Possible unit ommision in `Overall heat transfer coefficient` in the DOCs

[alongd]

In the documentation for class cantera.Wall(), the unit for the overall heat transfer coefficient (U) is listed as [W/m²] on the following page: Cantera Documentation.

I believe the correct unit should be [W/m²·K] to properly reflect the temperature dependency in the heat transfer coefficient. If the original unit ([W/m²]) is indeed correct, could someone please clarify how to apply this unit in practice? For example, I have the thermal conductivity value of a wall in [W/m·K] and intended to calculate U by dividing the thermal conductivity by the wall thickness, which yields [W/m²·K]. This seems to conflict with the current documentation.

[bryanwweber]

Hi @alongd! Thanks for asking this. The short answer is that the units are correct in the documentation. Perhaps heat transfer coefficient is a misnomer here, a better term might be the total rate of heat transfer per unit area. You can verify this by looking at the energy equation evaluation for the wall:

https://github.com/Cantera/cantera/blob/dd26e1835193d35ceace46f48e1b08ac18d76f45/src/zeroD/Wall.cpp#L86

The heat flux is simply multiplied by the wall area.

In your case, the conduction equation is something like

\dot{Q} = k A dT/dx => \dot{Q}/A = k dT/dx

So you need to multiply your thermal conductivity by the temperature gradient in the wall (if it's constant) or possibly integrate it over the thickness.