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Thermal Convection : Patterns, Evolution and Stability



Thermal Convection : Patterns, Evolution and Stability

Marcello Lappa

ISBN: 978-0-470-74999-9 November 2009 690 Pages

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Thermal Convection - Patterns, Stages of Evolution and Stability Behavior provides the reader with an ensemble picture of the subject, illustrating the state-of-the-art and providing the researchers from universities and industry with a basis on which they are able to estimate the possible impact of a variety of parameters. Unlike earlier books on the subject, the heavy mathematical background underlying and governing the behaviors illustrated in the text are kept to a minimum.

The text clarifies some still unresolved controversies pertaining to the physical nature of the dominating driving force responsible for asymmetric/oscillatory convection in various natural phenomena and/or technologically important processes and can help researchers in elaborating and validating new, more complex models, in accelerating the current trend towards predictable and reproducible natural phenomena and in establishing an adequate scientific foundation to industrial processes.

Thermal Convection - Patterns, Stages of Evolution and Stability Behavior is intended as a useful reference guide for specialists in disciplines such as the metallurgy and foundry field and researchers and scientists who are now coordinating their efforts to improve the quality of semiconductor or macromolecular crystals. The text may also be of use to organic chemists and materials scientists, atmosphere and planetary physicists, as well as an advanced level text for students taking part in courses on the physics of fluids, fluid mechanics, the behavior and evolution of non-linear systems, environmental phenomena and materials engineering.



