Mathematical Models of Convection 1st Edition by Victor Andreev ISBN 9783110258592 3110258595

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ISBN 10: 3110258595
ISBN 13: 9783110258592 
Author: Victor Andreev

Mathematical Models of Convection 1st Edition Table of contents:

1 Equations of fluid motion

1.1 Basic hypotheses of continuum

1.2 Two methods for the continuum description. Translation formula

1.3 Integral conservation laws. Equations of continuous motion

1.4 Thermodynamics aspects

1.5 Classical models of liquids and gases

2 Conditions on the interface between fluids and on solid walls

2.1 Notion of the interface

2.2 Kinematic condition

2.3 Dynamic condition

2.4 Elements of thermodynamics of the interface

2.5 Conditions of continuity

2.6 Energy transfer across the interface

2.7 Free surfaces

2.8 Additional conditions

3 Models of convection of an isothermally incompressible fluid

3.1 Isothermally incompressible fluid

3.2 Equations of thermal convection of an isothermally incompressible fluid

3.3 Model of linear thermal expansion

3.4 Some submodels

3.5 On boundary conditions

3.6 Two problems of convection

4 Hierarchy of convection models in closed volumes

4.1 Initial relations

4.2 Similarity criteria

4.3 Transition to dimensional variables

4.4 Expansion in the small parameter

4.5 Equations of microconvection of an isothermally incompressible fluid

4.6 Oberbeck-Boussinesq equations

4.7 Linear model of the transitional process

4.8 Some conclusions

4.9 Convection of nonisothermal liquids and gases under microgravity conditions

4.10 Convection of a thermally inhomogeneous weakly compressible fluid

4.11 Exact solutions in an infinite band

4.12 Analysis of well-posedness of the initial-boundary problem for equations of convection of a wea

5 Invariant submodels of microconvection equations

5.1 Basic model and its group properties

5.2 Optimal subsystems of the subalgebras Θ1 and Θ2, factor-systems, and some solutions

5.3 On one steady solution of microconvection equations in a vertical layer

5.4 Solvability of a nonstandard boundary-value problem

5.5 Unsteady solution of microconvection equations in an infinite band

5.6 Invariant solutions of microconvection equations that describe the motion with an interface

6 Group properties of equations of thermodiffusion motion

6.1 Lie group of thermodiffusion equations

6.2 Group properties of two-dimensional equations

6.3 Invariant submodels and exact solutions of thermodiffusion equations

7 Stability of equilibrium states in the Oberbeck-Boussinesq model

7.1 Convective instability of a horizontal layer with oscillations of temperature on the free bounda

7.2 Instability of a liquid layers with an interface

7.3 Convection in a rotating fluid layer under microgravity conditions

8 Small perturbations and stability of plane layers in the microconvection model

8.1 Equations of small perturbations

8.2 Stability of the equilibrium state of a plane layer with solid walls

8.3 Emergence of microconvection in a plane layer with a free boundary

8.4 Stability of a steady flow in a vertical layer

9 Numerical simulation of convective flows under microgravity conditions

9.1 Numerical methods used for calculations

9.2 Numerical study of unsteady microconvection in canonical domains with solid boundaries

9.3 Numerical study of steady microconvection in domains with free boundaries

9.4 Study of convection induced by volume expansion

9.5 Convection in miscible fluids

10 Convective flows in tubes and layers

10.1 Group-theoretical nature of the Birikh solution and its generalizations

10.2 An axial convective flow in a rotating tube with a longitudinal temperature gradient

10.3 Unsteady analogs of the Birikh solutions

10.4 Model of viscous layer deformation by thermocapillary forces

Bibliography

Index

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