This is exactly what i did in my kitchen when I renovated it. Here are
The first pic shows the short elbow I used for inside the wall. It is
3 1/4X10". The picture just shows how it sits in the wall.
The second picture shows the complete duct work assembled. Note that
its right next to a stud. I had originally planned for 15" cabinets on
either side of the stove, but when I gutted the kitchen, I noticed the
stud would be in the way of the duct, so i simply shifted everything
over 3" by getting a 12" cabinet on one side and an 18" cabinet on the
other. i had not yet ordered tha cabinets yet, so obviously it worked
for me. I tried my best to install the ductwork where the microwave
was going, plus I left about 1" play up and down
The third picture, although far away, shows another shot of the
ductwork behind the drywall lift. When it gets up in the ceiling, it
then transistions from a rect to 6" round elbow, then continues in 6"
round eventually going out the roof.
The 4th and 5th pictures show the finished product.
One note, I eliminated the damper door that comes with the microwave
since it would block the duct going up the wall when it it opens. I
just kept the flange. The Broan vent hood on the roof has a damper
already and having gone through a winter , I've had no problems with
drafts or cold.