Mass Transfer Operations for the Practicing Engineer - Louis Theodore - E-Book

Mass Transfer Operations for the Practicing Engineer E-Book

Louis Theodore

0,0
160,99 €

-100%
Sammeln Sie Punkte in unserem Gutscheinprogramm und kaufen Sie E-Books und Hörbücher mit bis zu 100% Rabatt.

Mehr erfahren.
Beschreibung

An invaluable guide for problem solving in mass transfer operations This book takes a highly pragmatic approach to providing the principles and applications of mass transfer operations by offering a valuable, easily accessible guide to solving engineering problems. Both traditional and novel mass transfer processes receive treatment. As with all of the books in this series, emphasis is placed on an example-based approach to illustrating key engineering concepts. The book is divided into two major parts. It starts with the principles underlying engineering problems--showing readers how to apply general engineering principles to the topic of mass transfer operations. It then goes on to provide step-by-step guidance for traditional mass transfer operations, including distillation, absorption and stripping, and adsorption, plus novel mass transfer processes. Essential topics for professional engineering exams are also covered. Geared towards chemical, environmental, civil, and mechanical engineers working on real-world industrial applications, Mass Transfer Operations for the Practicing Engineer features: * Numerous sample problems and solutions with real-world applications * Clear, precise explanations on how to carry out the basic calculations associated with mass transfer operations * Coverage of topics from the ground up for readers without prior knowledge of the subject * Overview of topics relevant to the ABET (Accreditation Board for Engineering and Technology) for those taking the Professional Engineering (PE) exams * Appendix containing relevant mass transfer operation charts and tables

Sie lesen das E-Book in den Legimi-Apps auf:

Android
iOS
von Legimi
zertifizierten E-Readern

Seitenzahl: 881

Veröffentlichungsjahr: 2011

Bewertungen
0,0
0
0
0
0
0
Mehr Informationen
Mehr Informationen
Legimi prüft nicht, ob Rezensionen von Nutzern stammen, die den betreffenden Titel tatsächlich gekauft oder gelesen/gehört haben. Wir entfernen aber gefälschte Rezensionen.



Contents

Cover

Half Title page

Title page

Copyright page

Dedication

Preface

Part One: Introduction

Chapter 1: History of Chemical Engineering and Mass Transfer Operations

References

Chapter 2: Transport Phenomena vs Unit Operations Approach

References

Chapter 3: Basic Calculations

Introduction

Units and Dimensions

Conversion of Units

The Gravitational Constant GC

Significant Figures and Scientific Notation(3)

References

Chapter 4: Process Variables

Introduction

Temperature

Pressure

Moles and Molecular Weight

Mass, Volume, and Density

Viscosity

Reynolds Number

PH

Vapor Pressure

Ideal Gas Law(7)

References

Chapter 5: Equilibrium vs Rate Considerations

Introduction

Equilibrium

Rate

Chemical Reactions

References

Chapter 6: Phase Equilibrium Principles

Introduction

Gibb’s Phase Rule

Raoult’s Law

Henry’s Law

Raoult’s Law Vs Henry’s Law(7)

Vapor-Liquid Equilibrium in Nonideal Solutions(1)

Vapor-Solid Equilibrium

Liquid–Solid Equilibrium

References

Chapter 7: Rate Principles

Introduction

The Operating Line

Fick’s Law

Mass Transfer Coefficients

Overall Mass Transfer Coefficient

References

Part Two: Applications: Component and Phase Separation Processes

Chapter 8: Introduction to Mass Transfer Operations

Introduction

Classification of Mass Transfer Operations

Mass Transfer Equipment

Characteristics of Mass Transfer Operations

References

Chapter 9: Distillation

Introduction

Flash Distillation

Batch Distillation

Continuous Distillation With Reflux

References

Chapter 9: Absorption and Stripping

Introduction

Description of Equipment

Design and Performance Equations–Packed Columns

Design and Performance Equations–Plate Columns

Stripping

Packed vs Plate Tower Comparison

Summary of Key Equations

References

Chapter 11: Adsorption(1,2)

