Page 138 - Process Modelling and Simulation With Finite Element Methods

Multiphysics 125

subject to

(3.10)

Here, nlim is the limiting dimensionless temperature that can be achieved upon
exhaustion of the reactant, r=O. The Peclet number, Pe, is either the thermal or
mass Peclet number (rl or r2).
Amundson proposed a one dimensional search to the above boundary value
problem, starting from a guess of n(x=l) and shooting back to x=O. In both of the
above cases, n,,=1.656.
Let’s first solve the single convection-diffusion-reaction equation (3.9) using
FEMLAB. Because it is a boundary value problem, FEM has a natural advantage
here.

Start up FEMLAB and enter the Model Navigator:

Model Navigator
Select I-D dimension
Select Chemical Engineering Module + convection and
diffusion
Element: Lagrange - quadratic
More>>
OK

Pull down the Draw menu and select Specify Geometry.

Draw Mode
0 Name: interval
Start: 0
stop: 1

Now for the boundary conditions. Pull down the Boundary menu and select
Boundary Settings.

Boundary Mode
Select domain 1
0 Check -N.n = Pe*( 1 -c)
0 Select domain 2
e Select -N.n = 0
Apply1 OK