|
|
1 | (4) |
|
2 The Recipe to Build a Mathematical Model |
|
|
5 | (8) |
|
|
6 | (2) |
|
2.2 The Recipe Applied to a Simple System |
|
|
8 | (5) |
|
3 Lumped-Parameter Models |
|
|
13 | (36) |
|
3.1 Some Introductory Examples |
|
|
13 | (8) |
|
3.2 Some Concepts About Convective Heat Exchange |
|
|
21 | (7) |
|
3.3 Some Concepts About Chemical Kinetics and Reactors |
|
|
28 | (21) |
|
3.3.1 Some Concepts About Kinetics of Chemical Reactions |
|
|
29 | (1) |
|
3.3.2 Some Concepts About Chemical Reactors |
|
|
30 | (17) |
|
|
47 | (2) |
|
4 Distributed-Parameter Models |
|
|
49 | (40) |
|
4.1 Some Introductory Examples |
|
|
49 | (9) |
|
4.2 Concepts About Transfer by Diffusion |
|
|
58 | (19) |
|
4.2.1 Diffusive Transport of Heat |
|
|
58 | (1) |
|
4.2.2 Diffusive Transport of Mass |
|
|
59 | (1) |
|
4.2.3 Diffusive Transport of Momentum |
|
|
60 | (2) |
|
4.2.4 Analogies Among All Diffusive Transports |
|
|
62 | (1) |
|
4.2.5 Examples Considering the Diffusive Effects on the Modeling |
|
|
62 | (15) |
|
4.3 Examples Considering Variations in More than One Dimension |
|
|
77 | (12) |
|
|
87 | (2) |
|
5 Solving an Algebraic Equations System |
|
|
89 | (24) |
|
5.1 Problems Involving Linear Algebraic Equations |
|
|
89 | (7) |
|
5.2 Problems Involving Nonlinear Algebraic Equations |
|
|
96 | (8) |
|
5.2.1 Demonstration of the NR Method to Solve a Nonlinear Algebraic Equations System |
|
|
97 | (4) |
|
5.2.2 Numerical Differentiation |
|
|
101 | (1) |
|
5.2.3 Using Excel to Solve a Nonlinear Algebraic Equation Using the NR Method |
|
|
102 | (2) |
|
5.3 Solving Linear and Nonlinear Algebraic Equations Using the Solver Tool |
|
|
104 | (9) |
|
|
111 | (2) |
|
6 Solving an Ordinary Differential Equations System |
|
|
113 | (32) |
|
|
113 | (3) |
|
6.2 Runge--Kutta Numerical Methods |
|
|
116 | (6) |
|
6.2.1 First Order Runge--Kutta Method, or Euler Method |
|
|
116 | (1) |
|
6.2.2 Second Order Runge--Kutta Method |
|
|
117 | (3) |
|
6.2.3 Runge--Kutta Method of the Fourth Order |
|
|
120 | (2) |
|
6.3 Solving ODEs Using an Excel Spreadsheet |
|
|
122 | (7) |
|
6.3.1 Solving a Single ODE Using Runge--Kutta Methods |
|
|
122 | (4) |
|
6.3.2 Solving a System of Interdependent ODEs Using Runge--Kutta Methods |
|
|
126 | (3) |
|
6.4 Solving ODEs Using Visual Basic |
|
|
129 | (16) |
|
6.4.1 Enabling Visual Basic in Excel |
|
|
130 | (1) |
|
6.4.2 Developing an Algorithm to Solve One ODE Using the Euler Method |
|
|
130 | (5) |
|
6.4.3 Developing an Algorithm to Solve One ODE Using the Runge--Kutta Fourth-Order Method |
|
|
135 | (1) |
|
6.4.4 Developing an Algorithm to Solve a System of ODEs Using the Euler and Fourth-Order Runge--Kutta Methods |
|
|
136 | (8) |
|
|
144 | (1) |
|
7 Solving a Partial Differential Equations System |
|
|
145 | (20) |
|
|
145 | (1) |
|
7.2 Finite Difference Method |
|
|
146 | (2) |
|
7.3 Introductory Example of Finite Difference Method Application |
|
|
148 | (1) |
|
7.4 Application of the Finite Difference Method |
|
|
149 | (16) |
|
7.4.1 PDEs Transformed into an Algebraic Equations System |
|
|
150 | (4) |
|
7.4.2 PDEs Transformed into an ODE System |
|
|
154 | (1) |
|
7.4.3 Solving a System of PDEs |
|
|
155 | (5) |
|
7.4.4 PDEs with Flux Boundary Conditions |
|
|
160 | (5) |
Appendix 7.1 |
|
165 | (3) |
Appendix 7.2 |
|
168 | (1) |
References |
|
169 | (2) |
Index |
|
171 | |