Instabilities theory
To understand when rolls can appear, an adimensionnal number has to be defined called Rayleigh Number :

For values over a certain one called Critical Rayleigh Number denoted Rac, rolls happen but their number is not determined. For the geometry that will be used here, Rac=1708.

Another adimensionnal number Epsilon is given by the formula:

Different flow configuration are possible in function of different values of Epsilon.

Some results are given when Epsilon<2 or 3.

The aim of this study will be to verify these for different fluids. It will be done by keeping a constant Rayleigh number and having a Prandtl number (Pr) variable in order to show its influence on the problem.