Insulation and air barrier are applied directly to the underside of the roof deck are common in applications where designers are seeking cost effective and energy efficient roof assemblies.
Unvented low slope roof.
Whatever method is used the amounts of insulation must achieve r values mandated by local codes.
In unvented flat or low slope roofs with parapets perform a full flood test to ensure leak free installation of roofing membrane.
Drying of unvented roofing assemblies is by definition only provided to the interior.
The insulation can go below the roof deck above the roof deck or both.
While this fact adds some risk to these assemblies compared for example to a traditional vented unconditioned attic with asphalt shingles this type of roof is very common.
Another approach is to build a cupola or ventilated doghouse in the middle of the low slope roof an approach championed by joe lstiburek.
Low slope and steep slope unvented roof systems i e.
Unvented low slope roofs are never designed to dry to the exterior because low slope roofing membranes are vapor barriers.
If the upper edge of a low slope shed roof intersects a vertical wall the most logical approach in my opinion is to detail the roof as an unvented roof.
Like a wall that is severely out of plumb an unvented roof has insulation packed into the framing cavities aligned with the sheathing.