natural / free convection in a vertical tube

Stephan

I'm trying to model natural convection in a vertical tube with a closed warm end and an open cold end (including and excluding axial heat flux in the wall). I suffer serious convergence problems. I tried several appoaches: initialysing a velocity profile - upward at the wall, downward in the centre of the pipe; modelling only 45 degrees of the pipe and periodic boundary conditions; varying the temperature difference between upper and lower bc. so far no physically reasonable results. has anybody some experience in this field or some hints?