Computer simulation of thermal convection in Rayleigh-Bénard cell ...

Hubert Jopek
Computer simulation of thermal convection in Rayleigh-Bénard cell
5.1. Introducing dimensionless variables
Now some dimensionless variables will be introduced in order to make the
system much easier to study. This procedure is very important for seeing which
combination of parameters is more important that the others.
The new dimensionless time variable t ' is introduced:
DT
t'= t , (5.12)
2
h
D
where the expression T
is a typical thermal diffusion time over the distance h .
2
h
Distance variables x ',
z'
:
x
x'
=
h
z
z'
=
h
. (5.13)
Temperature variable θ ' :
θ
θ ' = . (5.14)
δT
Having these variables defined, it's also possible to introduce a dimensionless
velocity:
dx'
DT
υ
x
' = = υ
2 x
dt'
h
. (5.15)
dz'
DT
υz
' = = υ
2 z
dt'
h
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