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It's a big stainless pot with a 4ft piece of 6" stainless flue welded to the lid and opened up through the lid. Currently insulated with a polarfleece blanket tied on, in time it'll have proper lagging. (The 'stack')
The u shaped slots at the top are 22mm wide by about 30 deep and the stick is 20mm dowel. Slots in the lid are much the same.
All this sits on a gas burner on its own cast iron stand.

I hang the parts in the stack using stainless steel mig wire.

I use a fume applicator to apply the blueing solution.
This is an aromatic oil burner with a stainless egg cup on top. The ceramic dish that came with it didn't last long...
A small dish of methylated spirits provides the heat to evaporate the solution (I use the aluminium cup off a cheap tealight candle... don't use the actual candle for this, some of the wax only evaporates instead of burning and can stick to the parts and prevent them from rusting.)
It sits in the pot on an upturned fruit tin as a stand to keep it out of the water. Some pieces of 30x10mm wood strips act as spacers for an air gap.

The blueing solution that I used was Mark Lee express brown solution. Yes browning. They both go black when you steam them. Just browning solution goes coffee black not blue black.
And Brownells won't ship the Mark Lee Express blue international...

I found this to be a good instructional.
https://youtu.be/VHyoUF50rF0

The differences in my process are that I use the stack both as the fume applicator/humidity box and steam chamber.
Keep the water about 2-4" deep. This is important later.
Once you've done the first heat cycle, back off the heat but keep the pot just simmering while you card the parts.
Now turn the gas off.
Put a splash of solution (just a few drops really) into the egg cup, fill the meths cup.
Have to work quick here, get it all done before the fumes start to come up.
Lift the stack off the pot. Put the parts back into the stack and the lid on.
Put the stand in the centre, put the applicator on it, light the meths.
Put the wooden sticks on and then the stack back over the pot.
Check through the airgap that the meths is still burning.
This is where the hot water helps, as its steam is going up the stack as well, assisting in the rusting process.

Leave it for 5-7 minutes for the meths to burn out.
Once this is done, remove fume applicator, stand and sticks, start gas burner to get the water boiling vigorously. I leave it for about 30 minutes for a heat cycle.