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Two (equivalent?) versions of Clausius-Duhem inequality?

  1. Oct 30, 2016 #1
    1. The problem statement, all variables and given/known data
    Hello everyone,
    I have a problem to solve, which I found hard and so looked for help on the web. Finally found this:
    https://books.google.co.uk/books?id...E#v=onepage&q=clausius-duhem inviscid&f=false
    which is great as on page 183 is the EXACT question I am supposed to solve. It's not fully shown on google but I can do the rest.

    There a a few differences:
    I have

    T=T(F,Θ,gradΘ)
    q=q(F,Θ,gradΘ)
    η=η(F,Θ,gradΘ)

    rather than
    T=T(ρ,Θ,gradΘ) etc. as in the link above.

    The Clausius-Duhem inequality shown throughout the book has terms a term

    +T⋅D

    in it. We learned this differently in class: Our inequality read the exact same as in the link above but had a term

    +tr(TD)

    instead.

    I would really like to understand why these two forms are equivalent before just using the form I found on the web and assuming it's correct. Is this to do with T vs. T?

    I feel like such a beginner (which I am!) :D

    Thank you so much for any advice!!
     
    Last edited: Oct 30, 2016
  2. jcsd
  3. Nov 4, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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