How fast does density change in an isobaric system?

[simple_logic]

Suppose the following

• an isobaric system
• an ideal heater⁽¹⁾ of infinite area on a single plane in a STP environment
• the heater is set to a given temperature

At a given distance perpendicular to the heater surface, what will the density of the gas be over time?

I spent a good part of the day getting nowhere, hopefully someone here can help.

Thank you,

S.L.

¹: All gas particle interactions with the heater result in the gas particle leaving at the set temperature of the heater

 

[Simon Bridge]

If you are asked for the density p(x,t) then there isn't enough information - without equilibrium there may be eddies and currents in the gas giving chaotic density fluctuations at any point. Presumably there is something else to take into account?

 

[simple_logic]

I would speculate that in an idealized system, this would be a function of the mean air particle speed, the mean collision frequency, energy accommodation coefficient, and possibly some relaxation constant/coefficient.

We can simplify the problem further by changing the STP environment to an infinite volume of 100kPa Argon at 293.2K

I'm interested in the approximate time it takes to get to equilibrium, and the quadratic relationship to distance.

Any takers?

 

[Aero51]

Look for a Navier-Stokes solver, it will get you an answer within 15% accuracy.