Introduction

Adsorption Classification

Adsorption Equilibria

Description of Equipment

Design and Performance Equations

Regeneration

References

Chapter 12: Liquid–Liquid and Solid–Liquid Extraction

Introduction

Liquid–Liquid Extraction

Solid-Liquid Extraction (Leaching)(4)

References

Chapter 13: Humidification and Drying

Introduction

Psychrometry and The Psychrometric Chart

Humidification

Drying

References

Chapter 14: Crystallization

Introduction

Phase Diagrams

The Crystallization Process

Crystal Physical Characteristics

Equipment

Describing Equations

Design Considerations

References

Chapter 15: Membrane Separation Processes

Introduction

Reverse Osmosis

Ultrafiltration

Microfiltration

Gas Permeation

References

Chapter 16: Phase Separation Equipment

Introduction

Fluid–Particle Dynamics

Gas–Solid (G–S) Equipment

Gas–Liquid (G–L) Equipment

Liquid–Solid (L–S) Equipment

Liquid–Liquid (L–L) Equipment

Solid-Solid (S-S) Equipment

References

Part Three: Other Topics

Chapter 17: Other and Novel Separation Processes

Freeze Crystallization

Ion Exchange

Liquid Ion Exchange

Resin Adsorption

Evaporation

Foam Fractionation

Dissociation Extraction

Electrophoresis

Vibrating Screens

References

Chapter 18: Economics and Finance

Introduction

The Need For Economic Analyses

Definitions

Principles of Accounting(4)

Applications

References

Chapter 19: Numerical Methods

Introduction

Applications

References

Chapter 20: Open-Ended Problems

Introduction

Developing Students’ Power of Critical Thinking(4)

Creativity

Brainstorming

Inquiring Minds

Failure, Uncertainty, Success: Are They Related?

Angels On A Pin(11)

Applications

References

Chapter 21: Ethics

Introduction

Teaching Ethics

Case Study Approach

Integrity

Moral Issues(8)

Guardianship

Engineering and Environmental Ethics(11)

Future Trends(11)

Applications

References

Chapter 22: Environmental Management and Safety Issues

Introduction

Environmental Issues of Concern(1)

Health Risk Assessment(2–4)

Hazard Risk Assessment(2–4, 8)

Applications

References

Appendix

Appendix A: Units

A.1 The Metric System

A.2 The SI System

A.3 Seven Base Units

A.4 Two Supplementary Units

A.5 SI Multiples And Prefixes

A.6 Conversion Constants (SI)

A.7 Selected Common Abbreviations

Appendix B: Miscellaneous Tables

Appendix C: Steam Tables

Index

Mass Transfer Operations for the Practicing Engineer

Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Theodore, Louis. Mass transfer operations for the practicing engineer/Louis Theodore, Francesco Ricci. p. cm. Includes Index. ISBN 978-0-470-57758-5 (hardback) 1. Engineering mathematics. 2. Mass transfer. I. Ricci, Francesco. II. Title. TA331.T476 2010 530.4’7501512—dc22 2010013924

To Ann Cadigan and Meg Norris:for putting up with me (LT)

and

To my mother Laura, my father Joseph, and my brother Joseph Jr: for reasons which need not be spoken (FR)

Preface

Mass transfer is one of the basic tenets of chemical engineering, and contains many practical concepts that are utilized in countless industrial applications. Therefore, the authors considered writing a practical text. The text would hopefully serve as a training tool for those individuals in academia and industry involved with mass transfer operations. Although the literature is inundated with texts emphasizing theory and theoretical derivations, the goal of this text is to present the subject from a strictly pragmatic point-of-view.

The book is divided into three parts: Introduction, Applications, and Other Topics. The first part provides a series of chapters concerned with principles that are required when solving most engineering problems, including those in mass transfer operations. The second part deals exclusively with specific mass transfer operations e.g., distillation, absorption and stripping, adsorption, and so on. The last part provides an overview of ABET (Accreditation Board for Engineering and Technology) related topics as they apply to mass transfer operations plus novel mass transfer processes. An Appendix is also included. An outline of the topics covered can be found in the Table of Contents.

