Moving finite element method: fundamentals and applications in chemical engineering

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Numerical Methods with Chemical Engineering Applications (Cambridge Series in ..

At this time, a special topic on the parameter estimation in ODE from experimental data is given. A generalized nonlinear least-square, curve-fitting procedure6' 7 is introduced and a problem of com- puterized kinetic analysis in the batch fermen- tation of penicillin is assigned to the students.

Finite element method - Gilbert Strang

The effectiveness and comparison of different methods in solving ODE are then presented. A suitable book covering the up-to-date information of both types of approximations does not exist. Thus, the lec- ture-notes for Topic III are mostly the original developments in the course. An outline in chapters and sections has been included in Table I. It should be mentioned that the developments of The problem of finding a polynomial of a specified degree to approximate a known function given either in an analytical form or as sets of discrete data is considered..

The computer listing of the latest publications as well as the hundreds of reference reports and reprints on the numerical solution of PDE given by Professor John H. Giese of University of Delaware have been most helpful. Ames, W. Dahlquist, G. Anderson, "Nu- merical Methods," Prentice-Hall Finlayson, B. Gear, C. Issacson, I. Keller, "Analysis of Nu- merical Methods," Wiley Lapidus, L. Lambert, J. Mitchell, A. Ralston, A. I , and Vol.

Richtmyer, R. Rosenbrock, R. Strang, G. Varga, R. Willoughby, R. Young, D. Zienkiewicz, O. For example, studies which are con- cerned with the method of line for PDE12 Chap- ter III-2 , the composite numerical solution of PDE13 Chapter III-3 to III-5 , finite element method for heat conduction analysis14 and fluid flow problems15 Chapter III-9 , collocation A generalized non-linear least square, curve-fitting procedure is introduced and a problem of computerized kinetic analysis in the batch fermentation of penicillin is assigned While further discussions on the course contents and source material for Topic III are not possible within the limits of this article, a detailed write- up and specific subject references on the numerical solution of PDE can be obtained by writing to the author.

Homework problems are assigned to the class weekly. Each student is required to conduct an independent course project and to submit a term paper which includes: a a concise literature survey of the most important publications in the topic chosen, b a critical analysis of the computational techniques involved and a proper evaluation of the "state of the art," and c suggestions for further investigations as well as a preliminary analysis of the feasibility of the proposed research areas.

Since no course examinations are given, this provides more opportunities for each student to pursue the specific subjects of interest. Typical subjects on the term projects chosen by the class during the last year include the method of characteristics, the method of lines, the ana- lysis of chromatographic system, the colloca- tion method, and the extrapolation technique for the solution of PDE and nonlinear algebraic equa- tions.

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It is encouraging to mention that several of these projects conducted by the class in the course have led to some quite original research Continued on page FALL A7? From through , Tulsa University conducted a M. This pro- gram created a need for a graduate course which would familiarize B.

Since the ChE Department has ad- ministered the University of Tulsa Environmen- tal Protection UTEPP program-a non-profit, cooperative, petroleum industry-sponsored re- search program committed to studying present and future environmental protection problems in petroleum and related industries. Obviously, stu- dents working in UTEPP also require graduate- level instruction in industrial pollution control. Current industrial pollution con- trol practices and design procedures are intro- duced as painlessly as possible. This is accom- plished by emphasizing the relevancy of conven- tional, undergraduate chemical engineering.

In other words, biological oxidation processes are de- scribed as chemical reactors; but, of course, new concepts such as the inherently varying waste- water "feed" volume and concentration and the sensitivity of "bugs" to shock loads are carefully described.

Chemical engineering education

Similarly, ammonia stripping is dis- cussed using standard ChE desorption nomencla- ture; and liquid condensation in pressure-relief lines is treated as a standard thermodynamic "flash calculation. This televised procedure permitted maximum use of class time because an overhead TV camera made it possible to project printed pages on the TV receiving screens. This mini- mized the timeconsuming writing of notes on the blackboard and the laborious copying by students. While two texts were recommended but not required the majority of the course material was selected from recent articles see references for a partial listing.

The references must be up- dated every year because of the great current interest in this field.

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  8. Frequently students were Francis S. He holds the following degrees in. Chemical Engineering:-B. He is a profes- sional engineer, registered in Oklahoma, Pennsylvania and Texas. Because "Industrial Pollution Control" covered such a wide range of topics, expert guest lecturers were used:-e. Paul Buthod for petroleum re- fining; Erle Donaldson for subsurface disposal; Dick Martin for noise control and Robert Reed for combustion and incineration.

    Since , the University of Tulsa has spon- sored ten one-week short courses for industry on wastewater and air pollution control as applied to petroleum refining and related petrochemicals. Students enrolled in "Industrial Pollution Control" have always been encouraged to attend these short courses free of charge and were given complimentary notes for the short course.

    These short courses have enriched "Industrial Pollution Control" im- measurably. Last fall, for example, the students attended 35 hours of lectures on air pollution con- trol and received approximately pages of notes and design case histories. In-class treatment of air pollution then consisted of discussing points of student uncertainty and working extra prob- lems.

    Students were graded on 1 their solutions to the design problems; 2 two "term-papers" or more comprehensive design projects; and 3 their in-class presentation and defense of their design projects. The chief concept presented is: increased processing is accompanied by in- creased production of potential pollutants.

    Nelson Refinery Wastewater Treatment 1 hr lecture A brief summary is given of major uses of process water in a refinery emphasizing current recycling of process water and methods of minimizing volume of wastewater produced. Advantages of segregated sewers. Overview of primary, second- ary, and tertiary treatment with emphasis on ar- rangement of treatment steps.

    Manning FWPCA The course not only focuses on the general theories of industrial pollution control to provide breadth of understanding; but also emphasizes petroleum- related design examples to provide the required specialization. Current industrial pollution control practices and design procedures are introduced by emphasizing the relevancy of conventional undergraduate ChE.

    Biological Treatment 2 weeks, 3 problems Biological phenomena and related importance in understanding biological waste treatment are presented. Laboratory methods for modeling aerobic growth kinetics.