# Rayleigh number for vertical cylinder with free convection

1. Jun 18, 2013

### SSeth

Hi @ all,

i want to simulate the cooling behavior of liquid aluminum in a vertical cylinder(simplified geometry of a real transport crucible), the cylinder is cooled down by the surrounding air from all sides, from top and from buttom, i expect free convection in the liquid

to simulate this i have to decide between laminar or tubulent solvers.

i want to decide this by the rayleigh numer Ra>10^9 =turbulent

but i have a problem, i have lots of literature for the convection !!!around!!! a cylinder but zero for the convection !!!inside!!! a vertical cylinder,

so what is the characteristic length for the rayleigh number !!!inside!!!! an vertical cylinder? the diameter or height? do i have to take into account the top and the buttom if yes how?

the correlation equation for D/L>=35/Gr^(1/4) is valid by the way,

if you know a relation/ literature for the nusselt number in this situation, it would be helpful

thx @ all any kind of help is welcome