Abstract
The problem of determining the critical conditions in a non-circular cylinder of infinite length is examined, in which the reaction is of zero order and where the Frank-Kamenetskii approximation to the reaction rate has been made. The generators are assumed parallel and the boundary of a cross section is given by
r
= 1 +
ε
cos
θ
(
ε
≪ 1), where (
r
,
θ
) are plane polar coordinates. The surface conditions assumed are (i) uniform temperature and (ii) newtonian cooling. By suitable expansions of the interior temperature and the Frank-Kamenetskii parameter
δ
, it is shown that the critical value of
δ
for (ii) is
δ
crit
(
ε, B
) = 8
σ
c
/(1 +
σ
c
)
2
exp[ – (4
σ
c
)/
B
(1 +
σ
c
)] x [1 -
ε
2
{
σ
2
c
/1 +
σ
c
) + (1/
B
)
σ
c
(1 + 3
σ
c
)/(1 +
σ
c
)
2
} +
O
(
ε
4
)], Where
σ
c
= -2/
B
+ (1 + 4/
B
2
)
½
and where
B
is a Biot number proportional to the surface-heat transfer coefficient. For (i), the simple result
δ
crit
(
ε
, ∞) = 2 -
ε
2
+
O
(
ε
4
), is obtained.
Cited by
2 articles.
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