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