Whats the point log mean temp difference(LMTD) any why use it?

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SUMMARY

The discussion centers on the advantages of using the Log Mean Temperature Difference (LMTD) over traditional mean calculations in thermal resistance problems, specifically in coaxial cable applications. The participant discovered that the area in such scenarios is not constant, necessitating the use of LMTD for accurate thermal analysis. The conclusion drawn is that LMTD provides a more precise representation of temperature differences across varying cross-sectional areas, making it essential for effective thermal resistance calculations.

PREREQUISITES
  • Understanding of thermal resistance concepts
  • Familiarity with coaxial cable geometry
  • Knowledge of temperature difference calculations
  • Basic calculus for integration
NEXT STEPS
  • Research the derivation and application of Log Mean Temperature Difference (LMTD)
  • Study the thermal resistance equations for coaxial cables
  • Explore numerical methods for integrating non-constant areas
  • Learn about alternative temperature difference methods, such as the Arithmetic Mean Temperature Difference (AMTD)
USEFUL FOR

Engineers, thermal analysts, and students studying heat transfer who seek to enhance their understanding of temperature difference calculations in thermal systems.

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I have a solution to a problem but don't understand why to use LMTD vs the usual type of mean.

I was working on a problem of trying to find the thermal resistance through a coaxial cable(hollow cylinder) and sort of knew the trick was that the area was not constant thus something had to be done to account for that. I was thinking of just integrating the area from the inner diameter to the outer but that was wrong. with a little searching I found that what I needed to use was the LOG MEAN of the area and substitute that for the area.


Here is my question: What is the point of using the log mean vs. the typical mean or just a integral of the area, and why would I have just come up with that method(Log Mean) as compared to the previous methods when given such a problem?
 
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LMTD is more accurate I believe.

You can read more http://www.engineeringtoolbox.com/arithmetic-logarithmic-mean-temperature-d_436.html" .
 
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