## Sunday, December 31, 2023

### Dead-air spaces and convection cells

 Fluid dynamics of gas between two panes of glass or between drywall and outer wall of a house. The portion of the Air Velocity profile circled in red is where shear losses occur.
Back in the 1970's people started worrying about the energy efficiency of their windows.

Some VERY basic research identified that the insulating ability of double-pane windows does not increase linearly with increasing distance between the panes.

As the panes got farther apart, the insulating ability grows far more slowly than expected.

It was attributed to convective circulation cells spontaneously springing up between the two panes.

The same amount of energy is pumping the cells regardless of the distance between the panes but the larger distances have less loss to shear and the longer "pumping" distances allow the fluid to reach higher velocities.

It was speculated that at distances of 0.75 inches (give or take a little bit) the cells self-extinguished due to the shear losses where two adjacent cells met. The bottom of one cell flows in the direction from cold-to-warm while the top of the next cell tries to flow from warm-to-cold, that is, in the opposite direction.

There are also shear-losses in the "boundary layer" between the pane (solid and stationary) and the air flowing vertically close to that pane. A dead-air space that is 4" will have more gentle velocity gradients (for the same mean velocity) than a much narrower space. Shear-losses are driven by the velocity gradient.

While the insulating ability of the windows might increase at distances greater than 0.75", it does not grow very fast and the loss of space does not justify larger air-spaces.

At least, this was the state-of-the-art in 1980 when I sat enthralled (OK, maybe not enthralled) in Professor Foss's Fluids Class.

1. When I first read your title I thought you were referencing Hadley Convection Cells in the Atmosphere...(I'm a weather geek)
So the answer to your question does the "insulating ability of the windows might increase at distances greater than 0.75?"
The convection cells still operate even with 10 miles of separation (from the surface to the Tropopause).