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Mathematical Models of Convection

:	Victor K. Andreev, Yuri A. Gaponenko, Olga N. Goncharova, Vladislav V. Pukhnachev
:	Mathematical Models of Convection
:	Walter de Gruyter GmbH& Co.KG
:	9783110258592
:	De Gruyter Studies in Mathematical PhysicsISSN
:	1
:	CHF 125.10
:

:	Theoretische Physik
:	English

:	432
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

< >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.

< >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; andVladislav V. Pukhnachev,Lavrentye Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia.

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