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Concentration Profile in a Tubular Reactor

​
reactor length
15
reactor radius
0.5
diffusivity
0.005
axial velocity
0.5
Consider a dilute solution with a solute concentration
c
0
, in laminar flow. This enters a tubular reactor with a catalytic wall that instantaneously and irreversibly converts the solute to its isomer. The system can be described by the equation[1]:
v
max
1-
2
r
R
∂c
∂z
=
1
r
∂
∂r
r
∂c
∂r
.
Assume that axial diffusion can be neglected in comparison to axial convection. Here
v
max
is the maximum laminar parabolic velocity,
r
and
z
are the radial and axial coordinates, respectively,
R
is the reactor radius,
c
is the concentration of the newly formed isomer and is the diffusion coefficient. The boundary conditions are:
c(r,0)=
c
0
,
c(R,z)=0
,
∂c(0,z)
∂r
=0
.
Models like the one described here are useful in obtaining mass transfer data on metallic surfaces in studies designed to prevent or retard the oxidation of iron.

References

[1] R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena, rev. 2nd ed., New York: John Wiley & Sons, Inc., 2007

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