Environmental Engineering Reference
In-Depth Information
Figure 5.6
The distribution of the gas tem-
perature and the number density of excit-
ed molecules in the thermal wave of vibra-
tional relaxation for different limiting ratios
between the diffusion coefficient of excited
molecules
and the thermal diffusivity coeffi-
cient
of the gas: (a)
D
D
and (b)
D
has the form
N
D
N
max
(
N
max
N
0
)exp(
ux
/
D
)if
x
>
0, where
N
0
is the num-
ber density of the excited molecules at
x
D
0and
N
0
is the integration constant. In
the region
x
0 vibrational relaxation is of importance, but the gas temperature
is constant. This leads to
<
r
u
2
D
1
D
u
2
D
,
2
N
D
N
0
exp(
α
x
),
x
<
0,
α
D
C
τ
1/[
Nk
(
T
m
)]. The transition region, where the gas temperature is not
at its maximum, but the vibrational relaxation is essential, is narrow under the
conditions considered. Hence, at
x
τ
D
where
0theaboveexpressionsmustgivethesame
results both for the number density of excited molecules and for their derivatives.
We obtain
D
r
2
D
τ
T
D
p
2
DNk
(
T
m
),
D
u
D
,
α
D
u
D
.
(5.40)
In this case the propagation of the thermal wave of vibrational relaxation is gov-
erned by the diffusion of excited molecules in a hot region where vibrati
onal
re-
laxation takes place. Hence, the wave velocity is of the order of
u
p
D
/
in
accordan
ce w
ith (5.40). The width of the front of the thermal wave is estimated as
Δ
τ
p
D
x
τ
.
