Can gas kinetic theory explain heat transfer from gas to a container?

[cmb]

If one considers the kinetic theory of gases, can a first order estimate of thermal transfer be performed by considering momentum exchange at the container's surface?

I understand the basics of explaining and calculating pressure with the kinetic theory of gases, but if we assume energy is transferred between the gas molecules and those of the container in each component collision, can this give us an estimate of heat flux between the contained gas and the container, if they are at different temperatures?

 

[Chestermiller]

Summary: If one considers the kinetic theory of gases, can a first order estimate of thermal transfer be performed by considering momentum exchange at the container's surface?

If one considers the kinetic theory of gases, can a first order estimate of thermal transfer be performed by considering momentum exchange at the container's surface?

I understand the basics of explaining and calculating pressure with the kinetic theory of gases, but if we assume energy is transferred between the gas molecules and those of the container in each component collision, can this give us an estimate of heat flux between the contained gas and the container, if they are at different temperatures?

Do you think that it is possible for temperature to vary with spatial position in a gas? Or do you think that the temperature is discontinuous at the interface between the gas and the container?

 

[cmb]

Of course, but I have no view on that. The question is whether the thermal flux can be approximated by kinetic theory, and if that requires an estimate of thermal gradient in the gas then, sure, how could that be calculated to get to that end point?

This is a straight question, not a piece of homework where I have much clue myself.

 

[Chestermiller]

Of course, but I have no view on that. The question is whether the thermal flux can be approximated by kinetic theory, and if that requires an estimate of thermal gradient in the gas then, sure, how could that be calculated to get to that end point?

This is a straight question, not a piece of homework where I have much clue myself.

Kinetic theory can be used to determine the thermal conductivity of the gas (see Transport Phenomena by Bird, Stewart, and Lightfoot), and the thermal conductivity can be used in a heat transfer analysis to get the thermal flux. Is that a satisfactory approach?

 

[cmb]

I think the answer is 'no', then?

Where two objects collide in an elastic collision, where one is stationary (by definition as the inertial frame), they share the momentum of the incoming object. What I was thinking was that there might be a model of a gas as a series of 'objects' coming into collision with 'stationary objects' in the container wall. Then we might conclude an exchange of momentum from that.

The momentum the 'wall objects' have received will therefore warm up the wall as they are bound into the wall.

Eventually, some equilibrium will be reached where the 'wall objects' are oscillating fast enough that an exchange of momentum is just as likely to the gas objects as from them.

With that model in mind, I was wondering if it might reveal the thermal flux across the gas/solid boundary?

 

[Chestermiller]

Check out the development in Bird et al and see what you think.

 

[cmb]

OK. Where can I read a copy?