1 Equations, General Concepts and Methods of Analysis.

1.1 Pattern Formation and Nonlinear Dynamics.

1.2 The Navier–Stokes Equations.

1.3 Energy Equality and Dissipative Structures.

1.4 Flow Stability, Bifurcations and Transition to Chaos.

1.5 Linear Stability Analysis: Principles and Methods.

1.6 Energy Stability Theory.

1.7 Numerical Integration of the Navier–Stokes Equations.

1.8 Some Universal Properties of Chaotic States.

1.9 The Maxwell Equations.

2 Classical Models, Characteristic Numbers and Scaling Arguments.

2.1 Buoyancy Convection and the Boussinesq Model.

2.2 Convection in Space.

2.3 Marangoni Flow.

2.4 Exact Solutions of the Navier–Stokes Equations for Thermal Problems.

2.5 Conductive, Transition and Boundary-layer Regimes.

3 Examples of Thermal Fluid Convection and Pattern Formation in Nature and Technology.

3.1 Technological Processes: Small-scale Laboratory and Industrial Setups.

3.2 Examples of Thermal Fluid Convection and Pattern Formation at the Mesoscale.

3.3 Planetary Structure and Dynamics: Convective Phenomena.

3.4 Atmospheric and Oceanic Phenomena.

4 Thermogravitational Convection: The Rayleigh–Bénard Problem.

4.1 Nonconfined Fluid Layers and Ideal Straight Rolls.

4.2 The Busse Balloon.

4.3 Some Considerations About the Role of Dislocation Dynamics.

4.4 Tertiary and Quaternary Modes of Convection.

4.5 Spoke Pattern Convection.

4.6 Spiral Defect Chaos, Hexagons and Squares.

4.7 Convection with Lateral Walls.

4.8 Two-dimensional Models.

4.9 Three-dimensional Parallelepipedic Enclosures: Classification of Solutions and Possible Symmetries.

4.10 The Circular Cylindrical Problem.

4.11 Spirals: Genesis, Properties and Dynamics.

4.12 From Spirals to SDC: The Extensive Chaos Problem.

4.13 Three-dimensional Convection in a Spherical Shell.

5 The Dynamics of Thermal Plumes and Related Regimes of Motion.

5.1 Introduction.

5.2 Free Plume Regimes.

5.3 The Flywheel Mechanism: The ‘Wind’ of Turbulence.

5.4 Multiplume Configurations Originated from Discrete Sources of Buoyancy.

6 Systems Heated from the Side: The Hadley Flow.

6.1 The Infinite Horizontal Layer.

6.2 Two-dimensional Horizontal Enclosures.

6.3 The Infinite Vertical Layer: Cats-eye Patterns and Temperature Waves.

6.4 Three-dimensional Parallelepipedic Enclosures.

6.5 Cylindrical Geometries under Various Heating Conditions.

7 Thermogravitational Convection in Inclined Systems.

7.1 Inclined Layer Convection.

7.2 Inclined Side-heated Slots.

8 Thermovibrational Convection.

8.1 Equations and Relevant Parameters.

8.2 Fields Decomposition.

8.3 The TFD Distortions.

8.4 High Frequencies and the Thermovibrational Theory.

8.5 States of Quasi-equilibrium and Related Stability.

8.6 Primary and Secondary Patterns of Symmetry.

8.7 Medium and Low Frequencies: Possible Regimes and Flow Patterns.

9 Marangoni–Bénard Convection.

9.1 Introduction.

9.2 High Prandtl Number Liquids: Patterns with Hexagons, Squares and Triangles.

9.3 Liquid Metals: Inverted Hexagons and High-order Solutions.

9.4 Effects of Lateral Confinement.

9.5 Temperature Gradient Inclination.

10 Thermocapillary Convection.

10.1 Basic Features of Steady Marangoni Convection.

10.2 Stationary Multicellular Flow and Hydrothermal Waves.

10.3 Annular Configurations.

10.4 The Liquid Bridge.

11 Mixed Buoyancy–Marangoni Convection.

11.1 The Canonical Problem: The Infinite Horizontal Layer.

11.2 Finite-sized Systems Filled with Liquid Metals.

11.3 Typical Terrestrial Laboratory Experiments with Transparent Liquids.

11.4 The Rectangular Liquid Layer.

11.5 Effects Originating from the Walls.

11.6 The Open Vertical Cavity.

11.7 The Annular Pool.

11.8 The Liquid Bridge on the Ground.

12 Hybrid Regimes with Vibrations.

12.1 RB Convection with Vertical Shaking.

12.2 Complex Order, Quasi-periodic Crystals and Superlattices.

12.3 RB Convection with Horizontal or Oblique Shaking.

12.4 Laterally Heated Systems and Parametric Resonances.

12.5 Control of Thermogravitational Convection.

12.6 Mixed Marangoni–Thermovibrational Convection.

12.7 Modulation of Marangoni–Bénard Convection.

13 Flow Control by Magnetic Fields.

13.1 Static and Uniform Magnetic Fields.

13.2 Historical Developments and Current Status.

13.3 Rotating Magnetic Fields.

13.4 Gradients of Magnetic Fields and Virtual Microgravity.



“In our opinion, this book will be useful for experts in fluid mechanics, nonlinear dynamics, and applied mathematics, as well as physicists and engineers.  The book can be used also by graduate students.”  (Mathematical Reviews, 2012)

"Undoubtedly, the book can be considered as a mandatory reading for everybody whose research involves thermal convection effects. . . For experts it offers a good overview of the current status of
"hot" problems in thermal convection. The book can be strongly recommended for MSc and PhD students whose research includes thermal convection problems, as well as to engineers whose projects involve nonisothermal buoyancy- and thermocapillary-driven flows." (Cryst. Res. Technol, 2011)

"Despite the word "convection" appearing in the title, this excellent monograph is not a book
on heat transfer . . . Otherwise, this is an excellent text which I recommend for those seriously interested in thermally driven convection." (Computational Thermal Sciences, 2011)

"It represents the most comprehensive single volume monograph on convection phenomena available at the present time. I am glad to have the book on my shelf and I will recommend it to anyone with interest in convection as an inspiring guide through its myriad manifestations." (Radostin D. Simitev, October 2010)"This excellent monograph will be warmly welcomed by university teachers and researchers working in the field of thermal convection, and it will be useful for graduate students looking for a short way from basic notions to the current state of the art in that field." (European Journal of Mechanics B/Fluids, September 2010)

"It is a treasure-trove of phenomenological details ordered in a systematic way.  It represents the most comprehensive single-volume monograph on convection phenomena available at the present time.  I am glad to have the book on my shelf and I will recommend it to anyone with interest in convection as an inspiring guide through its myriad manifestations." (Journal of Geophysical and Astrophysical Fluid Dynamics, February 2011)