# Comparison of One- and Two-Dimensional Models of Plate Reactors

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This Demonstration compares three mathematical models of a plate chemical reactor in which an adiabatic reaction takes place. The fluid containing the reactants flows in the channel between two parallel plates; the distance between the plates is much smaller than their width or length. The models assume a steady-state condition with constant material properties. The first model is one-dimensional; it considers only horizontal convective transport. The others are two-dimensional models that consider horizontal convection and vertical diffusion as well; they differ only in the horizontal fluid velocity profiles: one is laminar flow and the other is plug flow.

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Contributed by: Clay Gruesbeck (October 2018)

Open content licensed under CC BY-NC-SA

## Details

The equations for the one-dimensional model are:

and

.

These are the equations for the two-dimensional plug flow model:

and

,

and the two-dimensional model with laminar flow has these equations [1]:

and

.

The average (cup) values of concentration and temperature for the models with the flat velocity profiles are:

and

,

and for the model with the laminar flow:

and

,

where

is the distance between the plates

is the fluid specific gravity

is the mean horizontal velocity

is the concentration of component

is the fluid temperature

and are the horizontal and vertical coordinates, respectively

is the pre-exponential factor

is the activation energy

is the heat of reaction

is the gas constant

is the diffusivity

is the thermal conductivity

Reference

[1] R. B. Bird, W. E. Stewart and E. N. Lightfoot, *Transport Phenomena*, 2nd ed., New York: John Wiley & Sons, Inc., 2002.

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