I noticed I needed to clarify this. Running thru the attached garage and out its end exterior wall would be the longest run Running to the soffitt on the back of the house would be shorter Running up to roof would be shortest.

The stress on the roof beams should be least at their ends, so the amount of structural enhancement needed to allow a roof penetration for a horizontal duct near the hood height should be less than for penetrating higher on the roof. You might want to consult with an architect who can engineer a solution for that location. I can't help with any illustrations, although you might check out Soler & Palau's web site. I vaguely remember that they had some unusual duct runs shown there. kas

There was a vent where the middle can went in, So they closed off - not sure if that's the technical term - that vent when they installed the cans. So we needed to put a vent in the kitchen to replace the one that was closed off/taken by the can. I said in the middle of the kitchen assuming they would think in the middle middle not in the middle of the cans. I know I know, one should NEVER assume with construction, but this was an unexpected little hiccup amongst many others that come with renovating an old house. Maybe it should be in line with the one in the breakfast room area- the one closest to the camera

Mine is from builder. It is one of Thermolec air heaters ( http://www.thermolec.com/en/productView.aspx?type=product&id=77) plus a separate current triggered flapper. The heater tries to heat the air to 15 C (PWM), activated by the air flow. It is a passive one and connects to the air return of the furnace via a 10 inch duct. It is not as sophisticated and highly performed as Kas's.