Sorry, I think I see what you are trying to do; but no, you did not get the convection principle, and you are still full member of the perpetual motion fraternity with your concept.
Which is disjunctive from the physics fraternity.
Convection works by actually heating the air, not moving it past a hot surface without heat transfer.
Any draft the chimney will produce comes from having heated the air in the chimney. No heating, no draft.
Which is what you are suggesting: Less heating, same draft.
Your water jacket somehow magically multiplies the energy by storing it.
It does not.
If you don't believe me, just build it. If it works, I will buy you a beer.
You will of course be able to afford your own beer, because you will be obscenely rich from just having solved the world's energy issues.
Ooops, you won't: The US patent office requires a working model for filing patents for perpetual motion machine. Not for any other kind of machine, but for perpetual motion ones.
Seems they got sick and tired of having the same conversation that we are having now long ago.
One of three things is happening here. Either I am REALLY bad at explaining what I propose or you are REALLY bad at interpreting it, or you're intentionally mis-reading what I'm saying just to stir the pot. I'm putting my money on #3 and yet somehow feel compelled to post against my better judgement.
Get off the perpetual motion machine thing. I get it, what I propose has nothing to do with it. No magic multiplier, only a more consistent flow. Besides the sun is the energy input so there's nothing perpetual here. I'm glad that now you can spell it though, that's an improvement.
For starters do you take issue with the OP's concept of a black sun-heated chimney moving air itself or do you take issue with the addition of thermal mass that I proposed?
So how exactly do you (or the OP) propose the air gets heated? Sun right? That's why it was proposed to be black right? Sun heats tube, tube transfers heat to air, hot air moves up. Yes? With such an obvious addition of energy into the system I don't get where you're getting hung up on the perpetual motion idea.
My point is that if there is a larger reservoir of heat in the tube (as provided by the sun) it would be less affected by the cooling effect of the necessary transfer of heat to the air in the chimney that will soon be gone. A hot chimney works better than an ambient temperature one and while it would take longer for the sun (heat input to system) to heat it up to working temperature it would also take longer for it to fizzle out. I was proposing that it would be a more consistent flow.
If the chimney is built out of 1 atom thick material, the materiel would be heated, it would transfer heat to the air, the air would move up and be displaced by cooler air from below. The cooler air would cool the chimney and any disruption of sun energy heating the system would now interrupt flow until the sun heated the material again and it transferred its heat to the air again. If the chimney had a lot more than 1 atom of mass it would take a lot longer for the thermal input of the sun to heat it and for the convection to start, but as the chimney did it's job and was moving cooler air from below it would take longer for it to cool the chimney and smooth out disruptions of energy input and outflow to the system.
This would act to add consistency to the airflow as forces acted on the chimney to cool it. What if a slight wind came up at the anchorage and began to cool the chimney from the outside? Which would be better the more massive water jacket chimney or 1 atom chimney? What about when the sun goes behind the cloud for a minute?