Thermal Convection in a Cylindrical Enclosure withWavy Sidewall - Selected Topics of Computational and Experimental Fluid Mechanics - page 387

Fig. 4 Average Nusselt
number for the enclosure
heated from below , ʓ = 0 . 1

and ʵ = 0 . 3

Fig. 5 Isotherms and stream
function for the enclosure
heated from below ,
Ra 10 5 , = ʛ = 1 / 5and

ʵ = 0 . 3. a ʓ = 0 . 3,

10 − 5 . ʔˈ = 8 . 7 ×

b ʓ = 0 . 05,

10 − 3 ʔˈ = 9 . 2 ×

, and when Ra is of order 10 5

Nusselt number increases with ʛ the heat transfer

changes considerably, as shown in Fig. 4 .
The dimensionless wave amplitude also defines the features of the convection
cells and temperature distribution (see Fig. 5 ). Large wave amplitude causes the
multiple cells pattern to induce slow motion in the whole cavity. Such a multiple cell
convection pattern is associated to thermal stratification. On the other hand, when
the wave amplitude is small there are two large convection cells and no thermal
stratification exists. When the wave amplitude increases the average Nusselt number
diminishes because of the thermal stratification and the resulting slow flow (Fig. 5 a).
For small wave amplitude the heat transfer increases due to the transport by two
large convection cells (see Fig. 5 b). Even for small Rayleigh numbers the effect of
the wave amplitude on the average Nusselt number is notable, as can be seen in Fig. 6 .
The wave amplitude effect on heat transfer becomes more important as the Rayleigh
number increases because convection dominates and the wall geometry defines the
shape and velocity of the convection cells.
The cavity aspect ratio is a primary parameter for the convection patterns as shown
in Fig. 7 . If the cavity is tall, i.e. is small, a multiple convection cell pattern and a

stratified temperature distribution hold along the whole cavity. If the cavity is short,
two convection cells and no thermal stratification are present. Moreover, there exist
thermal boundary layers near the upper and lower walls, while the fluid flow close

ʵ