Water is dripping from the furnace exaust flue
If you installed a high efficiency sealed combustion chamber system the flue should have been changed to pvc. The old school ducting should not have passed inspection as it is not designed to be pressurized, there is not much pressure but it is there. Actually there should be both a supply line and the exhaust, normally connected to a coaxial roof jack so the system has fresh air and can exhaust without creating pressure differentials. In my state this install would be a code violation on several levels.