Andreev / Gaponenko / Goncharova Mathematical Models of Convection

1. Auflage 2012
ISBN: 978-3-11-025859-2
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 5, 432 Seiten

Reihe: De Gruyter Studies in Mathematical PhysicsISSN

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

Zielgruppe

Theoretical Physicists, Theoretical Chemists, Materials Scientists; Academic Libraries

Autoren/Hrsg.

Andreev, Victor K.

Gaponenko, Yuri A.

Goncharova, Olga N.

Pukhnachev, Vladislav V.

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik
• Naturwissenschaften Physik Angewandte Physik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre

Inhaltsverzeichnis

1;Preface;5
2;List of contributing authors;11
3;1 Equations of fluid motion;17
3.1;1.1 Basic hypotheses of continuum;17
3.2;1.2 Two methods for the continuum description. Translation formula;20
3.3;1.3 Integral conservation laws. Equations of continuous motion;23
3.4;1.4 Thermodynamics aspects;29
3.5;1.5 Classical models of liquids and gases;32
4;2 Conditions on the interface between fluids and on solid walls;40
4.1;2.1 Notion of the interface;40
4.2;2.2 Kinematic condition;41
4.3;2.3 Dynamic condition;42
4.4;2.4 Elements of thermodynamics of the interface;47
4.5;2.5 Conditions of continuity;49
4.6;2.6 Energy transfer across the interface;50
4.7;2.7 Free surfaces;55
4.8;2.8 Additional conditions;57
5;3 Models of convection of an isothermally incompressible fluid;60
5.1;3.1 Isothermally incompressible fluid;60
5.2;3.2 Equations of thermal convection of an isothermally incompressible fluid;62
5.3;3.3 Model of linear thermal expansion;63
5.4;3.4 Some submodels;65
5.5;3.5 On boundary conditions;67
5.6;3.6 Two problems of convection;69
6;4 Hierarchy of convection models in closed volumes;76
6.1;4.1 Initial relations;76
6.2;4.2 Similarity criteria;78
6.3;4.3 Transition to dimensional variables;80
6.4;4.4 Expansion in the small parameter;83
6.5;4.5 Equations of microconvection of an isothermally incompressible fluid;87
6.6;4.6 Oberbeck-Boussinesq equations;90
6.7;4.7 Linear model of the transitional process;91
6.8;4.8 Some conclusions;94
6.9;4.9 Convection of nonisothermal liquids and gases under microgravity conditions;97
6.10;4.10 Convection of a thermally inhomogeneous weakly compressible fluid;104
6.11;4.11 Exact solutions in an infinite band;109
6.12;4.12 Analysis of well-posedness of the initial-boundary problem for equations of convection of a weakly compressible fluid;121
7;5 Invariant submodels of microconvection equations;131
7.1;5.1 Basic model and its group properties;131
7.2;5.2 Optimal subsystems of the subalgebras T1 and T2, factor-systems, and some solutions;134
7.3;5.3 On one steady solution of microconvection equations in a vertical layer;142
7.4;5.4 Solvability of a nonstandard boundary-value problem;153
7.5;5.5 Unsteady solution of microconvection equations in an infinite band;160
7.6;5.6 Invariant solutions of microconvection equations that describe the motion with an interface;166
8;6 Group properties of equations of thermodiffusion motion;173
8.1;6.1 Lie group of thermodiffusion equations;173
8.2;6.2 Group properties of two-dimensional equations;190
8.3;6.3 Invariant submodels and exact solutions of thermodiffusion equations;198
9;7 Stability of equilibrium states in the Oberbeck-Boussinesq model;214
9.1;7.1 Convective instability of a horizontal layer with oscillations of temperature on the free boundary;214
9.2;7.2 Instability of a liquid layers with an interface;224
9.3;7.3 Convection in a rotating fluid layer under microgravity conditions;233
10;8 Small perturbations and stability of plane layers in the microconvection model;243
10.1;8.1 Equations of small perturbations;243
10.2;8.2 Stability of the equilibrium state of a plane layer with solid walls;247
10.3;8.3 Emergence of microconvection in a plane layer with a free boundary;257
10.4;8.4 Stability of a steady flow in a vertical layer;268
11;9 Numerical simulation of convective flows under microgravity conditions;279
11.1;9.1 Numerical methods used for calculations;279
11.2;9.2 Numerical study of unsteady microconvection in canonical domains with solid boundaries;290
11.3;9.3 Numerical study of steady microconvection in domains with free boundaries;307
11.4;9.4 Study of convection induced by volume expansion;323
11.5;9.5 Convection in miscible fluids;343
12;10 Convective flows in tubes and layers;363
12.1;10.1 Group-theoretical nature of the Birikh solution and its generalizations;363
12.2;10.2 An axial convective flow in a rotating tube with a longitudinal temperature gradient;371
12.3;10.3 Unsteady analogs of the Birikh solutions;379
12.4;10.4 Model of viscous layer deformation by thermocapillary forces;393
13;Bibliography;417
14;Index;431

Über Autor(innen)

Victor K. Andreev, Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia; Yuri A. Gaponenko, Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia; Olga N. Goncharova, Altai State University, Barnaul, Russia; and Vladislav V. Pukhnachev, Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia.