Page 51 - Process Modelling and Simulation With Finite Element Methods

38 Process Modelling and Simulation with Finite Element Methods

times are set to linspace (0, 2*pi, 500) , i.e. tenfold smaller time-step, than
u1(t=2n)=0.999939 with ode1 5s.
These two figures (1.3 & 1.4) clarify that FEMLAB can reproduce the
numerical integration of the cosine and sine functions with high fidelity if given
a small enough time step. Although we think of sine and cosine as “analytic
functions,” when tabulated this way, it is clear that the distinction between
analytic functions and those that require numerical integration is specious - they
are no more analytic than Bessel functions, elliptic functions, etc.

1.3.2 Numerical integration: Tubular reactor design

In this subsection, a coupled set of first order nonlinear ODES are solved
simultaneously for the design of a tubular reactor undergoing a homogeneous
chemical reaction. Typically, the key element in the design of a tubular reactor
is the estimate of the length of the reactor.
A tubular reactor is used to dehydrate gaseous ethyl alcohol at 2 bar and
150°C. The formula for this chemical reaction is

Ul IUl)

Figure 1.3 u 1 (t) over one period.