If the two rectangular ducts have a combined area greater than that circular one you wont have issues with flow restriction.
Venting microwave through wall stud in way.
If you don t want to cut the stud install 2 rectangular ducts on each side of the stud and split the original duct into two.
From microwave up into the cabinet is what you have now.
It appears when this house was built provision was made for venting out the rear of the microwave into the standard 2 4 wall up the cavity inside the wall then up through duct work in the attic through the roof.
I fixed it so that now it vents the kitchen smoke and odors through the wall and outside.
Line up microwave to duct and connect by placing it on the wall bracket or connecting bolts above.
Re install trim or siding.
This usually takes two people.
I saw this done on this old house when they installed a new microwave hood on an outside wall.
Total distance is about a foot performance will be barely compromised.
Option 1 results in a very twisty exhaust path while option 2 is obviously a ton of work.
Connect it all with a piece of flexible dryer vent hose.
A stud in a wall supporting or otherwise can be cut and boxed.
But the builder just left the microwave s fan blowing back into the kitchen.
If a floor joist or a beam is massively in the way you ll need some custom ducting or cancel the job entirely.
I d cut a generous square at the bottom of the wall so you can cut out the plate in the stud bay.
Just use flexible dryer vent and be done.
The manual for the microwave says to absolutely not use flexible ducting.
Buy the sheet metal boot that converts from 3x10 rectangle on the top of the otr microwave to 5 or 6 inch round duct.
It is designed to work like a hood.
Sacrifice the cabinet above the stove by snaking an exhaust duct up from the hood over to one side of the stud and then through the wall.
Basically i would start by breaking out the drywall around the proposed opening and that stud in the middle.
Install exterior vent hood utilizing proper exterior installation techniques applicable to your siding material.
You will have to remove quite a bit of drywall and most likely that wall cabinet directly above the oven.
Can anyone think of any other options.
Use 3m flashing tape or vycor or tyvek tape to assist ensure that water will not enter the building envelope.
Studs run vertically through a wall.
Attach two flex elbows and steer around the duct and straight out the wall.
Get a dryer vent going from outside to inside of the house.
Photo of unit installed it was heavy and bulky.
My microwave oven is mounted to an exterior wall above the stove.
Seal all joints with metal tape and get a quality exterior hood with an exhaust flapper.
Think of an turning into a line with a box in the middle.