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Generalized transport equation

Generalized transport equation. Reynolds decomposition: Define “macroscopic”, bulk velocity u=<v> Then v= u+c Where c is fluctuation of velocity. Note: <c>=0, <v>=< u+c >. Multi-fluid equations.

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Generalized transport equation

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  1. Generalized transport equation Reynolds decomposition: Define “macroscopic”, bulk velocity u=<v> Then v=u+c Where c is fluctuation of velocity. Note: <c>=0, <v>=<u+c>

  2. Multi-fluid equations After substituting Χ’s into the generalized transport equation and some work we get the multi-fluid equations for particle type a: Continuity equation Momentum equation Energy equation Where: Heat flux Pressure tensor Scalar pressure Energy density

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