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Homework Help: Navier-Stokes equations with temperature term

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data

    C dimensionless solute concentration
    C0 constant
    Grc solutal Grashof number
    Grh thermal Grashof number
    Le Lewis number
    N buoyancy ratio N = Grc/Grh
    Pr Prandtl number
    r dimensionless radial coordinate
    t dimensionless time coordinate
    z dimensionless axial coordinate
    θ dimensionless temperature
    w dimensionless stream function
    x dimensionless vorticity

    The governing axisymmetric equations for the Newtonian
    and laminar binary fluid neglecting heat generation,
    viscous dissipation, chemical reaction and thermal radiation
    can be expressed as:

    2. Relevant equations


    3. The attempt at a solution

    This is a part from an article from R. Cai and C. Gou. My firs assignment is to start with a differential small element and derive this equations. I think first one is a kind of Navier-Stokes equation, the second one is to define worticity the third one is energy equation and the last one is the mass conversion equation.

    I could obtain the last two equations but I cannot do the same for the first equation. Is it really Navier-Stokes equation? If so, how can I add the thermal term. I can just obtain inertial and viscous parts but thermal term. May be it is a part of pressure gradient but I couldn't do anything at all. Could someone possibly give me a hint about the thermal term?
  2. jcsd
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