Applied mathematics and modeling for chemical engineers pdf download

Notify me of new posts by email. Welcome to EasyEngineering, One of the trusted educational blog. Check your Email after Joining and Confirm your mail id to get updates alerts. Other Useful Links. Do PDF Download. Your Comments About This Post. Is our service is satisfied, Anything want to say? Cancel reply. Please enter your comment!

Please enter your name here. You have entered an incorrect email address! Leave this field empty. Trending Today. Load more. Get New Updates Email Alerts Enter your email address to subscribe this blog and receive notifications of new posts by email. Join With us. Today Updates.

August 8. July June Duggal Free Download June Charles H. Roth, Larry Weedy, B. Timoshenko, Donovan H. Smith Book…. Jain, S. Iyengar, R. Jain Book Free Download. Ganesh, G. Balasubramanian Book Free Download. Stroud Free Download. Please enter your comment! Please enter your name here. Page 2. Page 3. Page 4. Page 5. Page 6. Page 7. Page 8.

Page 9. Page Page A. Page B. Page E. Page Appendix F: Nomenclature Page Postface Page A Page B Page C Page D Page E Page F Page G Page I Page L Page M Page N Page P Page Q Page R Page S Page T Page Z Rice , Duong D. This document was uploaded by our user. The uploader already confirmed that they had the permission to publish it. Report DMCA. E-Book Overview Bridges the gap between classical analysis and modern applications. Following the chapter on the model building stage, it introduces traditional techniques for solving ordinary differential equations, adding new material on approximate solution methods such as perturbation techniques and elementary numerical solutions.

Also includes analytical methods to deal with important classes of finite-difference equations. The last half discusses numerical solution techniques and partial differential equations. Do University of Queensland St. Elbe Savoula Amanatidis Pedro A. The cover was printed by Phoenix Color Corp. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Sections and of the United States Copyright Act without the permission of the copyright owner is unlawful.

Duong D. ISBN 1. Differential equations. Chemical processes—Mathematical models. Chemical engineering—Mathematics. Duong, D. R37 '. This book has nurtured several generations on the importance of problem formulation by elementary differential balances. Modeling or idealization of processes has now become standard operating procedure, but, unfortunately, the sophistication of the modeling exercise has not been matched by textbooks on the solution of such models in quantitative mathematical terms.

Moreover, the widespread availability of computer software packages has weakened the generational skills in classical analysis. The purpose of this book is to attempt to bridge the gap between classical analysis and modern applications.

Thus, emphasis is directed in Chapter 1 to the proper representation of a physicochemical situation into correct mathematical language. It is important to recognize that if a problem is incorrectly posed in the first instance, then any solution will do.

The thought process of "idealizing," or approximating an actual situation, is now commonly called "modeling. We try to give emphasis to this well-known truth by selecting literature examples, which sustain experimental verification. Following the model building stage, we introduce classical methods in Chapters 2 and 3 for solving ordinary differential equations ODE , adding new material in Chapter 6 on approximate solution methods, which include perturbation techniques and elementary numerical solutions.

This seems altogether appropriate, since most models are approximate in the first instance. Finally, because of the propensity of staged processing in chemical engineering, we introduce analytical methods to deal with important classes of finite-difference equations in Chapter 5. In Chapters 7 to 12 we deal with numerical solution methods, and partial differential equations PDE are presented. Classical techniques, such as combination of variables and separation of variables, are covered in detail.

This allows sets of PDEs to be solved as handily as algebraic sets. Approximate and numerical methods close out the treatment of PDEs in Chapter This book is designed for teaching. It meets the needs of a modern undergraduate curriculum, but it can also be used for first year graduate students.

The homework problems are ranked by numerical subscript or an asterisk. Thus, subscript 1 denotes mainly computational problems, whereas subscripts 2 and 3 require more synthesis and analysis. Problems with an asterisk are the most difficult and are suited for graduate students. Chapters 1 through 6 comprise a suitable package for a one-semester, junior level course 3 credit hours. Chapters 7 to 12 can be taught as a one-semester course for advanced senior or graduate level students.

Academics find increasingly less time to write textbooks, owing to demands on the research front. Fredenslund and K. Ostergaard, for their efforts in making sabbatical leave there in so successful, and extends a special note of thanks to M.

