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Energy conservation for a Newtonian fluid?

  1. May 11, 2017 #1
    1. The problem statement, all variables and given/known data
    vsoqrs.png
    ρ= density, vi = i-th velocity component, gi=i-th component of gravity vector, p=pressure, μ= viscosity, D/Dt = material derivative
    2. Relevant equations
    Continuity equation: div v = 0
    3. The attempt at a solution
    acbhwo.png
     
  2. jcsd
  3. May 16, 2017 #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.
     
  4. May 24, 2017 #3
    The derivation you are looking for is in Transport Phenomena by Bird, Stewart, and Lightfoot. It involves dotting the equation of motion (momentum balance equation) with the velocity vector. Incidentally, this is called the Mechanical Energy Balance Equation. It can be combined with the Overall Energy Balance equation to yield the Thermal Energy Balance equation.
     
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