The authors cannot claim sole authorship to all of the essay material and illustrative examples in this text. The present book has evolved from a host of sources, including: notes, homework problems and exam problems prepared by several faculty for a required one-semester, three-credit, “Principles III: Mass Transfer” undergraduate course offered at Manhattan College; L. Theodore and J. Barden, “Mass Transfer”, A Theodore Tutorial, East Williston, NY, 1994; J. Reynolds, J. Jeris, and L. Theodore, “Handbook of Chemical and Environmental Engineering Calculations,” John Wiley & Sons, Hoboken, NJ, 2004, and J. Santoleri, J. Reynolds, and L. Theodore, “Introduction to Hazardous Waste Management,” 2nd edition, John Wiley & Sons, Hoboken, NJ, 2000. Although the bulk of the problems are original and/or taken from sources that the authors have been directly involved with, every effort has been made to acknowledge material drawn from other sources.

It is hoped that we have placed in the hands of academic, industrial, and government personnel, a book that covers the principles and applications of mass transfer in a thorough and clear manner. Upon completion of the text, the reader should have acquired not only a working knowledge of the principles of mass transfer operations, but also experience in their application; and, the reader should find himself/herself approaching advanced texts, engineering literature and industrial applications (even unique ones) with more confidence. We strongly believe that, while understanding the basic concepts is of paramount importance, this knowledge may be rendered virtually useless to an engineer if he/she cannot apply these concepts to real-world situations. This is the essence of engineering.

Last, but not least, we believe that this modest work will help the majority of individuals working and/or studying in the field of engineering to obtain a more complete understanding of mass transfer operations. If you have come this far and read through most of the Preface, you have more than just a passing interest in this subject. We strongly suggest that you try this text; we think you will like it.

Our sincere thanks are extended to Dr. Paul Marnell at Manhattan College for his invaluable help in contributing to Chapter 9 on Distillation and Chapter 14 on Crystallization. Thanks are also due to Anne Mohan for her assistance in preparing the first draft of Chapter 13 (Humidification and Drying) and to Brian Bermingham and Min Feng Zheng for their assistance during the preparation of Chapter 12 (Liquid–Liquid and Solid–Liquid Extraction). Finally, Shannon O’Brien, Kathryn Scherpf and Kimberly Valentine did an exceptional job in reviewing the manuscript and page proofs.

April 2010

FRANCESCO RICCILOUIS THEODORE

NOTE: An additional resource is available for this text. An accompanying website contains over 200 additional problems and 15 hours of exams; solutions for the problems and exams are available at www.wiley.com for those who adopt the book for training and/or academic purposes.

Part OneIntroduction

The purpose of this Part can be found in its title. The book itself offers the reader the fundamentals of mass transfer operations with appropriate practical applications, and serves as an introduction to the specialized and more sophisticated texts in this area. The reader should realize that the contents are geared towards practitioners in this field, as well as students of science and engineering, not chemical engineers per se. Simply put, topics of interest to all practicing engineers have been included. Finally, it should also be noted that the microscopic approach of mass transfer operations is not treated in any required undergraduate Manhattan College offering. The Manhattan approach is to place more emphasis on real-world and design applications. However, microscopic approach material is available in the literature, as noted in the ensuing chapters. The decision on whether to include the material presented ultimately depends on the reader and/or the approach and mentality of both the instructor and the institution.

A general discussion of the philosophy and the contents of this introductory section follows.

Since the chapters in this Part provide an introduction and overview of mass transfer operations, there is some duplication due to the nature of the overlapping nature of overview/introductory material, particularly those dealing with principles. Part One chapter contents include:

1 History of Chemical Engineering and Mass Transfer Operations

2 Transport Phenomena vs Unit Operations Approach

3 Basic Calculations

4 Process Variables

5 Equilibrium vs Rate Considerations

6 Phase Equilibrium Principles

7 Rate Principles

Topics covered in the first two introductory chapters include a history of chemical engineering and mass transfer operations, and a discussion of transport phenomena vs unit operations. The remaining chapters are concerned with introductory engineering principles. The next Part is concerned with describing and designing the various mass transfer unit operations and equipment.

