Heat Transport and Chemical Reaction in Tubular Reactor with Laminar Flow

heat of reaction parameter

0.25

radial position

0.25

rate of reaction parameter

1.

axial position

0.25

This Demonstration shows the temperature and concentration profiles of an insulated tubular reactor in which a first-order, irreversible reaction

A

k

→

B

takes place in a fluid undergoing laminar flow.

Assuming that temperature does not affect the fluid properties and that axial diffusion can be neglected in comparison to axial convection, the energy and mass balances for this system are:

ρ

v

max

C

p

1-

2

y

o



∂T

∂x

=k

1

y

∂

∂y

y

∂T

∂y

+ℛΔH

,

ρ

v

max

1-

2

y

o



∂C

∂x

=

1

y

∂

∂y

y

∂C

∂y

-ℛ

,

ℛ=

k

o

exp

-E

RT

C

,

with boundary conditions:

C(0,y)=

C

o

,

T(0,y)=

T

o

,

T(x,

y

o

)=

T

o

,

∂C(x,0)

∂y

=0

,

∂C(x,R)

∂y

=0

.

Here

ρ

is the fluid density,

v

max

is the maximum laminar parabolic velocity,

C

p

is the fluid heat capacity,

k

is the thermal conductivity,

ℛ

and

ΔH

are the rate and heat of reaction, respectively, and

x

and

y

are the axial and radial coordinates, while

y

o

stands for the reactor radius,

k

o

is the pre-exponential factor,

E

is the activation energy,

R

is the gas constant,

C

is the concentration of reactant

A

,



is the diffusion coefficient,

C

o

is the concentration of reactant

A

entering the reactor, and

T

o

is the temperature of the wall of the reactor and the fluid entering the reactor.