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E-raamat: Modeling and Simulation in Thermal and Fluids Engineering

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(IIT Roorkee, India)
  • Formaat: 370 pages
  • Ilmumisaeg: 29-Jul-2022
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781000610598
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Modeling and Simulation in Thermal and Fluids EngineeringSuurem pilt
  • Formaat: 370 pages
  • Ilmumisaeg: 29-Jul-2022
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781000610598
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This textbook comprehensively covers the fundamentals behind mathematical modeling of engineering problems to obtain the required solution.

It comprehensively discusses modeling concepts through conservation principles with a proper blending of mathematical expressions. The text discusses the basics of governing equations in algebraic and differential forms and examines the importance of mathematics as a tool in modeling. It covers important topics including modeling of heat transfer problems, modeling of flow problems, modeling advection-diffusion problems and Navier-Stokes equations in depth. Pedagogical features including solved problems and unsolved exercises are interspersed throughout the text for better understanding.

The textbook is primarily written for senior undergraduate and graduate students in the field of mechanical engineering for courses on modeling and simulation. The textbook will be accompanied by teaching resource including a solution manual for the instructors.
Preface xiii
Author Biography xvii
Chapter 1 Introduction
1(40)
1.1 Modeling
3(9)
1.1.1 Physical Models
3(1)
1.1.2 Mathematical Models
4(4)
1.1.2.1 Perfect Gas Equation
8(1)
1.1.2.2 Hooke's Law
8(1)
1.1.2.3 Deflection of Beam under Load
9(1)
1.1.2.4 Fluid Mechanics
10(1)
1.1.2.5 Heat Transfer
11(1)
1.2 Simulation
12(1)
1.3 Conservation Principles
13(7)
1.3.1 Mass Conservation
14(1)
1.3.2 Momentum Conservation
15(2)
1.3.3 Energy Conservation
17(1)
1.3.4 Species Conservation
18(2)
1.4 Types of Physical Problems
20(5)
1.4.1 Equilibrium Problems
21(2)
1.4.2 Eigen Value Problems
23(1)
1.4.3 Propagation Problems
23(2)
1.5 Models in Engineering Analysis
25(4)
1.5.1 Lumped Parameter Model
25(3)
1.5.2 Continuum Based Model
28(1)
1.6 Solution of Differential Equations
29(12)
1.6.1 Analytical Techniques
30(2)
1.6.2 Numerical Techniques
32(3)
1.6.3 Computing Techniques
35(1)
References
36(1)
Exercise Problems
36(2)
Quiz Questions
38(3)
Chapter 2 Conservation Equations
41(52)
2.1 Solid Medium
42(17)
2.1.1 Energy Transport in Unsteady State Conditions
43(3)
2.1.1.1 Generalized Conduction Equation in Cartesian Coordinates
46(2)
2.1.1.2 Generalized Conduction Equation in Cylindrical Coordinates
48(2)
2.1.1.3 Generalized Conduction Equation in Spherical Coordinates
50(1)
2.1.1.4 Initial and Boundary Conditions
50(1)
2.1.1.5 Initial Condition
51(1)
2.1.1.6 Boundary Conditions
51(2)
2.1.2 Energy Transport in Steady State Condition
53(1)
2.1.2.1 Steady State Heat Conduction in Plane Wall
54(2)
2.1.2.2 Steady State Heat Conduction in Cylinder
56(2)
2.1.2.3 Steady State Heat Conduction in Sphere
58(1)
2.2 Fluid Medium
59(34)
2.2.1 Mass Conservation
61(4)
2.2.1.1 Material Derivative Form
65(1)
2.2.1.2 Incompressible Fluid Flow
66(1)
2.2.2 Momentum Conservation
66(6)
2.2.2.1 Relation between Stress and Viscosity
72(1)
2.2.2.2 Momentum Balance Equations for Incompressible Flow (u=constant)
73(2)
2.2.3 Energy Conservation
75(1)
2.2.3.1 Energy Balance
76(2)
2.2.3.2 Rate of Change of Energy in CV
78(1)
2.2.3.3 Net Efflux of Energy from CV
78(1)
2.2.3.4 Rate of Work Done by Surface Forces
78(1)
2.2.3.5 Work Done by Body Forces
79(1)
2.2.3.6 Net Addition of Heat due to Conduction and Radiation Heat Transfer
