Knee walls are vertical walls with attic space directly behind them. They are often found in houses with finished attics and dormer windows, such as in story-and-a-half designs.
One approach to constructing an energy-efficient knee wall is to first air seal the knee wall using conventional techniques (i.e., seal the bottom plate, seal penetrations through the drywall, etc.). The open joist ends below the knee wall should be plugged with squares of cardboard, metal flashing, or rigid insulation; cellulose insulation blown at a high density; or batt insulation stuffed into plastic bags. The plugs should be sealed to the joists using caulk or spray foam.
The knee wall and attic floor in the attic space behind it should be insulated to recommended levels. The same techniques for achieving higher insulation levels in cathedral ceilings can be applied to knee walls. Twine is often used to hold the batt insulation in place. The technique of adding rigid foam insulation over the framing is particularly effective. Rigid insulation can be notched to fit over the floor joists. Sealing rigid insulation to floor joists effectively blocks open floor joists.
A better approach is to insulate and air seal the rafter space along the sloping ceiling of the knee wall attic space. The rafters should receive recommended insulation levels. They should be covered with a sealed air barrier, such as drywall or foil-faced hardboard. The barrier must be caulked to the top plate of the exterior wall below the attic space and to the top plate of the knee wall itself. All other cracks and holes must be sealed aswell. One advantage of this technique is that any ductwork located in this space is now inside the conditioned space.