Condensation can occur when ascending combustion gases meet cooler temperatures in higher parts of the flue finally dropping below the dew point.
Condensation inside chimney liner.
A chimney cap had been added to the chimney above the furnace flue when the roofing had been done to complement the existing cap above the fireplace flue.
As you know if you plug the top of the chimney above the fireplace the flue liner condensation will trickle down to the fireplace.
You position the branch of the tee so it is facing down toward the floor.
The wetness on the outside faces of the chimney occurs when the condensate migrates through the mortar.
You insert one end of the run of the tee into the liner where the liner emerges from the chimney.
Usually a new liner will resolve this problem.
Then reconnect the flue to the other end of the run.
Instead of allowing moisture to evaporate the condensation may just soak the brick interior and then drip down.
On occasion we have identified the wetness around a chimney to be due to the condensation of the airborne moisture in the exhaust gases discharged by the furnace on the cold chimney walls.
This is often a problem when the liner used is not the ideal size or material.
In some cases the heat from the fire will cause the condensate to evaporate.
Condensation inside the chimney can cause a leaking chimney.