Teaching arc‐length continuation in the chemical engineering graduate program using MATLAB

• Published in: Computer applications in engineering education 2018-07, Vol.26 (4), p.1033-1049
• Main Authors: Al‐Mubaiyedh, Usamah A., Binous, Housam
• Format: Article
• Language: English
• Subjects: Applications of mathematics; Applied mathematics; arc‐length continuation; Boundary value problems; Case studies; Chemical engineering; chemical engineering thermodynamics; Chemical reactions; Colleges & universities; Compressibility; Continuously stirred tank reactors; Equations of state; graduate‐level education; Mathematical analysis; MATLAB; Molar volume; Natural gas; Nonlinear equations; Nonlinear systems; Numerical methods; Organic chemistry; Propylene; steady‐state multiplicity; Teachers; Teaching; Teaching methods; Temperature effects
• ISSN: 1061-3773; 1099-0542
• DOI: 10.1002/cae.21954

We present the solution of six problems drawn from the chemical engineering and applied mathematics fields of study. These problems are solved using the arc‐length continuation method. Among a large number of examples, we have chosen to treat the following case studies because they illustrate basic concepts such as solution multiplicity when dealing with systems of nonlinear algebraic equations or boundary value problems: 1) Plotting an ∞‐shaped curve called the Bernoulli's Lemniscate; 2) Computing the Joule‐Thomson inversion curve for a pure gas using the Soave‐Redlich‐Kwong cubic equation of state; 3) Predicting the Compressibility Factor and Molar Volume versus the Reduced Temperature; 4) Determining region where steady‐state multiplicity is observed in a continuous stirred‐tank reactor (CSTR) with multiple reactions and heat effects; 5) Finding the steady‐state temperature and conversion of a Propylene Glycol Reactor; and 6) Investigating the Frank–Kamenetskii problem arising in the self‐heating of a reactive solid. Reader should be advised that problem 1 may seem slightly mathematical in nature. However, case studies 2–6 could be very useful to instructors involved in teaching not only numerical methods but also chemical thermodynamics and chemical reaction engineering. For one of the above listed case studies, we unveil the MATLAB© code, that we have employed, in the Appendix. In addition, we will emphasize on the versatility of this mathematical software through the extensive usage of the built‐in command fsolve, for the presently undertaken computations. Finally, we conclude this paper by sharing our experience teaching this subject to graduate students at King Fahd University of Petroleum & Minerals.