Navier-Stokes equations with temperature term

  • Thread starter Zalajbeg
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Homework Statement



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:

Homework Equations



http://postimage.org/image/4gv0vv657/

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?
 

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