This Demonstration computes the concentration and temperature profiles in a tubular reactor for low Péclet numbers (
using the shooting method (blue solid curve), as well as the orthogonal collocation method with shifted Legendre polynomials and eight internal collocation points (the red dots). Perfect agreement is obtained (see the first two snapshots).
For large values of the
number, the reactor behavior approaches that of a plug flow reactor (PFR), and in the limit as
, the system become singular. Consequently the boundary value problem becomes increasingly stiff with increasing
, the shooting method fails to converge. Thus for
, only orthogonal collocation results are shown (see red dots). To assess the accuracy of the collocation method, we computed the residual error for the temperature and concentration profiles. The residual error is shown in the plots; it measures how closely the solution satisfies the ordinary differential equations and boundary conditions. We also compared our results with data taken from  at
(blue circles), as can be seen in the last two snapshots. The concentration profile is in good agreement with , but our temperature profile is at best only in qualitative agreement.