Computer engineering, mathematical modeling

Khandan, N. 2002. Modeling Tools for Environmental Engineers and Scientists. Boca Raton, FL CRC Press. The author describes some 50 computer models developed with 8 different software packages. Intended for nonprogrammers to develop computer-based mathematical models for natural and engineered environmental systems, this book includes a review of mathematical modeling and fundamental concepts such as material balance, reactor configurations, and fate and transport of environmental contaminants. 

Molecular modeling has evolved as a synthesis of techniques from a number of disciplines—organic chemistry, medicinal chemistry, physical chemistry, chemical physics, computer science, mathematics, and statistics. With the development of quantum mechanics (1,2) ia the early 1900s, the laws of physics necessary to relate molecular electronic stmcture to observable properties were defined. In a confluence of related developments, engineering and the national defense both played roles ia the development of computing machinery itself ia the United States (3). This evolution had a direct impact on computing ia chemistry, as the newly developed devices could be appHed to problems ia chemistry, permitting solutions to problems previously considered intractable. 

Before the advent of modem computer-aided mathematics, most mathematical models of real chemical processes were so idealized that they had severely limited utility— being reduced to one dimerrsion and a few variables, or Unearized, or limited to simplified variability of parameters. The increased availability of supercomputers along with progress in computational mathematics and numerical functional analysis is revolutionizing the way in which chemical engineers approach the theory and engineering of chemical processes. The means are at hand to model process physics and chenustry from the... 

Constraints in optimization arise because a process must describe the physical bounds on the variables, empirical relations, and physical laws that apply to a specific problem, as mentioned in Section 1.4. How to develop models that take into account these constraints is the main focus of this chapter. Mathematical models are employed in all areas of science, engineering, and business to solve problems, design equipment, interpret data, and communicate information. Eykhoff (1974) defined a mathematical model as a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in a usable form. For the purpose of optimization, we shall be concerned with developing quantitative expressions that will enable us to use mathematics and computer calculations to extract useful information. To optimize a process models may need to be developed for the objective function/, equality constraints g, and inequality constraints h. 

Mathematical modelling, in biochemical engineering, 77 41 Mathematical models of glass melting, 72 605 process-control, 20 687-691 Mathematical optimization approach, in computer- aided molecular design, 26 1037... 

S. Elnashaie, F. Alhabdin, S. Elshishini, The vital role of mathematical modelling in chemical engineering education, Math Comput Modelling, 17 (1993), p. 3-11... 

Perspective, The use of a mathematical model on a computer to simulate a chemical process is now approximately two decades old. The field, which has been referred to as steady state chemical process simulation, flowsheeting or computer aided chemical process design to emphasize various shadings and meanings has had a major impact on moving chemical process design from essentially an art form of the 1950 s to an accepted engineering science today. 

Empiricism—at one level little more than a synonym for reliance on experimental observation—need not be blind. In many cases, it is the crucial starting point for detailed analysis it is the source of the critical hypotheses which underlie successful theories, whose predictions are later verified by further experimental observation. Few scientists would contest this last statement. This has relevance to the comments made above about computer simulation, in that the latter can only be as good as the mathematical models on which it is based. In any new engineering situation, there may well be areas of uncertainty, say about the nature of the fluid in question, which mean that the relations required by a fully general computational fluid mechanics simulator program are not known. 

It is true to say that the selection of suitable mathematical models has involved a clear physical understanding of the processes involved and so can be viewed as the province of the chemical engineer it is also true that progress would have been more rapid if the actual mathematical and computational analyses had been carried out by experts, rather than by chemical engineering graduate students or postdoctoral workers. 

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