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

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The discussion centers on the use of Log Mean Temperature Difference (LMTD) in calculating thermal resistance through a coaxial cable. The user initially considered using a standard mean or integrating the area but realized that the area is not constant, necessitating the use of LMTD for accuracy. LMTD accounts for varying temperatures across the surface area, providing a more precise measurement than typical means. The user seeks clarification on why LMTD is preferred over other methods in such thermal calculations. Ultimately, LMTD is recognized as a more accurate approach for problems involving non-uniform temperature distributions.
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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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