Environmental Engineering Reference
In-Depth Information
Fig. 9
Isotherms and stream
function for the enclosure
heated from the
top
and
ʵ
=
0
.
3,
ʓ
=
0
.
1and
10
3
,
ʛ
=
1
/
5.
a
Ra
=
10
−
7
.
ʔˈ
=
8
.
8
×
10
4
,
b
Ra
=
10
−
6
.
ʔˈ
=
8
.
6
×
10
5
,
ʔˈ
=
1
.
1
×
10
−
2
.
d
Ra
=
10
6
,
ʔˈ
=
7
.
3
×
10
−
2
c
Ra
=
4.2 Enclosure Heated from the Top
The second case studied considers that the cavity is heated from the top, cooled
from below, while the lateral wavy wall is adiabatic. Dimensionless temperature
and stream function distributions for Rayleigh numbers between 10
3
and 10
6
are
shown in Fig.
9
. The stream function shows multiple convection cells near the wavy
wall when the Rayleigh number is of order 10
3
. The cavity presents a stratified
temperature distribution due to a weak convective transport. When the Rayleigh
number increases around 10
4
, the thermal stratification persists, while the fluid flow
intensifies, according to the stream function values which increase at least one order
of magnitude. For
Ra
10
5
the flow presents two convection cells, the lower
cell with a clockwise rotation, and thermal distribution with notable temperature
gradients near the upper and lower walls. Those temperature gradients become even
more intensive for
Ra
=
10
6
, when heat transfer is dominated by the two convection
=
cells.
Figure
10
shows that the convection flow and the heat transfer are notably affected
by the dimensionless wavelength,
ʛ
, particularly for high Rayleigh numbers. When
ʛ
is small there exists an almost stagnant thermally stratified core with multiple low
velocity convection cells near the wavy wall. On the other hand, if
is large, there
are two convection cells with no thermal stratification. Convection cells and ther-
ʛ
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