In order for the wood in the stove to burn well, it is necessary to provide traction

In order for the wood in the stove to burn well, it is necessary to provide traction (the flow of fresh air into the stove). Why does this require a sufficiently high chimney?

A longer pipe holds more air; during combustion in the furnace, a large amount of carbon dioxide and other combustion products are formed, heated to a high temperature. And as the temperature rises, the gases become less dense and more volatile, respectively, a pressure difference is formed in the pipe and the convective movement of heated gas flows upward, at the same time, due to the reduced pressure, air rushes there from the street. The longer the pipe, the greater the convective thrust and the pressure difference.