The drawing on the left shows a typical configuration of chimney flue use. The left chimney flue is connected to the water heater and furnace in the basement and the flue on the right is connected to the upstair fireplace.
The drawing on the right shows a side view of a typical fireplace
chimney. Note that the flue is
offset back of the chimney and ends at the smoke shelf. The
firebox where the fire occurs
is in front. the 2 areas are connected by the flue damper.