Mike Hord wrote:
> I need to run a tank of water (10 US
> Gal, or ~38L) from very close to 0C to 50C, in
> a predictable, controllable manner over a span
> of some days.
>
> I am buying a 300GPH aquarium filter which
> has a provision for fitting a 100W heater in the
> flow of water.

100W sounds like way too little for this.

There are important answers you left out.  How accurate do you need the
temperature control to be?  How fast must it respond?  How fast must you be
able to heat the water?

I once built a darkroom waterbath with a really dumb controller, but
it worked very well.  This bath was probably about a gallon
in one of those platics tubs you can get lots of places for washing dishes
or whatever.  I also used an aquarium pump to keep the water circulating.
That guaranteed that temperature differences at different points would be
minimal and that there was always circulation past the thermistor sensors.
The control algorithm was just to turn a relay on or off every 64 power line
cycles based on whether the temperature was above or below the set point.
It worked very well.  Once the setpoint was reached, you could barely see
movement on the photographic thermometer.  It probably kept the temperature
to about 1/4 degree F.  For a heater I used a commercial immersion
heater intended to warm your coffee right in the cup.  They were cheap and
available back in 1980, and all the safety issues had already been dealt
with.

That heater was probably 50-100W, which is why 100W sounds like way to
little in your case.

Of course instead of guessing, you should have done the math. [rant] Why is
it people seem allergic to doing this.  This stuff is straight out of high
school physics. [/rant]  Anyway, you have 10 gallons, which is about 80
pounds of water, which therfore requires 80 BTU to heat one degF, or 144 BTU
to heat 1 degC.  144 BTU is about 152Kj.  That means it will take over 25
minutes for 100W to raise the temperature 1C with no loss to the outside.
This sounds woefully inadequate.

Raising the temperature 1C in 1 minute is probably a reasonable goal,
assuming you don't need it faster (you never said).  You can immediately see
that requires around 2.5KW plus whatever is lost to the outside.  Also note
that this is very slow compared to how you can control the power input.  You
can easily decide to turn the heater on or not for 10 seconds at a time and
still get very good regulation.

To measure the power loss to the outside, fill the tank with maximum
temperature water by whatever means, turn on the circulation pump, and close
it up.  Record temperature over time.  It should be an exponential decay
approaching ambient, and will probably take a few days to get within
measurement error of ambient.  However, you only need to record the first
few hours.  You are interested in the maximum power loss, which occurs at
maximum temperature.  The rate of change at maximum temperature will tell
you the power loss your heater needs to deal with.

For example, let's say the temperature drops 2C/hour at 50C.  2C/hour is
3.6F/hour.  You have 80 pounds of water, so that's 288 BTU/hour = 304Kj/hour
= 84.4j/S = about 85 watts.  If that's the case, a 2.5KW heater should still
be fine.


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