Chapter 1

History of Chemical Engineering and Mass Transfer Operations

A discussion on the field of chemical engineering is warranted before proceeding to some specific details regarding mass transfer operations (MTO) and the contents of this first chapter. A reasonable question to ask is: What is Chemical Engineering? An outdated, but once official definition provided by the American Institute of Chemical Engineers is:

Chemical Engineering is that branch of engineering concerned with the development and application of manufacturing processes in which chemical or certain physical changes are involved. These processes may usually be resolved into a coordinated series of unit physical “operations” (hence part of the name of the chapter and book) and chemical processes. The work of the chemical engineer is concerned primarily with the design, construction, and operation of equipment and plants in which these unit operations and processes are applied. Chemistry, physics, and mathematics are the underlying sciences of chemical engineering, and economics is its guide in practice.

The above definition was appropriate up until a few decades ago when the profession branched out from the chemical industry. Today, that definition has changed. Although it is still based on chemical fundamentals and physical principles, these principles have been de-emphasized in order to allow for the expansion of the profession to other areas (biotechnology, semiconductors, fuel cells, environment, etc.). These areas include environmental management, health and safety, computer applications, and economics and finance. This has led to many new definitions of chemical engineering, several of which are either too specific or too vague. A definition proposed here is simply that “Chemical Engineers solve problems”. Mass transfer is the one subject area that somewhat uniquely falls in the domain of the chemical engineer. It is often presented after fluid flow(1) and heat transfer,(2) since fluids are involved as well as heat transfer and heat effects can become important in any of the mass transfer unit operations.

A classical approach to chemical engineering education, which is still used today, has been to develop problem solving skills through the study of several topics. One of the topics that has withstood the test of time is mass transfer operations; the area that this book is concerned with. In many mass transfer operations, one component of a fluid phase is transferred to another phase because the component is more soluble in the latter phase. The resulting distribution of components between phases depends upon the equilibrium of the system. Mass transfer operations may also be used to separate products (and reactants) and may be used to remove byproducts or impurities to obtain highly pure products. Finally, it can be used to purify raw materials.

Although the chemical engineering profession is usually thought to have originated shortly before 1900, many of the processes associated with this discipline were developed in antiquity. For example, filtration operations were carried out 5000 years ago by the Egyptians. MTOs such as crystallization, precipitation, and distillation soon followed. During this period, other MTOs evolved from a mixture of craft, mysticism, incorrect theories, and empirical guesses.

In a very real sense, the chemical industry dates back to prehistoric times when people first attempted to control and modify their environment. The chemical industry developed as did any other trade or craft. With little knowledge of chemical science and no means of chemical analysis, the earliest chemical “engineers” had to rely on previous art and superstition. As one would imagine, progress was slow. This changed with time. The chemical industry in the world today is a sprawling complex of raw-material sources, manufacturing plants, and distribution facilities which supply society with thousands of chemical products, most of which were unknown over a century ago. In the latter half of the nineteenth century, an increased demand arose for engineers trained in the fundamentals of chemical processes. This demand was ultimately met by chemical engineers.

The first attempt to organize the principles of chemical processing and to clarify the professional area of chemical engineering was made in England by George E. Davis. In 1880, he organized a Society of Chemical Engineers and gave a series of lectures in 1887 which were later expanded and published in 1901 as A Handbook of Chemical Engineering. In 1888, the first course in chemical engineering in the United States was organized at the Massachusetts Institute of Technology by Lewis M. Norton, a professor of industrial chemistry. The course applied aspects of chemistry and mechanical engineering to chemical processes.(3)

Chemical engineering began to gain professional acceptance in the early years of the twentieth century. The American Chemical Society had been founded in 1876 and, in 1908, it organized a Division of Industrial Chemists and Chemical Engineers while authorizing the publication of the Journal of Industrial and Engineering Chemis ry. Also in 1908, a group of prominent chemical engineers met in Philadelphia and founded the American Institute of Chemical Engineers.(3)

The mold for what is now called chemical engineering was fashioned at the 1922 meeting of the American Institute of Chemical Engineers when A. D. Little’s committee presented its report on chemical engineering education. The 1922 meeting marked the official endorsement of the unit operations concept and saw the approval of a “declaration of independence” for the profession.(3) A key component of this report included the following:

Any chemical process, on whatever scale conducted, may be resolved into a coordinated series of what may be termed “unit operations,” as pulverizing, mixing, heating, roasting, absorbing, precipitation, crystallizing, filtering, dissolving, and so on. The number of these basic unit operations is not very large and relatively few of them are involved in any particular process… An ability to cope broadly and adequately with the demands of this (the chemical engineer’s) profession can be attained only through the analysis of processes into the unit actions as they are carried out on the commercial scale under the conditions imposed by practice.

