Concentric Tube Heat Exchanger - Clarification on Energy Balance

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SUMMARY

The discussion centers on modeling the transfer function for the temperature response of water exiting a concentric tube heat exchanger in relation to input water velocity. The user references Seborg's "Process Dynamics and Controls" for initial equations but diverges due to specific application differences. Key variables discussed include A_s and A_L, which represent heat transfer areas for the outer and inner tubes, respectively. The user seeks clarification on the variable Aw, questioning whether it denotes an average or total heat transfer area, and expresses a resolution to their confusion after rest.

PREREQUISITES
  • Understanding of heat exchanger principles
  • Familiarity with transfer functions in control systems
  • Knowledge of process dynamics as outlined in Seborg's "Process Dynamics and Controls"
  • Basic mathematical modeling skills
NEXT STEPS
  • Research the derivation of transfer functions for heat exchangers
  • Study the application of heat transfer area calculations in concentric tube designs
  • Explore advanced topics in process dynamics and controls
  • Investigate common modeling errors and their resolutions in thermal systems
USEFUL FOR

Engineers and researchers involved in thermal system design, particularly those focusing on heat exchanger modeling and control system dynamics.

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I'm trying to model a Transfer function for the response of the deviation in temperature of water coming out of the concentric tube heat exchanger in response to an input velocity of water function.


THE PROBLEM

I start the derivation with a couple equations in Seborg's Process Dynamics and Controls and then go off on deriving on my own since my application of the equations are different then what they were using them to show.

A short snippet before I started my derivation:

axyEGvn.png


rNCaXUH.png


Now I understand what A_s and A_L are (the area available for heat transfer for those two... the length times 2(pi)R for the outside and inside radii, respectively).

What the heck is Aw? Is that an average of the two areas or the total amount of area available for heat transfer?

I got my model into standard form for what I want, but I'm having trouble putting in actual numbers.

Any help is much appreciated!
 
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It's not clear from the OP where Aw is used.
 
SteamKing said:
It's not clear from the OP where Aw is used.

Feel dumb now, I was up awake for an extremely long stretch of time and read the equation wrong... in my mind somehow the variable subscripts were flipped.

I am not confused after a good night's rest :D
 

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