Nonadiabatic Tubular Reactor with Recycle
Nonadiabatic Tubular Reactor with Recycle
Consider a nonadiabatic tubular reactor with negligible mass and heat dispersions and recycle where a first-order exothermic reaction takes place [1]. This system is governed by the following two dimensionless partial differential equations and boundary conditions BC1 and BC2:
∂x
∂t
R+1
Da
∂x
∂z
θ
1+θ/γ
Lw=-+B(1-x)exp-α(θ-)
∂θ
∂t
R+1
Da
∂θ
∂z
θ
1+θ/γ
θ
c
BC1: ,
x(0,t)=x(1,t)
R
R+1
BC2: .
θ(0,t)=θ(1,t)
R
R+1
Here is concentration and is temperature, is the activation energy, is the heat evolution parameter, =0.05 is the dimensionless cooling temperature, is the dimensionless cooling parameter, is the recycle ratio, is the Damköhler number, and is the Lewis number.
x
θ
γ=25
B=8.3
θ
c
α=2.0
R=10
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 the parameters.
Lw=2.05
Da=0.53
x
1
θ
1
t