Environmental Engineering Reference
In-Depth Information
Fig. 10
Isotherms and
stream function for the
enclosure heated from the
top
,
Ra
10
5
,
=
ʓ
=
0
.
1and
ʵ
=
0
.
3.
a
ʛ
=
1
/
10,
10
−
6
.
ʔˈ
=
7
.
1
×
b
ʛ
=
1
/
3,
10
−
3
ʔˈ
=
9
.
2
×
Fig. 11
Average Nusselt
number for the enclosure
heated from the
top
,
ʓ
=
0
.
1
and
ʵ
=
0
.
3
mal distribution become sensitive to the wall geometry, specially for high Rayleigh
numbers. Figure
11
presents the average Nusselt number as function of
Ra
when
ʵ
=
3. When the Rayleigh number is lower
than 10
4
the heat transfer is dominated by conduction and the average Nusselt num-
ber is approximately 1 (see Fig.
11
). Above
Ra
0
.
3,
ʓ
=
0
.
1 and
ʛ
=
1
/
10
,
1
/
5
,
1
/
10
4
the average Nusselt number
=
, particularly when
Ra
is over 10
5
. Additionally, when
increases with
ʛ
ʛ
is large its
specific value does not change the convection heat transfer because large
ʛ
yields a
two cell flow pattern.
A comparison between Fig.
12
a, b reveals that the increment of the wave ampli-
tude causes a decrement of the convection velocity, according to the values of
ʔˈ
corresponding to each condition. Therefore, if the wave amplitude increases the aver-
age Nusselt number diminishes because of the thermal stratification and the resulting
slowflow. On the other hand, for small wave amplitude the heat transfer increases due
to the transport by two large convection cells (see Fig.
13
). Even for small Rayleigh
numbers the effect of the wave amplitude on the average Nusselt number is notable
and becomes even more important as the Rayleigh number increases. Indeed, the
wave amplitude restricts the convection heat transfer.
Figure
14
shows amultiple convection cell patternwhich is thermally stratified and
stands along the whole cavity when the cavity is tall. Contrarily, when the cavity is
short there are two convection cells with negligible fluid flow near the wavy wall and
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