Environmental Engineering Reference
In-Depth Information
Figure 4.3
The thermal conductance divided by temperature
K
/
T
,which
is reduced by the zero-temperature universal value
π
2
k
B
/
3
h
, as a function
of the reduced temperature
k
B
T
/
for different structural parameters,
where
=
ω
m
+
1
−
ω
m
=
π
v
T
/
W
I
. Here, the defect is void. (a)-(c)
correspond to
K
/
T
of modes 0, 1, and 2, respectively, and (d) corresponds
/
to the total
K
T
. Please refer to Ref. [51]for further details.
temperature (Fig. 4.3d), which seems consistent with experimental
results. Moreover, the reduced thermal conductance
K
/
T
of the
zero mode decreases with the increase of the thickness of the void
defect; while the case is just the reverse for higher modes at a
certain temperature. These indicate the effects of the void defect
on the thermal conductance sensitively depend on the index of the
modes.
When the defect consists of clamped material, namely the hard
wall boundary condition should be satisfied between the defect
and surroundings, it is seen that these results shown in Fig. 4.4
are obviously distinguishing from that for the void defect. Firstly,
in the limit
T
0, the quantum thermal conductance is not
observed. There exists a threshold temperature where the zero
→
