Heat Transport and Chemical Reaction in Tubular Reactor with Laminar Flow

This Demonstration shows the temperature and concentration profiles of an insulated tubular reactor in which a first-order, irreversible reaction 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:
,
,
,
with boundary conditions:
,
,
,
,
.
Here is the fluid density, is the maximum laminar parabolic velocity, is the fluid heat capacity, is the thermal conductivity, and are the rate and heat of reaction, respectively, and and are the axial and radial coordinates, while stands for the reactor radius, is the pre-exponential factor, is the activation energy, is the gas constant, is the concentration of reactant , is the diffusion coefficient, is the concentration of reactant entering the reactor, and is the temperature of the wall of the reactor and the fluid entering the reactor.

SNAPSHOTS

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DETAILS

It is convenient to use the following dimensionless quantities:
,
,
,
;
here is the mass flow rate divided by the cross-sectional area of the tubular reactor.
The dimensionless form of the conservation equations is:
,
,
with the boundary conditions:
,
,
,
,
.
Dimensionless parameters are defined as follows:
,
,
,
.
This system of coupled differential equations is solved with the built-in function NDSolve, and the radial and axial profiles of temperature and concentration of reactant are shown for different values of the radial and axial distance, the rate of reaction parameter and the heat of reaction parameter .
Reference
[1] R. I. Rothenberg and J. M. Smith, "Heat Transfer and Reaction in Laminar Tube Flow," AIChE Journal, 12 (2), 1966 pp. 213–220. doi:10.1002/aic.690120204.
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