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Heat transfer: Plane wall criterium

  1. Feb 17, 2014 #1
    Hello fellow scientists,

    I'm working on describing the heat that's being stored in a sanitation pipe when hot water starts flowing through the pipe. I'm starting off with a simplified approach by assuming that the water in the pipe suddenly changes from 20°C to 60°C.

    I found a good start by making 'Example 5.4 of Incropera' where a pipe is suddenly exposed to hot oil internally.

    My question: In the mentioned example they make a simplification by approaching the pipe as a half plane wall. The pipe of the example is 1m in diameter and 4cm in thickness. Is there a criterion which makes that the (half) plane wall approach can be followed? Would there be another way?
    I would be working with standard copper and PE-X sanitation pipes with an internal diamter ranging from 10mm (1mm thick for copper, 2mm for PEX) to 50mm (1,5mm thick copper, 4mm PEX).

    The example in the book has the following order:
    Assumptions made:
    a) Pipe approached as a half plane wall. The midsection coincides with the outer surface.
    b) Pipe's outer surface is adiabatic so δT/δx|x=0=0

    Analysis:
    1) Bi and Fo for Plane wall at a certain time
    2) θ_0= C*exp(-ζ² Fo)
    Get C and ζ from Table.
    3) Use ζ to calculate the other temperatures.

    Once I have the values of C and ζ, I plot the graph using EES


    I have started my research into heat transfer just recently and made some exercises on steady state heat transfer and the lumped capacitance model. I'm working with EES to make my exercises. I remade some bookexamples and had a fast look into Bessel functions. I know this subject is a work of long effort, but I would be grateful if someone could give me a clear direction where to go now.

    -Brick-
     
    Last edited: Feb 17, 2014
  2. jcsd
  3. Feb 17, 2014 #2

    SteamKing

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    'Criterium' is a race or competition of some sort. 'Criterion', plural 'criteria', a standard on which a judgment or decision is based, is the word to use in the OP.
     
  4. Feb 17, 2014 #3
    On this forum I found a post on a different problem.

    https://www.physicsforums.com/showthread.php?t=395855

    " With such a thin pipe wall compared to the radius, you can assume the pipe wall to act like a plane wall (the error in replacing 1/ln(ro/ri) with (ro+ri)/2(ro−ri) is about 0.1%), which lets you get rid of those logarithms. "

    The assumptions should be justified. I would expect a comparison between the inner and outer perimeter, and make a comparison between a rectangle and trapezoid...

    -Brick-
     
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