# 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