Definitely in back, if you can manage it. The deeper the hood the better; fumes always escape out the front if you have a shallow hood. In the back, they have nowhere to escape :)

did you mean leave the gap in the back or put the hood in the back?

gap in back. Hood to the front.

May I ask why you want a narrower insert? What are the constraints that limit what you can use for a capture area?

Whatever area you need to block should be stainless steel or other non-combustible cleanable metal.

the constraints are high CFM models. of all the models i found so far they are either too deep or too narrow, which only leaves us with the narrow choice.

what is the stainless steel material called that block off the space? I am not sure what term to search for purchase.

You will require a local metal fabricator to create a custom liner that covers all of the wood underneath.

To get an idea of the scope of CFM values available for different sizes of hood inserts/liners, please download and review the hood section of the Wolf Design Guide available at Wolf's web site. You can also use blowers that are external to the liner, either in-line in the ducting path or outside on the roof or wall.

Alternatively, you could use a hood sized to the cooking device, or a larger insert with a new hood shell in whatever wood finish that matches your cabinets. You will not be able to fully capture rising cooking plume effluent if the entry aperture of the hood does not overlap the pan by enough to make up for plume expansion.

i was wondering how difficult it is for a general contractor to cut a piece of 30x4" stainless steel to block off the gap. or is that somehting we can buy from local metal fabtricator?

A general contractor is unlikely to have a suitable slicing tool (shear) when he can go to a sheet metal shop and have a piece cut. You can do so also. Stainless steel is fairly hard, so having the sheet metal shop also punch holes where you intend to use screws, if any, is recommended.

With respect to an earlier question, I want to emphasize that raising the flow rate (CFM) will not overcome the limitations of having an insufficient capture area at the bottom of the hood unless the hood is effectively extended by side cabinets and/or side skirts. You can evaluate capture vs. escape by assuming a 7 to 10 degree (from vertical) plume divergence angle from pan edges. Generally, the hood flow does not suck the plumes up and into the hood; they get to the hood from natural thermal buoyancy. If the plumes are too large in diameter, some portions miss the hood. If the hood CFM is insufficient for the plume volume, then it is possible for some effluent to escape from being captured. It is not "contained."

In this schlieren image of a commercial griddle and hood, the CFM is sufficiently high to reduce plume divergence a bit (hood air is entraining some plume below the entry aperture) but not sufficient to ensure containment of the captured plume as some reflects out and escapes. (Plumes have momentum.) The second image shows the result of having high enough CFM.

If you have an undersized hood, you can ensure that what gets to the hood aperture is captured and contained by achieving an actual 90 CFM per square foot of entry aperture. If you want to try to capture a bit more, 90 CFM per square foot of the range surface area may help, but wok cooking or steak searing on a front burner is not likely to be fully captured and contained in such cases.

Note that actual CFM is conservatively 2/3 of blower rated CFM due to pressure losses in the hood, ducting, and make-up air paths.

Thank you for the detail drawing. So it seems it is best to put the Hood as far forward as possible to capture the escape, like someone mentioned above. Is that correct?

Range hood inserts with 30" exterior width and 19-1/4" depth are available. Appliances Connection has 10 of them.