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Mostly it is for the creosote build up thus reducing chimney fire events. Also the wall clearance is is reduced so you can have the fireplace closer to the wall. You want the heat to be from the fireplace not from the chimney pipe. The double wall pipes also offer better air flow and less smoke because of the airflow.

Interesting.

The heat reclaimer I saw is designed to vent that later of insulated chimney pipe. The reviews said it contributed to more creosote but worked very effectively for what it was made to do. Does the cooling of the chimney pipe cause condensation of creosote, is that how that works?

I am not totally sure. I know up here in Alaska that most people use the double wall pipping. Chimney pipes can get burn through in hot spots and cause fires, I am sure that happens with double wall pipping also.

There are so many choices and options and recommendations for chimneys and it does depend a lot on what type of stove, wood, pellet, coal, excetera. I don't know if you have ever heard of them, Jotul wood stoves from Norway. Check a lot of wood stove manufactures and see what the majority of tem say pipe wise.

Also some of the colder areas, like Canada, Russia, Poland, Iceland and see what those countries recommend.

We had a little Jotul Little Bear stove in one of the houses we had, worked pretty good and had a plate on top for a pan of water or coffee pot. There are so many wood stoves out there, shopping for the right one can be a nightmare just based on choices available.