Sai Gembali : In my honest opinion - forums like RG should not be a substitute for visiting a University course on fluid mechanics or read a basic text book on the matter. Both would answer your two questions in the first 1 or 2 lessons.

Regards,

Dr. Th. Frank.

I agree with Dr. Thomas. Plus, you can always start on Wikipedia articles : https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

This way you can see the general equations and what is the meaning of each term. Next you can go to a specialized Fluid Mechanics text book and look up for the case of interest, study how these kind of problems must be defined, and solve some practice problems.

Best Regards !

Maybe the question is about possible relevance of gravity for a vertical flow?

It depends on coupling heating flux at the wall.

But the NSE are always the same, indipendently from the wall orientation.

Filippo Maria Denaro : Possibly. But in order to receive a meaningful and targeting answer a little bit more care for the formulation of the question would be required in this case. People contributing with their answers are investing time and care from their side as well.

Regards,

Dr. Th. Frank.