Nonadiabatic Tubular Reactor with Negligible Mass Dispersion
Nonadiabatic Tubular Reactor with Negligible Mass Dispersion
Consider a nonadiabatic tubular reactor with negligible mass dispersion (i.e. ≫) 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:
ϕ
m
ϕ
h
∂x
∂t
1
2
ϕ
m
2
∂
∂
2
z
1
Da
∂x
∂z
θ
1+θ/γ
Lw=θ-+B(1-x)exp-α(θ-)
∂θ
∂t
1
2
ϕ
h
2
∂
∂
2
z
1
Da
∂θ
∂z
θ
1+θ/γ
θ
c
BC1: : ==0,
z=1
∂x
∂z
∂θ
∂z
BC2: : -x=0, -θ=0.
z=0
1
2
ϕ
m
∂x
∂z
1
Da
1
2
ϕ
h
∂θ
∂z
1
Da
Here is concentration and is temperature, is the activation energy, =0.1 is the heat Thiele modulus, = is the mass Thiele modulus, is the heat evolution parameter, is the dimensionless cooling temperature, is the dimensionless cooling parameter, is the Damköhler number, and is the Lewis number.
x
θ
γ=25
2
ϕ
h
2
ϕ
m
4
10
B=8.3
θ
c
α
Da
Lw
As can be seen from snapshot 1, periodic solutions are obtained for and . In the figure, (t)=x(z=1,t) and (t)=θ(z=1,t) are plotted versus in blue and green, respectively. Also, you can see from snapshot 1 that a limit cycle is obtained for the above values of and .
Lw=1.1
Da=0.1
x
1
θ
1
t
Lw
Da