Calc Heat Transfer Rate for Temp Even Out

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Discussion Overview

The discussion revolves around estimating the time it takes for the temperature of a mixed air component, specifically water vapor, to even out after a sudden temperature increase. The scope includes theoretical approaches to heat transfer, particularly in fluid dynamics and thermal conduction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests calculating the rate of momentum transfer from hotter to cooler molecules, proposing a decaying exponential model for the process.
  • Another participant notes that heat conduction is governed by the heat conduction equation, which is complex and depends on the system's configuration.
  • A different viewpoint emphasizes the need to derive an effective conductivity between hot and cold molecules, drawing parallels to fusion plasma physics where energy transfer occurs between different particle types.
  • One participant expresses uncertainty about the appropriate model for mixing fluids of different temperatures, mentioning the simultaneous occurrence of convection and conduction.
  • A final participant indicates a willingness to further research the topic and seek additional resources, such as a gas dynamics book.

Areas of Agreement / Disagreement

Participants express various viewpoints on the methods to estimate temperature equalization, with no consensus on a specific model or approach. The discussion remains unresolved regarding the best method to apply.

Contextual Notes

Participants acknowledge the complexity of the problem, including the dependence on system configuration and the interactions between different heat transfer mechanisms. Specific assumptions and definitions are not fully articulated.

sid_galt
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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?
 
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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.
 
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.
 
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.
 
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.
 
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.
 

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