We consider the problem of convective heat transport in the incompressible fluid flow and the motion of the fluid in the cylinder which is described by the Navier-Stokes equations with the heat equation.The exact solutions of the Navier-Stokes equations, the temperature field and the vorticity vector are obtained.
The Bulletin of Society for Mathematical Services and Standards (Volume 2)
V. Adanhounme et al., "Analytical Solutions for Navier-Stokes Equations in the Cylindrical Coordinates", The Bulletin of Society for Mathematical Services and Standards, Vol. 2, pp. 16-23, 2012