Environmental Engineering Reference
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Figure 3.11 The ballistic thermal conductance per unit area ( σ / S )of
graphene as a function of temperature ( T ), calculated by the Landauer
formula, which employs the phonon dispersion shown in Fig. 3.10. The
transport direction is chosen to be along the
Morthe
K direction. The
cross sectional area S
=
w
δ
,where w is the width of the graphene and
δ =
0.335 nm is chosen asthe layer separation in graphite.
thermal conductance at higher temperatures is almost unaffected.
Moreover, the induced inaccuracy in the calculated ballistic thermal
conductance is estimated to beless than 10% [41].
We calculated the ballistic thermal conductance of graphene
applying the Landauer formula using the computed phonon
dispersion (shown in Fig. 3.10). The calculated scaled ballistic
thermal conductance is presented in Fig. 3.11. Selecting different
transport directions in graphene leads to only slight difference in
thecalculatedscaledthermalconductance,consistentwithprevious
results [47]. This directly proves that thermal transport is isotropic
in graphene. The ballistic thermal conductance of graphene grows
as increasing temperature. At room temperature, a value of 4.4 4.5
nW/K/nm 2 isobtained.
Alternatively, we study the ballistic thermal conductance of
graphene indirectly by investigating thermal conduction of GNRs
and CNTs. The scaled ballistic thermal conductance of GNRs and
CNTs with various widths is presented in Fig. 3.8a. From those
results,weextrapolatethatthescaledballisticthermalconductance
 
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