Rayleigh-Benard Instabilities: 
Rayleigh number calculus
Laurent Selle (mfn17)
Jean Laporte (mfn10)

The Rayleigh number can be calculated with the formulas :

 Ra=alpha*DT*g*a^3/(nu*K)
K=lambda/(ro*Cp)

Where the constants are, for water in standard scientific units :

                        alpha   0,00018
                        g       9,81
                        a       0,01
                        nu      0,000001
                        lambda  0,6
                        ro      998,2
                        Cp      4182
                        K       1,43731E-07

and a is the distance between the two walls.

If a=1cm, then :
 

                        DT      Ra        Epsilon

                        0,12    1474
                        0,13    1597
                        0,14    1720
                        0,15    1843
 

                        0,3       3686      1,2
                        0,5       6143      2,6
                        0,7       8600      4,0

                        2,3       28257   15,5

                        5,5       67570   38,6
 

more data here
 
 

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