Page 156 - Process Modelling and Simulation With Finite Element Methods

Extended Multiphysics 143

U V W
Rzu0-U R=vO-V R=-W

The Neumann BCs for U,V,W require the normal component of r to vanish at
au
is
the outflow boundary. Since fi rU = 0, - the diffusive flux, this BC
an
enforces a no diffusive flux boundary condition. So all the flux is convective,
i.e. outflow. For the surface variables, however, r =O was specified, so entering
zero Neurnann conditions is a non-constraint (O=O).
Pull down the Mesh menu and select Parameters.

>>More
0 Max size near vertices: 1 0.0001 2 0.0001
Number of Elements in Subdomain: 1 1000
Apply

This results in a 1000 element meshing. Now for the Solver. Pull down the
Solver Menu and select Parameters. Check the Stationary Nonlinear solver
box, apply, then under Settings de-select the Automatic Scaling and select None.
Now, click on the Solve button. It takes FEMLAB 9 iterations to get there (this
is a highly nonlinear problem), but it converges to 10.' accuracy eventually.
Figures 4.3 and 4.4 show the behaviour of the reactant concentrations.
Figure 4.4 in particular requires interpretation. Because of kinetic asymmetry,
u" andcvanish in different sections of the reactor. Because v has greater mass
transfer coefficient it populates the surface initially, u" reacts instantaneously as
it arrives on the surface. As u is in bulk excess, however, eventually ;reacts
away as well, until we reach the crossover point, where both surface reactants
vanish. This is actually the point of greatest molecular efficiency, since any
molecule of u or v that arrives on the surface reacts here. The theory of