| Description |
1 online resource |
| Contents |
Intro; Foreword; Preface; Acknowledgements; Contents; 1 Introduction; References; Part I Mathematical Models of Flow Instability; 2 Fourier Transform and Wave Packets; 2.1 Integral Transforms; 2.2 The Fourier Transform; 2.2.1 Definition; 2.2.2 Inversion of the Fourier Transform; 2.2.3 Some Properties of the Fourier Transform; 2.2.4 Solution of the One-Dimensional Wave Equation; 2.2.5 Solution of the One-Dimensional Diffusion Equation; 2.2.6 Solution of the One-Dimensional Advection-Diffusion Equation; 2.2.7 Solution of the One-Dimensional Schrödinger Equation; 2.3 Plane Waves and Wave Packets |
|
2.3.1 Stationary Waves in x-Space and k-Space2.3.2 Travelling Wave Packets; 2.4 Three-Dimensional Fourier Transform and Wave Packets; References; 3 Large-time Behaviour of Wave Packets; 3.1 What is a Holomorphic Function?; 3.1.1 Derivative of a Complex-Valued Function; 3.1.2 Path Integration in mathbbC; 3.1.3 Homotopy; 3.2 Laurent Expansions, Singular Points; 3.3 Residues; 3.3.1 Evaluation of Integrals; 3.4 The Laplace Transform; 3.4.1 Inversion of the Laplace Transform; 3.4.2 Main Properties of the Laplace Transform; 3.4.3 Meromorphic Functions; 3.5 Saddle Points; 3.5.1 Stationary Point |
|
3.5.2 Paths from a Saddle Point3.5.3 Asymptotic Behaviour of Wave Packets at Large Times; References; 4 Instability of a Flow System; 4.1 Stability and Instability of a Mechanical System; 4.1.1 A Simple Mechanical System; 4.1.2 The Method of Small Perturbations; 4.2 Flow Stability with Burgers Equation; 4.2.1 Linear Stability Analysis; 4.2.2 Time Evolution of a Special Perturbation Wave Packet; 4.3 Stability of Channelised Burgers Flow; 4.3.1 Linear Stability Analysis; 4.4 Stability of a Convective Cahn-Hilliard Process; 4.4.1 Linear Stability Analysis |
|
4.5 Some Considerations on Convective and Absolute InstabilitiesReferences; Part II Flow and Convection in Porous Media; 5 The Equations of Fluid Flow; 5.1 The Description of Fluid Flow; 5.2 Reynolds' Transport Theorem; 5.3 Local Mass Balance Equation; 5.4 Forces Acting on a Fluid Body; 5.5 Local Momentum Balance Equation; 5.6 Local Angular Momentum Balance Equation; 5.7 Local Energy Balance Equation; 5.8 Viscous Stresses and Heat Flux; 5.9 The Oberbeck-Boussinesq Approximation; 5.10 Governing Equations of Mass Diffusion; 5.10.1 Transport Theorem for Mass Diffusion |
|
5.10.2 Concentrations and Mass Fluxes5.10.3 The Oberbeck-Boussinesq Approximation; 5.10.4 A Two-Component Mixture and Fick's Law; 5.11 Local Entropy Balance Equation; References; 6 Fluid Flow in Porous Media; 6.1 The Basic Features of Flow in Porous Media; 6.2 Local Momentum Balance in a Porous Medium; 6.3 Local Mass and Energy Balance Equations; 6.3.1 Local Thermal Non-equilibrium; 6.3.2 Viscous Dissipation; 6.4 The Buoyancy Force; 6.5 Non-Newtonian Flow in Porous Media; References; 7 Rayleigh-Bénard Convection; 7.1 Heating a Fluid Layer from Below; 7.2 The Rayleigh-Bénard Problem |
| Summary |
This book addresses the concepts of unstable flow solutions, convective instability and absolute instability, with reference to simple (or toy) mathematical models, which are mathematically simple despite their purely abstract character. Within this paradigm, the book introduces the basic mathematical tools, Fourier transform, normal modes, wavepackets and their dynamics, before reviewing the fundamental ideas behind the mathematical modelling of fluid flow and heat transfer in porous media. The author goes on to discuss the fundamentals of the Rayleigh-Bénard instability and other thermal instabilities of convective flows in porous media, and then analyses various examples of transition from convective to absolute instability in detail, with an emphasis on the formulation, deduction of the dispersion relation and study of the numerical data regarding the threshold of absolute instability. The clear descriptions of the analytical and numerical methods needed to obtain these parametric threshold data enable readers to apply them in different or more general cases. This book is of interest to postgraduates and researchers in mechanical and thermal engineering, civil engineering, geophysics, applied mathematics, fluid mechanics, and energy technology |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed January 9, 2019) |
| Subject |
Porous materials -- Stability
|
|
Fluid mechanics.
|
|
TECHNOLOGY & ENGINEERING -- Engineering (General)
|
|
TECHNOLOGY & ENGINEERING -- Reference.
|
|
Fluid mechanics
|
| Form |
Electronic book
|
| ISBN |
9783030061944 |
|
3030061949 |
|
9783030061951 |
|
3030061957 |
|
