Mathematical Models of Convection
Description
Phenomena of convection are abundant in nature as well as in industry. This volume addresses the subject of convection from the point of view of both, theory and application. While the first three chapters provide a refresher on fluid dynamics and heat transfer theory, the rest of the book describes the modern developments in theory. Thus it brings the reader to the "front" of the modern research.
This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fields.
Reviews / Votes
"This book presents a careful and detailed introduction to the modern mathematical models of convection. [.] In the reviewer's opinion, this book provides a fundamental and comprehensive presentation of the mathematical and physical theory of fluid flows in non-classical models of convection, pointing out the most important practical applications. The book is excellently written and readable. Results of numerical solutions are given graphically and in tabular form. The book will be of great interest to a wide range of specialists working in the area of convection. It can be also recommended as a text for seminars and courses, as well as for independent study." Zentralblatt für Mathematik
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Content
2 - List of contributing authors [Seite 11]
3 - 1 Equations of fluid motion [Seite 17]
3.1 - 1.1 Basic hypotheses of continuum [Seite 17]
3.2 - 1.2 Two methods for the continuum description. Translation formula [Seite 20]
3.3 - 1.3 Integral conservation laws. Equations of continuous motion [Seite 23]
3.4 - 1.4 Thermodynamics aspects [Seite 29]
3.5 - 1.5 Classical models of liquids and gases [Seite 32]
4 - 2 Conditions on the interface between fluids and on solid walls [Seite 40]
4.1 - 2.1 Notion of the interface [Seite 40]
4.2 - 2.2 Kinematic condition [Seite 41]
4.3 - 2.3 Dynamic condition [Seite 42]
4.4 - 2.4 Elements of thermodynamics of the interface [Seite 47]
4.5 - 2.5 Conditions of continuity [Seite 49]
4.6 - 2.6 Energy transfer across the interface [Seite 50]
4.7 - 2.7 Free surfaces [Seite 55]
4.8 - 2.8 Additional conditions [Seite 57]
5 - 3 Models of convection of an isothermally incompressible fluid [Seite 60]
5.1 - 3.1 Isothermally incompressible fluid [Seite 60]
5.2 - 3.2 Equations of thermal convection of an isothermally incompressible fluid [Seite 62]
5.3 - 3.3 Model of linear thermal expansion [Seite 63]
5.4 - 3.4 Some submodels [Seite 65]
5.5 - 3.5 On boundary conditions [Seite 67]
5.6 - 3.6 Two problems of convection [Seite 69]
6 - 4 Hierarchy of convection models in closed volumes [Seite 76]
6.1 - 4.1 Initial relations [Seite 76]
6.2 - 4.2 Similarity criteria [Seite 78]
6.3 - 4.3 Transition to dimensional variables [Seite 80]
6.4 - 4.4 Expansion in the small parameter [Seite 83]
6.5 - 4.5 Equations of microconvection of an isothermally incompressible fluid [Seite 87]
6.6 - 4.6 Oberbeck-Boussinesq equations [Seite 90]
6.7 - 4.7 Linear model of the transitional process [Seite 91]
6.8 - 4.8 Some conclusions [Seite 94]
6.9 - 4.9 Convection of nonisothermal liquids and gases under microgravity conditions [Seite 97]
6.10 - 4.10 Convection of a thermally inhomogeneous weakly compressible fluid [Seite 104]
6.11 - 4.11 Exact solutions in an infinite band [Seite 109]
6.12 - 4.12 Analysis of well-posedness of the initial-boundary problem for equations of convection of a weakly compressible fluid [Seite 121]
7 - 5 Invariant submodels of microconvection equations [Seite 131]
7.1 - 5.1 Basic model and its group properties [Seite 131]
7.2 - 5.2 Optimal subsystems of the subalgebras T1 and T2, factor-systems, and some solutions [Seite 134]
7.3 - 5.3 On one steady solution of microconvection equations in a vertical layer [Seite 142]
7.4 - 5.4 Solvability of a nonstandard boundary-value problem [Seite 153]
7.5 - 5.5 Unsteady solution of microconvection equations in an infinite band [Seite 160]
7.6 - 5.6 Invariant solutions of microconvection equations that describe the motion with an interface [Seite 166]
8 - 6 Group properties of equations of thermodiffusion motion [Seite 173]
8.1 - 6.1 Lie group of thermodiffusion equations [Seite 173]
8.2 - 6.2 Group properties of two-dimensional equations [Seite 190]
8.3 - 6.3 Invariant submodels and exact solutions of thermodiffusion equations [Seite 198]
9 - 7 Stability of equilibrium states in the Oberbeck-Boussinesq model [Seite 214]
9.1 - 7.1 Convective instability of a horizontal layer with oscillations of temperature on the free boundary [Seite 214]
9.2 - 7.2 Instability of a liquid layers with an interface [Seite 224]
9.3 - 7.3 Convection in a rotating fluid layer under microgravity conditions [Seite 233]
10 - 8 Small perturbations and stability of plane layers in the microconvection model [Seite 243]
10.1 - 8.1 Equations of small perturbations [Seite 243]
10.2 - 8.2 Stability of the equilibrium state of a plane layer with solid walls [Seite 247]
10.3 - 8.3 Emergence of microconvection in a plane layer with a free boundary [Seite 257]
10.4 - 8.4 Stability of a steady flow in a vertical layer [Seite 268]
11 - 9 Numerical simulation of convective flows under microgravity conditions [Seite 279]
11.1 - 9.1 Numerical methods used for calculations [Seite 279]
11.2 - 9.2 Numerical study of unsteady microconvection in canonical domains with solid boundaries [Seite 290]
11.3 - 9.3 Numerical study of steady microconvection in domains with free boundaries [Seite 307]
11.4 - 9.4 Study of convection induced by volume expansion [Seite 323]
11.5 - 9.5 Convection in miscible fluids [Seite 343]
12 - 10 Convective flows in tubes and layers [Seite 363]
12.1 - 10.1 Group-theoretical nature of the Birikh solution and its generalizations [Seite 363]
12.2 - 10.2 An axial convective flow in a rotating tube with a longitudinal temperature gradient [Seite 371]
12.3 - 10.3 Unsteady analogs of the Birikh solutions [Seite 379]
12.4 - 10.4 Model of viscous layer deformation by thermocapillary forces [Seite 393]
13 - Bibliography [Seite 417]
14 - Index [Seite 431]
