We limite our study to influence of the boundaries conditions.
 

- Geometry :
 

We choose to take  1 centimeter in Z direction. So, we have same length in Z direction and X direction. We 'll see consequence below.
 

- Meshing :
 
 
 

We choose cartesian mesh. There are two reasons : first, the geometry is enough simple, then we can't use an classic unstructured mesh because to study Rayleigh Benard instabilities with FLUENT, we must activate option !PRESTO  but this option doesn't exist with an unstructured mesh.

Moreover, in order to avoid prohibitive computation, we take  20 x 40 x 40 nodes.
 
 

- Boundaries conditions :
 
 

In order to study the "same" problem  of 2D study, we take boundaries conditions showed below :
 
 

- Convergence's behaviour :
 
 

Due to number of nodes relatively limited, CPU time is not important  (see below).
 
 

- Results :
 
 

We obtain comparable results with 2D study.
 
 

- Boundaries conditions of symmetry :
 

We change the boundaries conditions  of the two horizontal plans which had wall conditions and we applicate symmetry conditions. We obtain following results :
 
 

We should be obtain a similar solution with 2D solution (indeed, we take same boundaries conditions :symmetry) but the result is totally different. It seems there are two symmetric planes.
How come we obtain such as results ?
We have take same lengthes in X direction and Z direction, this can explain why the solution has this particular form. A idea to break these symmetric plans could be to take differents lengthes for X segment and Z segment. So, the geometry have not more symmetric planes, and the solution too.