It also went on to state that:

Chemical Engineering, as distinguished from the aggregate number of subjects comprised in courses of that name, is not a composite of chemistry and mechanical and civil engineering, but is itself a branch of engineering…

A time line diagram of the history of chemical engineering between the profession’s founding to the present day is shown in Figure 1.1.(3) As can be seen from the time line, the profession has reached a crossroads regarding the future education/curriculum for chemical engineers. This is highlighted by the differences of Transport Phenomena and Unit Operations, a topic that is treated in the next chapter.

Figure 1.1 Chemical engineering time line.(3)

REFERENCES

1. P. ABULENCIA and L. THEODORE, “Fluid Flow for the Practicing Engineer,” John Wiley & Sons, Hoboken, NJ, 2009.

2. L. THEODORE, “Heat Transfer for the Practicing Engineer” John Wiley & Sons, Hoboken, NJ, 2011 (in preparation).

3. N. SERINO, “2005 Chemical Engineering 125th Year Anniversary Calendar,” term project, submitted to L. Theodore, 2004.

4. R. BIRD, W. STEWART, and E. LIGHTFOOT, “Transport Phenomena,” 2nd edition, John Wiley & Sons, Hoboken, NJ, 2002.

NOTE: Additional problems are available for all readers at www.wiley.com. Follow links for this title. These problems may be used for additional review, homework, and/or exam purposes.

Chapter 2

Transport Phenomena vs Unit Operations Approach

The history of Unit Operations is interesting. As indicated in the previous chapter, chemical engineering courses were originally based on the study of unit processes and/or industrial technologies. However, it soon became apparent that the changes produced in equipment from different industries were similar in nature, i.e., there was a commonality in the mass transfer operations in the petroleum industry as with the utility industry. These similar operations became known as Unit Operations. This approach to chemical engineering was promulgated in the Little report discussed earlier, and has, with varying degrees and emphasis, dominated the profession to this day.

The Unit Operations approach was adopted by the profession soon after its inception. During the 130 years (since 1880) that the profession has been in existence as a branch of engineering, society’s needs have changed tremendously and so has chemical engineering.

The teaching of Unit Operations at the undergraduate level has remained relatively unchanged since the publication of several early- to mid-1900 texts. However, by the middle of the 20th century, there was a slow movement from the unit operation concept to a more theoretical treatment called transport phenomena or, more simply, engineering science. The focal point of this science is the rigorous mathematical description of all physical rate processes in terms of mass, heat, or momentum crossing phase boundaries. This approach took hold of the education/curriculum of the profession with the publication of the first edition of the Bird et al. book.(l) Some, including both authors of this text, feel that this concept set the profession back several decades since graduating chemical engineers, in terms of training, were more applied physicists than traditional chemical engineers. There has fortunately been a return to the traditional approach to chemical engineering, primarily as a result of the efforts of ABET (Accreditation Board for Engineering and Technology). Detractors to this pragmatic approach argue that this type of theoretical education experience provides answers to what and how, but not necessarily why, i.e., it provides a greater understanding of both fundamental physical and chemical processes. However, in terms of reality, nearly all chemical engineers are now presently involved with the why questions. Therefore, material normally covered here has been replaced, in part, with a new emphasis on solving design and open-ended problems; this approach is emphasized in this text.