80(1)
2.2.3.7 Heat Generation within Control Volume
81(6)
2.2.4 Species Conservation
87(1)
References
88(1)
Exercise Problems
88(2)
Quiz Questions
90(3)
Chapter 3 Finite Difference and Finite Volume Methods
93(54)
3.1 Finite Difference Method
95(28)
3.1.1 One-Dimensional Conduction
95(2)
3.1.2 Taylor's Series Principle
97(3)
3.1.3 Polynomial Method
100(2)
3.1.4 Application to Ordinary Differential Equations
102(2)
3.1.4.1 Equations for the Boundary Nodes 1 and M
104(3)
3.1.5 Application to Partial Differential Equations
107(1)
3.1.5.1 Two-Dimensional Conduction Equation
107(4)
3.1.5.2 Difference Equations for Boundary Conditions
111(3)
3.1.5.3 Corner Nodes
114(5)
3.1.5.4 Boundary Nodes
119(1)
3.1.5.5 Comparison of Two-Dimensional Conduction Results with Analytical Solution
120(3)
3.2 Finite Volume Method
123(24)
3.2.1 Heat Flux Boundary Condition at M (x=L)
127(1)
3.2.2 Convective Boundary Condition at Node M (x=L)
128(1)
3.2.3 Example Problem for Finite Volume Method-Fin
128(1)
3.2.4 One-Dimensional and Two-Dimensional Applications
128(1)
3.2.4.1 One-Dimensional Application
128(3)
3.2.4.2 Two-Dimensional Application
131(2)
3.2.4.3 Boundary Conditions
133(3)
3.2.4.4 Corner Nodes
136(2)
3.2.5 Complex Geometry and Variable Property
138(1)
3.2.5.1 Complex Geometry
139(1)
3.2.5.2 Variable Property
140(1)
3.2.5.3 Variable Area
141(2)
References
143(1)
Exercise Problems
144(2)
Quiz Questions
146(1)
Chapter 4 Finite Element Method
147(62)
4.1 Galerkin's Weighted Residual Method
148(14)
4.1.1 Integration of Shape Functions
154(4)
4.1.2 Boundary Conditions
158(1)
4.1.2.1 Convective Boundary Condition
158(1)
4.1.2.2 Dirichlet Boundary Condition
159(1)
4.1.3 Example Problem: Fin (Computer Code fin_FEM.for)
159(3)
4.2 Domain Discretization and Isoparametric Formulation
162(6)
4.2.1 Domain Discretization
162(1)
4.2.2 Isoparametric Formulation
163(5)
4.3 Discretization of One-Dimensional Domain
168(2)
4.4 Discretization of Two-Dimensional Domain
170(6)
4.4.1 Rectangular and Quadrilateral Elements
172(4)
4.5 Discretization of Three-Dimensional Domain
176(4)
4.6 Mesh Generation
180(2)
4.7 Transfinite Interpolation Technique (TFI)
182(12)
4.7.1 Multi-Block TFI Grid Generation
188(1)
4.7.2 Three-Dimensional TFI Meshing
188(6)
4.8 Time-Dependent Problems
194(15)
4.8.1 Stability Conditions
199(1)
4.8.1.1 Explicit Scheme
200(1)
4.8.1.2 Implicit Scheme
201(1)
4.8.1.3 Semi-Implicit Scheme (Crank-Nicholson Scheme)
202(1)
4.8.1.4 Significance of Fourier Number
202(2)
4.8.1.5 Alternate Direction Implicit (ADI) Method
204(1)
References
205(1)
Exercise Problems
205(2)
Quiz Questions
207(2)
Chapter 5 Modeling of Heat Transfer Problems
209(48)
5.1 Heat Transfer Problem -- One-Dimensional Conduction with Heat Generation
210(15)
5.1.1 Derivation of Energy Conservation Equation
211(2)
5.1.2 Identification of Boundary Conditions
213(1)
5.1.3 Solution Using Finite Element Method
213(2)
5.1.4 Incorporation of Boundary Condition
215(2)
5.1.5 Computational Algorithm
217(1)
5.1.6 Computer Programming
217(3)
5.1.7 Mesh Sensitivity and Validation Results
220(1)
5.1.8 Simulation Parameters and Results
221(4)
5.2 Two-Dimensional Problem -- Heat and Mass Transfer through Soil: Landmine Detection
225(32)
5.2.1 Derivation of Conservation Equations
226(1)
5.2.1.1 Conservation Equation for Heat and Moisture Transport within the Soil Medium
227(4)
5.2.2 Initial and Boundary Conditions
231(1)
5.2.2.1 Initial Conditions
231(1)
5.2.2.2 Boundary Conditions -- Soil Medium
232(1)
5.2.2.3 Top Side
232(1)
5.2.2.4 Bottom Side
233(1)
5.2.2.5 Vertical Sides
233(1)
5.2.2.6 Mine-Soil Interface Boundary Condition
233(1)
5.2.3 Solution Using Finite Element Method
234(1)
5.2.4 Inclusion of Convective Boundary Condition on the Top Surface of the Soil Medium
235(4)
5.2.5 Solution of Energy Equation for the Landmine
