Condensation at roof, down outside of furnace/water heater vent. What is happening

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I am getting condensation dripping down the outside face of my furnace vent at the roof. I think I know why this is happening I'm just curious how to remedy it.
There is a cast iron exhaust pipe that travels from my basement to above the roof. What you are seeing in picture 1 below is the aluminum sleeve and cap I installed when replacing my roof. The sleeve slides over top of the cast iron pipe, and the cap sits on top of the sleeve. Where the cast iron pipe stops at about the ridge of the roof, the sleeve extends a foot or two above the ridge. What I think is happening is when the steam in the exhaust goes out the top of the cast iron, it still has to travel a few feet to get outside of the sleeve and it is condensating between the top of the cast iron and the top of the sleeve onto the inside face of the sleeve. It is then dripping down to the roof plane, hitting the outside face of the cast iron, and dripping down the face into my house.

Is this what is happening? If so, what is the best remedy?

I considered cutting down the sleeve to be flush with the top of the cast iron.
Thank you in advance for your help.

Picture 1
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Best Answer

What is happening, you have diagnosed correctly, in my opinion.

How to fix it, not so well.

The standard projection for chimneys from roofs is "2 feet above any part of the roof within 10 feet", or in this case, 2 feet above the ridge. You need to extend the "actual chimney" to meet this (IMHO) not cut down the sleeve to meet the "too short chimney." The chimney should extend higher than the "sleeve" and have a rain collar to divert any water coming down the chimney outside the sleeve.