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E-raamat: Continuum Modeling: An Approach Through Practical Examples

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Continuum Modeling: An Approach Through Practical ExamplesSuurem pilt
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This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes. The focus of this presentation lies on many practical examples covering aspects such as coupled flow, diffusion and reaction in porous media or microwave heating of a pizza, as well as traffic issues in bacterial colonies and energy harvesting from geothermal wells. The target audience comprises primarily graduate students in pure and applied mathematics as well as working practitioners in engineering who are faced by nonstandard rheological topics like those typically arising in the food industry.

Arvustused

The book is quite short and contains subjects that usually are more exotic and/or advanced with respect to the basic topics of a continuum mechanics course. I have enjoyed reading this short book and I think it gives a fresh look into the standard topics of a continuum mechanics course at a level . I think this book is a nice addition in a field where a long list of textbooks is available. (Giuseppe Saccomandi, Mathematical Reviews, March, 2016)

1 Scaling and Estimation of Physical Systems
1(18)
1.1 Background
1(1)
1.2 Units, Scales, Dimensions
2(4)
1.2.1 A Look at a Functional Equation
4(2)
1.3 Basic Dimensional Estimations
6(5)
1.3.1 Ruling Out Pathologic Functional Dependencies
6(5)
1.4 Two Scaling Estimations
11(3)
1.4.1 Estimating Heights of Droplets on Flat Surfaces
11(2)
1.4.2 The Voice of the Dragon
13(1)
1.5 Nondimensionalization in Action
14(2)
1.6 Notes and Comments
16(3)
2 Balance Equations in Continuum Physics
19(38)
2.1 Basic Notions
19(1)
2.1.1 Notation, Body and Configurations, Coordinates
19(1)
2.2 Global Balance Laws
20(2)
2.3 Local Balance Laws
22(11)
2.3.1 The Continuity Equation
23(1)
2.3.2 Derivation of the Momentum Equation
24(2)
2.3.3 Principle of Conservation of Linear Momentum
26(2)
2.3.4 Balance of the angular momentum
28(1)
2.3.5 Balance of Total Energy
28(2)
2.3.6 Comments on Conservation of Momenta
30(1)
2.3.7 The Local Form of Clausius--Duhem Inequality, Admissible Thermodynamic Processes
31(2)
2.4 Towards Derivations of Boundary Conditions
33(7)
2.4.1 Shocks
33(1)
2.4.2 Rankine--Hugoniot Jump Relations
34(2)
2.4.3 Practical Examples of Boundary Conditions
36(4)
2.5 Examples of Constitutive Equations
40(6)
2.5.1 Constitutive Equations for the Stress Tensor T
40(2)
2.5.2 More on Constitutive Laws: Deviations from Modeling Incompressible Fluids
42(1)
2.5.3 Summary of Equations to Viscous and Inviscid Fluids
43(1)
2.5.4 How to Account for Temperature Effects on Fluids?
44(1)
2.5.5 Summary of Equations for a Material (Fluid or Solid) Undergoing an Admissible Thermodynamics Process
44(2)
2.6 Constitutive Equations for Transport Fluxes j and q
46(1)
2.7 Practical Examples
47(9)
2.7.1 Model for a Simple Fluid---The Poiseuille Flow
47(1)
2.7.2 The Hot Coffee Problem
48(2)
2.7.3 Chemical Kinetics
50(4)
2.7.4 Geothermal Flow
54(2)
2.8 Notes and Comments
56(1)
3 Transport Fluxes
57(14)
3.1 Conservation Laws
57(1)
3.2 Two Derivations of the Darcy's Law
58(6)
3.2.1 Periodic Arrangements of Microstructures
58(4)
3.2.2 Random Microstructures
62(2)
3.3 A Heuristic Look at Thermodiffusion
64(3)
3.3.1 Joint Dynamics of Particles and Heat in a Discrete Heterogeneous Medium
64(1)
3.3.2 Derivation of a Macroscopic Model for Thermodiffusion
65(2)
3.4 Kinetic Interpretation of an Evolution System for Hot Colloids
67(2)
3.4.1 Model Structure
67(1)
3.4.2 Dimension Reduction
68(1)
3.5 Notes and Comments
69(2)
References 71
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