Chemistry Reference
In-Depth Information
Fig. 1.3
Sample zones: I,
reaction occurs with a
noticeable rate; II, preheat
zone
be taken into account under the assumption that it is approximately equal to that of
the equation for a thermoneutral reaction. Then one can write a thermal conductivity
equation as
exp
d
2
T
dx
2
+
M
δ
dT
dx
±
Qk
0
ac
E
R
T
Bi
δ
−
−
2
(
T
−
T
∞
)=0
.
(1.23)
Integration of this equation over the interval 0 to
x
1
gives
1 +
1 + 4Bi
/
M
2
2
⎛
⎞
2
x
=
x
1
dT
dx
q
2
λ
2
+
M
2
Bi
δ
⎝
⎠
=
2
−
δ
2
(1.24)
exp
,
×
(
T
S
−
T
∞
)
2
±
2
Qk
0
R
T
S
acE
E
R
T
S
T
∞
)
2
−
(
T
1
−
−
where
x
1
is the thickness of the reaction zone,
q
is the heat flow towards the end
surface, and
T
1
is the temperature on the border between the two zones.
To find
q
, one can use the heat-balance equation:
∞
Q
]+
α
δ
q
=
U
ρ
[
c
(
T
S
−
T
∞
)
∓
(
T
−
T
∞
)
dx
.
0
The contribution of the heat emitted from the lateral sample surface in the reaction
zone to the overall heat loss is always much less than that of the preheat zone.
Therefore, during the estimation of the overall heat loss, one can substitute
T
for
T
M
in the integral without causing significant error. Then
1 + 4Bi
/
M
2
∞
−
1
(
T
−
T
∞
)
dx
=(
T
S
−
T
∞
)M
δ
,
(1.25)
2Bi
0
and
1 +
1 + 4Bi
/
M
2
2
⎡
⎤
q
λ
=
M
δ
Q
c
⎣
(
T
S
−
⎦
.
T
∞
)
∓
(1.26)
Let us consider the first two terms on the right hand side of Eq. (1.24):
