snap-action thermostats in a small glazed box painted dark
on the inside, exposed to the sun, in series with their $16.55 5E266
adjustable thermostat next to the glass, under the insulation on the east
or west side, set to a slightly higher temperature than the aquarium heater,
to solar heat the aquarium. 

That 5E266 thermostat might make a good alternative to the aquarium heater
thermostat, for 12 VDC switching, since it is rated for switching a 22 amp
resistive load at 110 VAC, or a 3/4 HP inductive load. It has a fixed
differential of 2 F. What temperature range do the fish require?

Suppose they can live in 75-85 F water. The aquarium has an RC thermal time
constant of about 10 gal x 8 lb/gal x 1 Btu/F-lb/2.7 Btu/hr-F = 30 hours.
If we warm the water to 85 F with the sun, it will cool to 75 F when
75 = 68 + (85-68)exp(-t/30), ie 7/17 = exp(-t/30) or ln(7/27) = -t/30 or
t = -30ln(7/17) = 20 hours. If the aquarium were twice as large in every
dimension, it would have 4 times the thermal conductance and 8 times the
volume of water, with a thermal time constant of 60 hours, so our fishy
friends could go for almost 2 days with no sun, before requiring backup heat.

If a narrower temperature range or thermal storage for more cloudy days
in a row were needed, we could either increase the size of the aquarium, or
add another higher temperature thermal storage aquarium containing no fish
or a solar closet to the back of the first one. What would the steady state
temperature of this thermal storage aquarium be in January in Philadelphia,
with about 1000 Btu/ft^2 falling on a south window over a 6 hour day, and
800 Btu/ft^2 passing through 2 layers of aquarium polycarbonate plastic,
if the aquarium were surrounded by R10 insulation at night, in a 68 F room?
Here's the approximate thermal situation:

1600 Btu = 6hr(T-68)4ft^2/R2       south wall, day
         +18hr(T-68)4ft^2/R20      south wall, night
         +24hr(T-68)6ft^2/R20      sides and top, 24 hours
         +24hrx9.5Wx3.41Btu/Wh     back, 24 hours, or

823 Btu = (T-68)(12+3.6+7.2) = 22.8(T-68), so T = 68 + 823/22.8 = 104 F. 

The fish aquarium needs about 450 Btu/day to stay at 75 F. If the heat store 
aquarium can keep the fish aquarium at 75 F until the heat store reaches 80 F,
it would store about (104-80)10x8 = 1920 Btu of useful heat, enough for about
4 days at a constant fish temperature of 75 F.

If we made the heat store an insulated back part of the fish aquarium, and
heated the fish aquarium from the glazing waste heat as the sun heated that
warmer part of the aquarium, in a very small-scale solar thermal cogeneration
system, we would have better performance...

Nick