The transitional section of a chimney between the firebox and the flue is the smoke chamber. Usually, it resembles an upside-down funnel in the middle connecting the two. The brickwork is stepped inward or corbelled then should be parged smooth. In the real world, many smoke chambers are un-parged with gaps and holes exposed which is a potential fire hazard. Many are jagged and irregular which create flow and performance issues. We have several methods with which to correct these deficiencies.
Repairing a flue liner used to be almost impossible. However, due to some new techniques, doing this type of repair on a chimney system is now very possible.