I have something very similar in reverse. I have a 36 inch wide glass canopy hood with an upper cabinet on the left side and no upper on the right. The back door is over to the right. My backsplash tile goes up to the ceiling. It doesn't look strange. And no one has ever said it looked off balance.

Thanks everyone sooooo much for your replies @kas The damper is just a flap controlled by a servo motor that opens and close as the pressure in the exhaust duct changes. So I don't think orientation matters as it depends on the pressure drop in the house to draw in outside air. But what I worry is that there is not enough room in the wall to fit a 6" or 8" duct, and they dont sell a unit with rectangular duct. May have to do some modification myself. Yea I do realize that the cooking heat is going out in the hood. Basically what I want is that a big part of the air will go from outside -> damper -> bottom of stove -> rise up and feed the effluent -> hood -> outside, instead of drawing all the air from inside the house. For the air that spills out under the range I will probably need a pair of wool socks lol. But most of the time I wont need the full power of the hood for more than 30 min so I guess I can handle that. @eshmh Yes I have done the calculation with the depressurization limit of the house. Since my house is an older construction (50 year old), it will have ACH50 rate at about 6. That way house leaking can supply a portion of the make up air. Yes I do agree that the insulation in the area of the duct is going to suffer due to the duct taking basically the whole thickness of wall insulation. What is the condensation issue you mentioned? I have never heard of that before and would really like to know more about it. @3ilovepie This is the hood I have decided to get. 36" wall hood with heat lamp @teachmkt1 Yea I saw your post about the ikea shelf and that is what prompted me to think about warming shelf idea. That is exactly what I plan on getting. In most of my cooking scenario, it will be the front 2 hobs being used at full power. The back will likely be used for simmering a big pot of soup or something.

I can see your conundrum . . . the hood is just a bit on the shallow side and the narrowing of the chase as it goes to the ceiling means the body of the unit comes into play as well. It's possible that the Best by Broan, model PK22 would fit. It might be best to consult an appliance store where they can handle the installation and check for fit before you purchase. Otherwise, I'd check to see if the cabinet manufacturer has a suggested unit that would fit. Good luck!

I don’t like wide cabinet-surround hoods because it makes your kitchen look like it has “The Great Wall of Cabinetry”. A stainless steel hood provides relief of the wall of cabinetry, as well as welcome gleam and reflection. Also, a wood surround is harder to clean than stainless steel. Also, typically cabinet makers make the hood surround too shallow so that the front burners aren’t covered. And finally, when you have a wood surround hood you must buy the liner and blower separately which sets up a whole bunch of questions as to the many choices in those. With a stainless steel hood it’s all-in-one, done. Make sure your duct to the outside is 8” or 10” diameter. Choose a canopy-shaped hood, not one of those flat ones. Make sure to get a hood that has baffle filters not mesh. The depth front-to-back must be minimum 22“, but 24” is better.