Mathcad for Chemical Engineers

175 Pages·2007·12.957 MB·English

by  Hertanto Adidharma, Valery Temyanko

Mathcad for
J :
Hertanto Adidharma
Valery Temyanko
Math cad for
Chemical Engineers
Hertanto Adidharma
University of Wyoming
Valery Temyanko
University of Arizona
© Copyright 2007 by Hertanto Adidharma and Valery Temyanko
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About the Authors
Hertanto Adidharma is currently a professor of chemical engi­
neering at the University of Wyoming. He has ten years experience
in chemical engineering education. He has taught various chemical
engineering courses: Material and Energy Balance, Transport Phe­
nomena, Chemical Reaction Engineering, Thermodynamics, Nu­
merical Methods, Computer Programming, Unit Operations, and
introduction to Chemical Engineering Computing. Before entering
teaching, he spent several years in chemical industry and became
an independent consultant.
Valery Temyanko is currently a Staff Engineer, Sr. at the Univer­
sity of Arizona. He has more than 10 years of industrial experi­
ence. Research and development of resin transfer molding (RTM),
reaction injection molding (RIM), reforming of fuel, process opti­
mization and control are the primary areas of his expertise.
Contents vii
Contents
Preface xi
Chapter 1. Introduction 1
Chapter 2. Getting Started with Mathcad 5
2.1. Mathcad Worksheet and User Interface 5
2.2. Variables and Functions 7
2.3. Arrays: Vector and Matrix 9
2.4. Working with Units 12
^2.5. Graphics Features 14
2.6. Symbolic Math Capabilities 18
Problems 20
Chapter 3. Non-Linear Equation 25
3.1. Polynomial 25
3.2. Non-Polynomial 31
Problems 33
Chapter 4. System of Equations 39
4.1. System of Linear Equations 39
4.2. System of Non-Linear Equations 45
4.3. System of Equations with Constraints 50
Problems 52
Chapter 5. Curve Fitting 59
5.1. Interpolation 59
5.1.1. Linear Interpolation 60
Vlll Contents
5.1.2. Cubic Spline 60
5.2. Regression 65
5.2.1. Linear Regression 66
5.2.2. Polynomial Regression 68
5.2.3. Non-Linear Regression 70
Problems 74
Chapter 6. Differentiation and Integration 79
6.1. Differentiation 79
6.2. Integration " 83
Problems 85
Chapter 7. Optimization 91
7.1. Extreme Value Problem 91
7.1.1. Unconstrained Function 91
7.1.2. Constrained Function 94
7.2. Linear Programming 99
7.3. Non-Linear Programming 103
Problems 106
Chapter 8. Differential Equation 111
8.1. Ordinary Differential Equation 111
8.1.1. First Order ODE ill
8.1.2. System of First Order ODEs 116
8.1.3. Higher Order ODE - Initial Value
Problem 117
8.1.4. Higher Order ODE - Boundary
Value Problem 119
Contents ix
8.1.5. Second Order ODE - Cylindrical/
Spherical Coordinate 121
8.1.6. System of Higher Order ODEs 122
8.2. Partial Differential Equation 129
8.2.1. Parabolic PDE 129
8.2.2. System of Parabolic PDEs 132
8.2.3. Elliptic PDE 133
Problems 137
Chapter 9. Miscellaneous 145
9.1. Data Handling 145
9.2. Data Exchange with Excel 145
9.3. Introduction to Mathcad Programming 149
9.3.1. Conditional (//'Statement) 149
9.3.2. Loops (for/while Statement) 151
Problems 160
Index 169
\
Preface xi
Preface
Xhis book serves as a must-to-have guide and quick refer­
ence for chemical engineers and those who would like to learn and
use Mathcad for their computational tool. The book is also in­
tended for one-semester course on Chemical Engineering Comput­
ing using Mathcad. Authors believe that unlike other computa­
tional software packages, Mathcad is very intuitive and thus easy
to learn.
There are several mathematical or computational software
packages available today. Among the most widely used are Maple,
Maxima, MatLab, Mathematica, Mathcad, and Excel. The prefer­
ence of one particular computational package over the others is
usually, ironically, based only on familiarity. The approach of
“familiar” software works with some limitations, but it is never the
most efficient way of problem solving. It is very important to
choose and use the latest software and not to be afraid of switching
and learning. This is the best time investment that one can do.
Given many years of experience in solving a wide variety of
chemical engineering tasks, authors are convinced that Mathcad is
easy to learn and easy to use, yet versatile and powerful. Thus, it is
an extremely important and useful software package for modem
chemical engineers. Although Mathcad 13 is the software package
chosen by the authors and will be used throughout the book, most
of the features discussed can also be applied using earlier versions
of Mathcad. Also, although Mathcad will always evolve into a
newer version, most of the contents in this book will be applicable
for any subsequent version of Mathcad.
The main objective of the book is to develop o6mputational
skills needed in chemical engineering applications. The readers
will leam how to solve different types of mathematical models. At
the same time, the book introduces readers to many chemical engi­
neering applications, such as
Xll Preface
• Property estimation
• Material and energy balance
• Thermodynamics
• Transport phenomena
• Kinetic and reactor design c
• Unit operations
• Process control
• Process economics
• Statistical thermodynamics
The already-developed mathematical models in those ap­
plications will be solved using Mathcad. The development of the
mathematical models itself, from fundamental theories, is beyond
the scope of this book. Readers must consult other chemical engi­
neering textbooks. For students, they usually leam how to develop
such models from other courses.
In this book, readers can leam how to use Mathcad func­
tions in clearly described procedures intended for quick reference.
To introduce readers to some related mathematical problems ap­
peared in chemical engineering applications, examples and prob­
lems are given in each chapter.
Finally, it is important to mention that the book is not in­
tended to give readers a complete manual of Mathcad, but rather to
provide them with the essential Mathcad functions and features
commonly needed in chemical engineering. After reading this
book, of course the readers are encouraged to keep exploring the
power of Mathcad.
Hertanto Adidharma
Valery Temyanko
Mathcad for
Chemical Engineers