Page 149 - Process Modelling and Simulation With Finite Element Methods

136 Process Modelling and Simulation with Finite Element Methods

fluid dynamics of the hemispherical obstruction. The concentration profile was
resolved on the most coarse mesh chosen.
Without too much aggrandizement, this chapter also shows the ease of
solution of highly nonlinear problems by parametric continuation (typically
automated by MATLAB programming). The chapter also shows how to include
variable physical properties and complicated field behaviors by interpolation
functions programmed in MATLAB m-file functions.
Multiphysics is a recurrent theme in this text, largely because “single
physics” is well studied. Thus, inherently, multiphysics descriptions are required
for state-of-the-art research models. So several more examples will follow.

References
1. Ramirez, W.F., Computational Methods for Process Simulation, 2nd ed.,
Butterworth Heinemann, Oxford, 1997.
2. Batchelor, G.K., “Heat transfer by free convection across a closed cavity
between vertical boundaries at different termperatures.“ Quart. J. Appl.
Maths. 12(3):209-233, 1954.
3. Velarde M.G. and Normand C. “Convection” Scientific American, 243( 1):
92-108, 1980.
4. Zienkiewicz, 0. C. and Taylor, R.L., The Finite Element Method. Volume 3:
Fluid Dynamics, Heinemann-Butterworth, 2000.
5. Hanselman D. and Littlefield B.,Mastering MATLAB 6: A comprehensive
tutorial and reference, Prentice Hall, Saddle River NJ, 2001, p. 294.
6. Clough, D.E. and Ramirez, W.F. “Stability of tubular reactors,” Simulation
16, 1971.
7. Danckwerts, P.V. “Continuous flow systems. Distribution of residence
times.” Chem. Eng. Sci. 2:l-18, 1953.
8. Amundson, N.R. Can. J. Ch. E. 43:99, 1965.
9. FEMLAB Chemical Engineering Module, User’s Guide, Version 2.2,
p. 2-74.