OK, let's try eliminating some variables with a simplified experiment!
Ignore temperature differences, just consider density:
Take a bucket of water, and a piece of Suitable Tubing (clear glass or plastic would be ideal), fill the tubing with a less-dense liquid (eg kerosene) and seal the bottom end with a finger. Plunge the tubing into the water (you can use warm water if you're as woosie) and take finger off the end.
Assuming that the top of the tube is below water level, what happens? The less dense kerosene is pushed out the top of the tube by denser water. - The less dense kerosene exerts less static pressure at the bottom of the.tube than the same head of water. The difference in static pressure is what causes the flow up the pipe.
Now repeat with a slight variation:
Raise the top end of the tube above the water surface before 'opening the damper' (you finger on the end) - kerosene will flow out again, until the static pressures equalise, with a taller column of kero - the level in the tube will be above the water surface, and once equalised you can move the tube up and down (slowly) and the level in the tube *will remain constant* above the water surface, water flowing in and out at the bottom, air at the top. This is a good way to measure liquid density relative to water,.I remember spending a science class doing it...
SO... We've established that the difference in density causes a difference in static pressure, and this starts the flow.
As cold, dense air enters the stove, it's heated by the fire, it gets less dense, so it's pushed out up the flue by more cold air. If we don't close the damper a bit all our logs burn too fast and we just heat the sky, not the house...
So, what if the tube in our experiment is full of water, not kero?
If the water's at the same temperature, nothing happens (the stove's cold!).
Now we apply some heat to the water in the bottom of the flue - back in school we put a few Amps through a coil of resistance wire in the tube - and the water warms and its density decreases.
The less dense water in the tube now exerts less static pressure, ans starts to flow up the flue, cold water enters the base and is warmed, on it goes... This is 'convection' or 'thermosyphon', and used to be how central (wet) heating and car radiators worked before cheap pumps came along!
HTH,
Dave H. (the other one)