General purpose and theorical overview

Definitions and notations

    :  the difference of temperature between the lower plate and the upper plate.
g : gravity (9.81 m/s)
d : distance between the plates
: thermal diffusivity
: thermal dilatation
: viscosity
Introduction

The natural convection occurs when a viscous, dilatable fluid is contained between 2 horizontal plates at different temperatures. This phenomenon is known as the Rayleigh-Benard  instability.
 
 
 

Conditions of the instability

The Rayleigh-Benard  instability develops when  is superior to a critical value ();  when  is inferior to the  value there is no instability.

The Rayleigh number

This critical value of  depends of many parameters like the type of fluid used or the distance between the plates so the instability criterion used is an adimensionnal number : the rayleigh number.

The critical value of the Rayleigh number is a constant, it doesn't change with the fluid or the conditions of the experiment. In theory, the critical value of the Rayleigh number is Rac = 1708.