Calc Heat Transfer Rate for Temp Even Out

[sid_galt]

If say the temperature of just one component of air e.g. water vapor suddenly rises (say through IR absorption), what method can be used to very roughly and quickly calculate the amount of time it will take for the temperature to even out?

 

[Astronuc]

One would have to calculate the rate of momentum transfer from the hotter molecules to the cooler molecules. I imagine the process is described by a decaying exponential.

 

[mezarashi]

Heat conduction is... well governed by the heat conduction equation which is a first order equation with respect to time and second order with respect to spatial dimensions. It would be hard to estimate the system with an easier equation without seeing what the system configuration is.

 

[Astronuc]

I believe the problem, as posed, suggests that one component, intimately mixed with the other components becomes hotter than that other components, so one would need to derive an effective conductivity between the hot molecules and the colder molecules.

A similar issue is found in fusion plasma physics where electrons can be heated then they transfer thermal energy to the ions, or hotter ions are injected into a colder plasma - but this latter example involves a spatial dependence - unlike the OP.

 

[mezarashi]

Hmm, I've never thought about a problem regarding mixes fluids of different temperature together and timing their approach to equilibrium. I'm blank on what model to use. You'd have a lot of convection, and conduction all happening at once together in the mixture... although I've never heard of it, the effective conduction may be the way to go for an estimate.

 

[sid_galt]

Thank you for the replies. I think I'll do some more search on the Internet to see if I can find something or get hold of a gas dynamics book when I can.