WOLFRAM|DEMONSTRATIONS PROJECT

Nonadiabatic Tubular Reactor with Negligible Mass Dispersion

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Lewis number
1.1
Damköhler number
0.1
Consider a nonadiabatic tubular reactor with negligible mass dispersion (i.e.
ϕ
m
≫
ϕ
h
) where a first-order exothermic reaction takes place [1, 2]. This system is governed by the following two dimensionless parabolic partial differential equations and boundary conditions BC1 and BC2:
∂x
∂t
=
1
2
ϕ
m
2
∂
x
∂
2
z
-
1
Da
∂x
∂z
+(1-x)exp
θ
1+θ/γ
,
Lw
∂θ
∂t
=
1
2
ϕ
h
2
∂
θ
∂
2
z
-
1
Da
∂θ
∂z
+B(1-x)exp
θ
1+θ/γ
-α(θ-
θ
c
)
,
BC1:
z=1
:
∂x
∂z
=
∂θ
∂z
=0
,
BC2:
z=0
:
1
2
ϕ
m
∂x
∂z
-
1
Da
x=0
,
1
2
ϕ
h
∂θ
∂z
-
1
Da
θ=0
.
Here
x
is concentration and
θ
is temperature,
γ=25
is the activation energy,
2
ϕ
h
=0.1
is the heat Thiele modulus,
2
ϕ
m
=
4
10
is the mass Thiele modulus,
B=8.3
is the heat evolution parameter,
θ
c
is the dimensionless cooling temperature,
α
is the dimensionless cooling parameter,
Da
is the Damköhler number, and
Lw
is the Lewis number.
As can be seen from snapshot 1, periodic solutions are obtained for
Lw=1.1
and
Da=0.1
. In the figure,
x
1
(t)=x(z=1,t)
and
θ
1
(t)=θ(z=1,t)
are plotted versus
t
in blue and green, respectively. Also, you can see from snapshot 1 that a limit cycle is obtained for the above values of
Lw
and
Da
.