Wood is gravity feed vertically into the beginning of the combustion chamber. The draft of the system pulls the flames horizontally through the primary combustion chamber. Further burning takes place vertically in the secondary combustion chamber called the heat riser. The combustion chambers are narrow, highly insulated, and specially shaped. These conditions keep the gases in a turbulent state for more complete combustion at temperatures from 1,500°-1,800°F.
Once combustion is complete, the exhaust exits out the heat riser into the first bell where most of the heat is given up to the chimney flue liners.
Here is an illustration of the same flow from a different angle. The opening between the heat riser and the first bell is lined with fireclay bricks.
Once the gases cool off, they fall to the bottom of the first bell and rise into a second bell chamber (which will never be as hot as the first bell). The colder gases are exhausted from the bottom of the second bell into the chimney.