Environmental Engineering Reference
In-Depth Information
Even though all convective flows share similarities, they are also different from
each other in detail, and include additional physical processes such as rotation, strat-
ification, salinity, pressure gradients, gravity gradients, phase changes, and magnetic
fields. These effects complicate what is already one of the most challenging problems
in nature, namely turbulence. It is thus useful, indeed essential, to study an ideal-
ized form of thermal convection in order to gain basic physical understanding. This
idealized flow is the Rayleigh-Bénard convection (RBC).
2 Rayleigh-Bénard Convection
In Rayleigh-Bénard convection the flow is confined to a cylindrical container of
height
H
and diameter
D
;
L
is called the aspect ratio. The sidewalls are
adiabatic and the bottom and top walls are conducting. The fluid motion is driven
by the temperature difference between the bottom hot plate and the cold top plate
(see Fig.
2
).
The dual-name assigned to the flow acknowledges the work of Henri Bénard
and Lord Rayleigh. Bénard's contribution started with his Ph.D. thesis from 1901,
in which he observed the famous hexagonal cells (see Fig.
3
) on a thin layer of
spermaceti (whale oil) placed on a heated metallic plate. For lack of theoretical
insight, these seminal observations were received with some reserve by the thesis
committee presided by the (future) 1908 Nobel laureate, Gabriel Lippman, who
stated “...though Bénard's main thesis was very peculiar, it did not bring significant
elements to our knowledge. ... the thesis should not to be considered as the best of
what Bénard could produce” (Wesfreid
2006
).
One who did not miss the theoretical insight was Lord Rayleigh, who first solved
the linearized stability problem in 1916. Under the Boussinesq approximation, which
assumes that the fluid properties are constant except in the buoyancy term, the equa-
tions that describe the system are relatively simple. For these equations the only
ʓ
=
D
/
D
T
t
H
T
b
Fig. 2
The image on the
left
shows a diagram of a Rayleigh-Bénard convection cell. The shadow-
graph images from Xi et al. (
2004
) show the structure of the thermal plumes and the mean wind
into which they organize
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