I was thinking of adding a coil to the inside through the side wall... similar to this...
I wonder if the tempeture gradient would be enough to get the wort to "stir itself" and stay uniformly cooled?
Yes the temperature gradient will cause motion - not that you'll need it. It the thermal input will also move through the wort simply because heat energy seeks cooler material. And you don't really care about it being a slow process because it's going to sit there for maybe weeks. Time is on your side. No agitation needed.
You can do that inside the poly chamber and it'll work excellently.
Out side not so much because plastic is a crappy convector.
Just one caveat: Be careful about cold flow when installing bulkhead fittings. Use O rings and don't over tighten.
And sanitation: Because of all the introduced stuff (threads, O rings, yadda yadda) you will need to be able to take it apart and clean it whenever you set up for a brew. Just resign yourself to that one extra task.
But, clean and snug, It should work very well.
In fact any one owning a conical that is not jacketed (poor babies) might want to take a long hard look at this elegant and simple idea.
I've seen SST conicals wrapped in copper pipe. I never saw any one soldering the pipe to the conical which they ought to do to get good convection. I'm guessing that people just can't bring themselves to solder to the it expensive conical.
On the poly conical I reccommend that you use a metal strip about 3/16 to 1/4 thick and no less than an inch preferably 1.5 - 2" wide and put one on at least on the outside running up and down to connect physically the two inlet and outlet ports.
This will provide stability and strength which the poly fermenter does not have and prevent stress cracking from the tension and stress that you will (of a certainty) be putting on the plastic. I'd think about getting a lengh of Stainless and poutting a 1.25" wide strip insode the fermenter to sandwich the bulkhead fittings into a unitary structure with the fermenter.
I used to build a lot of different vessels large and small from plastics and I can see that the stresses of that sort of thing will be an issue.
Drill the holes not with a common 2 flute twist drill, but with a Forstner bit or a hole saw or better yet (best actually) a Plunge router in a holding jig, having pre-drilled a little pilot hole to remove the center material o the router bit doesn't dither on the center (most router bits that size are not center cutting).
It is important when drilling plastic to get as clean a cut as possible cutting at a speed that generates as little heat as possible (or use coolant) because the act of machining will set up stresses in the polymer which can easily propagate and grow into bona fide cracks.
HDPE is pretty good about tolerating machining.
I believe most poly conicals are HDPE.
They should be UHDPE but no one would pay for that.
