# Q & A: How much does air conduct heat?

Q:
I need mesurements of how much heat is transfered via the air contained between two parallel (metallic) surfaces at a small distance moving between them. I need to know how that changes with pressure. Another case is two cylinders with the same axis, one rotating and with air at some pressure between them. Given a fixed temperature difference, how much heat is transfered per sqm and depending on pressure and distance. Are there such experimental data?
- George (age 49)
Athens, Greece
A:

The answer to that question can be either simple or complicated, depending on what range of distances etc. are involved. The simple case is when:

1. The spacing between the surfaces is small enough and the temperature difference small enough  so that you don't get much significant convection currents. Then all you have to worry about is simple heat conduction.

2. The spacing is big enough, and the gas density high enough, so that the "mean free path" of a gas molecule, the distance it goes before bumping into another one, is small compared to the spacing. Then you can use the standard bulk thermal conductivity of the gas in the calculation.

Then there's a bit of a surprising result. The thermal conductivity of the gas doesn't depend on pressure. The reason is that if you say double the pressure, there are twice as many gas molecules to carry the heat, but each only travels half as far before bumping into another and changing direction.  So if we look up the thermal conductivity of air () we find that a little above room temperature it's about 0.03 W/m-K. The heat flow will be
~ 0.03 W/m-K *(Area of surfaces)*(temperature difference)/(spacing between surfaces)

There must be lots of experimental data on this, so search around for "thermal conductivitity of air". Maybe this would be a good place to start:  .

Mike W.

(published on 02/22/2014)