The following paragraphs attempt to qualitatively describe the differences between the above two approaches. Both deal with the transfer of certain quantities (momentum, energy, and mass) from one point in a system to another. There are three basic transport mechanisms which can potentially be involved in a process. They are:

1 Radiation

2 Convection

3 Molecular Diffusion

The first mechanism, radiative transfer, arises as a result of wave motion and is not considered, since it may be justifiably neglected in most engineering applications. The second mechanism, convective transfer, occurs simply because of bulk motion. The final mechanism, molecular diffusion, can be defined as the transport mechanism arising as a result of gradients. For example, momentum is transferred in the presence of a velocity gradient; energy in the form of heat is transferred because of a temperature gradient; and, mass is transferred in the presence of a concentration gradient. These molecular diffusion effects are described by phenomenological laws.(1)

Momentum, energy, and mass are all conserved. As such, each quantity obeys the conservation law within a system:

(2.1)

This equation may also be written on a time rate basis:

(2.2)

The conservation law may be applied at the macroscopic, microscopic, or molecular level.

One can best illustrate the differences in these methods with an example. Consider a system in which a fluid is flowing through a cylindrical tube (see Fig. 2.1) and define the system as the fluid contained within the tube between points 1 and 2 at any time. If one is interested in determining changes occurring at the inlet and outlet of a system, the conservation law is applied on a “macroscopic” level to the entire system. The resultant equation (usually algebraic) describes the overall changes occurring to the system (or equipment). This approach is usually applied in the Unit Operation (or its equivalent) courses, an approach which is highlighted in this text and its two companion texts.(2,3)

Figure 2.1 Flow system.

In the microscopic/transport phenomena approach, detailed information concerning the behavior within a system is required; this is occasionally requested of and by the engineer. The conservation law is then applied to a differential element within the system that is large compared to an individual molecule, but small compared to the entire system. The resulting differential equation is then expanded via an integration in order to describe the behavior of the entire system.

The molecular approach involves the application of the conservation laws to individual molecules. This leads to a study of statistical and quantum mechanics—both of which are beyond the scope of this text. In any case, the description at the molecular level is of little value to the practicing engineer. However, the statistical averaging of molecular quantities in either a differential or finite element within a system can lead to a more meaningful description of the behavior of a system.

Both the microscopic and molecular approaches shed light on the physical reasons for the observed macroscopic phenomena. Ultimately, however, for the practicing engineer, these approaches may be valid but are akin to attempting to kill a fly with a machine gun. Developing and solving these equations (in spite of the advent of computer software packages) is typically not worth the trouble.

Traditionally, the applied mathematician has developed differential equations describing the detailed behavior of systems by applying the appropriate conservation law to a differential element or shell within the system. Equations were derived with each new application. The engineer later removed the need for these tedious and error-prone derivations by developing a general set of equations that could be used to describe systems. These have come to be referred to by many as the transport equations. In recent years, the trend toward expressing these equations in vector form has gained momentum (no pun intended). However, the shell-balance approach has been retained in most texts where the equations are presented in componential form, i.e., in three particular coordinate systems—rectangular, cylindrical, and spherical. The componential terms can be “lumped” together to produce a more concise equation in vector form. The vector equation can be, in turn, re-expanded into other coordinate systems. This information is available in the literature.(1,4)

ILLUSTRATIVE EXAMPLE 2.1

Explain why the practicing engineer/scientist invariably employs the macroscopic approach in the solution of real world problems.

SOLUTION: The macroscopic approach involves examining the relationship between changes occurring at the inlet and the outlet of a system. This approach attempts to identify and solve problems found in the real world, and is more straightforward than and preferable to the more involved microscopic approach. The microscopic approach, which requires an understanding of all internal variations taking place within the system that can lead up to an overall system result, simply may not be necessary.

REFERENCES

1. R. BIRD, W. STEWART, and E. LIGHTFOOT, “Transport Phenomena,” John Wiley & Sons, Hoboken, NJ, 1960.

2. L. THEODORE, “Heat Transfer for the Practicing Engineer” John Wiley & Sons, Hoboken, NJ, 2011 (in preparation).

3. P. ABULENCIA and L. THEODORE, “Fluid Flow for the Practicing Engineer” John Wiley & Sons, Hoboken, NJ, 2009.

4. L. THEODORE, “Introduction to Transport Phenomena” International Textbook Co., Scranton, PA, 1970.

NOTE: Additional problems are available for all readers at www.wiley.com. Follow links for this title. These problems may be used for additional review, homework, and/or exam purposes.