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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?