Chemical Engineering, Applied Mathematics

Focusing on the application of mathematics to chemical engineering, Applied Mathematical Methods for Chemical Engineers, Second Edition addresses the setup and verification of mathematical models using experimental or other independently derived data. 

Engineers apply risk assessment to pollution prevention in their strategies. Risk is expressed as a mathematical function of hazards and exposures. Risk assessment methods help quantify the degree of environmental impact for individual chemicals. Engineers apply technologies to control the risks as an element of the design processes and products, taking into account the likelihood that certain actions wiU occur. Thus,... 

The phase rule is a mathematical expression that describes the behavior of chemical systems in equilibrium. A chemical system is any combination of chemical substances. The substances exist as gas, liquid, or solid phases. The phase rule applies only to systems, called heterogeneous systems, in which two or more distinct phases are in equilibrium. A system cannot contain more than one gas phase, but can contain any number of liquid and solid phases. An alloy of copper and nickel, for example, contains two solid phases. The rule makes possible the simple correlation of very large quantities of physical data and limited prediction of the behavior of chemical systems. It is used particularly in alloy preparation, in chemical engineering, and in geology. 

Rice, R.G. and Do, D.D., 1995. Applied Mathematics and modelling for chemical engineers. New York Wiley. 

Mickley, H.S, Sherwood, T.K. and Reed, C.E. Applied Mathematics in Chemical Engineering, 2nd edn, (McGraw-Hill, New York, 1957). 

The following sections describe in more detail a number of areas in chemical engineering in which the ability to develop and apply detailed mathematical models should yield substantial rewards. 

Rice, R. G. and D. D. Duong. Applied Mathematics and Modeling for Chemical Engineers. Wiley, New York (1995). 

Loney, N.W. (2001) Applied Mathematical Methods for Chemical Engineers, CRC Press. 

Most of you have probably been exposed to Laplace transforms in a mathematics course, but we will lead off this chapter with a brief review of some of the most important relationships. Then we will derive the Laplace transformations of commonly encountered functions. Next we will develop the idea of transfer functions by observing what happens to the differential equations describing a process when they are Laplace-transformed. Finally, we will apply these techniques to some chemical engineering systems. 

Mickley, Sberwood, and Reed Applied Mathematics in Chemical Engineering... 

Department of Applied Mathematics and Computational Systems, IPICyT rfematSipicyt.edu.mx Department of Chemical Engineering, UdG victorga ccip.udg.mx... 

I learned about chemical reactors at the knees of Rutherford Aris and Neal Amundson, when, as a surface chemist, I taught recitation sections and then lectures in the Reaction Engineering undergraduate course at Minnesota. The text was Aris Elementary Chemical Reaction Analysis, a book that was obviously elegant but at first did not seem at all elementary. It described porous pellet diffusion effects in chemical reactors and the intricacies of nonisothermal reactors in a very logical way, but to many students it seemed to be an exercise in applied mathematics with dimensionless variables rather than a description of chemical reactors. 

When Amundson taught the graduate course in mathematics for chemical engineering, he always insisted that all boundary conditions arise from nature. He meant, I think, that a lot of simplification and imagination goes into the model itself, but the boundary conditions have to mirror the links between the system and its environment very faithfully. Thus if we have no doubt that the feed does get into the reactor, then we must have a condition that ensures this in the model. We probably do not wish to model the hydrodynamics of the entrance region, but the inlet must be an inlet. One merit of the wave model we have looked at briefly is that both boundary conditions apply to the inlet. 

There are any number of good books on this subject, and three come to mind J. D. Murray, Asymptotic Analysis. Oxford Clarendon Press, 1974 C. C. Lin and L. A. Segal, Mathematics Applied to Deterministic Problems in the Natural Sciences. New York Macmillan, 1974 and R. E. O Malley. Introduction to Singular Perturbations. New York Academic Press. 1974. See also Varma and Morbidelli. Mathematical Methods in Chemical Engineering. New York Oxford University Press, 1997. 

Sherwood, T. K., and C. E. Reed. Applied Mathematics in Chemical Engineering (New York McGraw-Hill Book Co., 1939). 

Scale- Up of Electrochemical Reactors. The intermediate scale of the pilot plant is frequendy used in the scale-up of an electrochemical reactor or process to full scale. Dimensional analysis (qv) has been used in chemical engineering scale-up to simplify and generalise a multivariant system, and may be applied to electrochemical systems, but has shown limitations. It is best used in conjunction with mathematical models. Scale-up often involves seeking a few critical parameters. For electrochemical cells, these parameters are generally current distribution and cell resistance. The characteristics of electrolytic process scale-up have been described (63—65). 

Chadia is a chemical engineer who has turned towards applied mathematics in her graduate studies at Auburn University and has helped us bridge the gap between our individual perspectives. 

Thomas K. Sherwood and C. E. Reed, Applied Mathematics in Chemical Engineering, McGraw-Hill, New York, 1939 William R. Marshall and Robert L. Pigford, The Application of Differential Equations to Chemical Engineering Problems, University of Delaware, Newark, 1947 A. B. Newman, Temperature Distribution in Internally Heated Cylinders, Trans. AlChE 24,44-53 (1930) T. B. Drew, Mathematical Attacks on Forced Convection Problems A Review, Trans. AlChE 26,26-79 (1931) Arvind Varma, Some Historical Notes on the Use of Mathematics in Chemical Engineering, pp. 353-387 in W. F. Furter, ed., A Century of Chemical Engineering [17]. 

It is my opinion that recent developments in the mathematical description of nonlinear dynamical systems have the potential for an enormous impact in the fields of fluid mechanics and transport phenomena. However, an attempt to assess this potential, based upon research accomplishments to date, is premature in any case, there are others better qualified than myself to undertake the task. Instead, I will offer a few general observations concerning the nature of the changes that may occur as the mathematical concepts of nonlinear dynamics become better known, better understood, more highly developed, and, lastly, applied to transport problems of interest to chemical engineers. 

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