Michelson for his thoughtful reviews of the manuscript and for critical discussions on the subject matter. He also acknowledges the influence of colleagues at all the universities where he took residence for short and lengthy periods including: University of Calgary, Canada; University of Queensland, Australia; University of Missouri, Columbia; University of Wisconsin, Madison; and of course Louisiana State University, Baton Rouge.

Richard G. Contents 5. This page has been reformatted by Knovel to provide easier navigation. Contents 9. Contents xv Contents xvii E. Chapter A Formulation of Physicochemical Problems 1. Thus, much is known about a physicochemical problem beforehand, derived from experience or experiment i. Most often, a theory evolves only after detailed observation of an event.

Thus, the first step in problem formulation is necessarily qualitative fuzzy logic. This first step usually involves drawing a picture of the system to be studied. The second step is the bringing together of all applicable physical and chemical information, conservation laws, and rate expressions. At this point, the engineer must make a series of critical decisions about the conversion of mental images to symbols, and at the same time, how detailed the model of a system must be.

Here, one must classify the real purposes of the modeling effort. Is the model to be used only for explaining trends in the operation of an existing piece of equipment? Is the model to be used for predictive or design purposes? Do we want steady-state or transient response? The scope and depth of these early decisions will determine the ultimate complexity of the final mathematical description.

The third step requires the setting down of finite or differential volume elements, followed by writing the conservation laws. In the limit, as the differential elements shrink, then differential equations arise naturally. Next, the problem of boundary conditions must be addressed, and this aspect must be treated with considerable circumspection.

When the problem is fully posed in quantitative terms, an appropriate mathematical solution method is sought out, which finally relates dependent responding variables to one or more independent changing variables. The final result may be an elementary mathematical formula, or a numerical solution portrayed as an array of numbers.

We start with the simplest possible model, adding complexity as the demands for precision increase. Often, the simple model will suffice for rough, qualitative purposes. However, certain economic constraints weigh heavily against overdesign, so predictions and designs based on the model may need to be more precise. This section also illustrates the "need to know" principle, which acts as a catalyst to stimulate the garnering together of mathematical techniques.

The problem posed in this section will appear repeatedly throughout the book, as more sophisticated techniques are applied to its complete solution. Model 1—Plug Flow As suggested in the beginning, we first formulate a mental picture and then draw a sketch of the system.

We bring together our thoughts for a simple plug flow model in Fig. One of the key assumptions here is plug flow, which means that the fluid velocity profile is plug shaped, in other words uniform at all radial positions. This almost always implies turbulent fluid flow conditions, so that fluid elements are well-mixed in the radial direction, hence the fluid temperature is fairly uniform in a plane normal to the flow field i.

If the tube is not too long or the temperature difference is not too severe, then the physical properties of the fluid will not change much, so our second Figure 1. A steady-state solution is desired. The physical properties p, density; Cp, specific heat; k, thermal conductivity, etc. The wall temperature is constant and uniform i. The velocity profile is plug shaped or flat, hence it is uniform with respect to z or r.

The fluid is well-mixed highly turbulent , so the temperature is uniform in the radial direction. Thermal conduction of heat along the axis is small relative to convection. The third step is to sketch, and act upon, a differential volume element of the system in this case, the flowing fluid to be modeled. We illustrate this elemental volume in Fig. Moreover, there are no chemical, nuclear, or electrical sources specified within the volume element, so heat generation is absent.

The only way heat can be exchanged is through the perimeter of the element by way of the temperature difference between wall and fluid. The contact area in this simple model is simply the perimeter of the element times its length. The constant heat transfer coefficient is denoted by h. Had we used Cp T — 7ref for enthalpy, the term 7ref would be cancelled in the elemental balance. Before solving this equation, it is good practice to group parameters into a single term lumping parameters.

As it stands, the above equation is classified as a linear, inhomogeneous equation of first order, which in general must be solved using the so-called Integrating-Factor method, as we discuss later in Chapter 2 Section 2. Nonetheless, a little common sense will allow us to obtain a final solution without any new techniques. All that remains is to find a suitable value for K. To do this, we recall the boundary condition denoted as T0 in Fig. The conservation law Eq. We rearrange this to a form appropriate for the fundamental lemma of calculus.

However, since two position coordinates are now allowed to change, we must define the process of partial differentiation, for example, Ih. Thus, we divide Eq.