239(1)
5.2.6 Computational Algorithm
240(2)
5.2.7 Computer Programming
242(1)
5.2.8 Simulation Parameters and Results
243(1)
5.2.9 Discussion of Simulation Results
244(1)
5.2.9.1 Mesh Sensitivity and Validation Results
244(3)
5.2.9.2 Simulation Results
247(6)
References
253(1)
Exercise Problems
254(1)
Quiz Questions
255(2)
Chapter 6 Modeling of Flow Problems
257(36)
6.1 Fluid Mechanics -- Filling of Water Tank
257(5)
6.1.1 Derivation of Mass and Momentum Conservation Equations
258(1)
6.1.2 Boundary Conditions and Initial Conditions
259(1)
6.1.3 Solution Using Analytical Method
260(1)
6.1.4 Computational Algorithm and Computer Program
260(1)
6.1.5 Simulation Parameters and Discussion of Results
261(1)
6.2 Two-Dimensional Flow Problems -- Stokes Flow
262(5)
6.2.1 Description of Problem
262(1)
6.2.2 Mathematical Modeling
263(4)
6.3 Three-Dimensional Stokes Flow
267(17)
6.3.1 Governing Equations for Three-Dimensional Stokes Flow
267(3)
6.3.2 Finite Element Solution Procedure
270(5)
6.3.3 Enforcement of Dirichlet Boundary Conditions in Finite Element Solution Procedure
275(1)
6.3.3.1 Computational Steps to Incorporate Dirichlet Boundary Conditions
276(2)
6.3.4 Global Matrix-Free Finite Element Algorithm
278(1)
6.3.4.1 Matrix Storage Schemes for Large Size Problems and Solvers
278(1)
6.3.4.2 BICGSTAB and Element-by-Element Scheme for Parallel Computing
278(1)
6.3.4.3 Procedure to Implement Global Matrix-Free Finite Element Algorithm
279(5)
6.4 Results for Three-Dimensional Stokes Flow
284(9)
6.4.1 Comparison of Memory Storage of GMFFE Algorithm with Column Format Scheme
286(1)
6.4.2 Flow Results for Three-Dimensional Stokes Flow Using 513 Mesh
286(1)
6.4.2.1 Mesh Sensitivity and Validation Results
286(2)
6.4.2.2 Velocity Vectors Distribution
288(2)
References
290(1)
Exercise Problems
290(2)
Quiz Questions
292(1)
Chapter 7 Navier-Stokes Equations
293(54)
7.1 Momentum Balance of Fluid in a System
293(3)
7.1.1 Fluid Dynamics
295(1)
7.2 Navier-Stokes Equations in Primitive Variables Form
296(15)
7.2.1 Navier-Stokes Equations
297(1)
7.2.2 Application of Predictor-Corrector Method
298(2)
7.2.3 Finite Element Solution Procedure
300(9)
7.2.4 Computational Algorithm
309(1)
7.2.4.1 Computer Program -- Subroutines
310(1)
7.3 Navier-Stokes Equations in Velocity-Vorticity Form
311(36)
7.3.1 Derivation of Velocity-Vorticity Equations as Generalized Formulation
313(5)
7.3.2 Computation of Vorticity Boundary Conditions
318(2)
7.3.2.1 Node i on Side AB -- For Wall Normal Parallel to Positive y-Axis
320(1)
7.3.2.2 Node j on Side CD -- For Wall Normal Parallel to Negative y-Axis
320(1)
7.3.2.3 Node k on Side DA -- For Wall Normal Parallel to Positive x-Axis
321(1)
7.3.2.4 Node m on Side BC -- For Wall Normal Parallel to Negative x-Axis
321(1)
7.3.3 Solution Using Finite Element Method
321(2)
7.3.4 Finite Element Formulation of Vorticity Transport Equation
323(3)
7.3.5 Finite Element Solution Procedure for Velocity Poisson Equations
326(1)
7.3.6 Computational Algorithm
327(2)
7.3.7 Simulation of Lid-Driven Square Cavity Flow Problem
329(1)
7.3.8 Simulation Results
329(7)
7.3.9 Simulation of Natural Convection in a Square Cavity
336(2)
7.3.9.1 Finite Element Solution Procedure
338(2)
7.3.9.2 Simulation Results for Natural Convection in a Differentially Heated Square Cavity
340(3)
References
343(1)
Exercise Problems
344(1)
Quiz Questions
345(2)
Index 347
Krishnan Murugesan is currently teaching at Indian Institute of Technology Roorkee, Roorkee, India in Mechanical and Industrial Engineering Department. He is specialized in broad research areas such as computational fluid dynamics, modeling of heat and moisture transport through porous solid, fuel cells, cooling towers, ground source heat pump systems.
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