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Other titles in the Fluid Mechanics and Its Applications series:
Fluid Mechanics and Its Applications #90: Convection in Fluids: A Rational Analysis and Asymptotic Modellingby R. Kh Zeytounian
Synopses & ReviewsPublisher Comments:In the present monograph, entirely devoted to "Convection in Fluids", the purpose is to present a unified rational approach of various convective phenomena in fluids (mainly considered as a thermally perfect gas or an expansible liquid), where the main driving mechanism is the buoyancy force (Archimedean thrust) or temperaturedependent surface tension in homogeneities (Marangoni effect). Also, the general mathematical formulation (for instance, in the Bénard problem  heated from below)and the effect of the free surface deformation are taken into account. In the case of the atmospheric thermal convection, the Coriolis force and stratification effects are also considered. The main motivation is to give a rational, analytical, analysis of main above mentioned physical effects in each case, on the basis of the full unsteady NavierStokes and Fourier (NSF) equations  for a Newtonian compressible viscous and heatconducting fluid  coupled with the associated initiales (at initial time), boundary (lowerat the solid plane) and free surface (upperin contact with ambiant air) conditions. This, obviously, is not an easy but a necessary task if we have in mind a rational modelling process with a view of a numerical coherent simulation on a high speed computer.
Synopsis:This monograph is entirely devoted to convection in fluids. It presents a unified rational approach of various convective phenomena in fluids where the main driving mechanism is the buoyancy force or temperaturedependent surface tension in homogeneities.
Synopsis:This monograph, entirely devoted to "Convection in Fluids", presents a unified rational approach of various convective phenomena in fluids (mainly considered as a thermally perfect gas or an expansible liquid), where the main driving mechanism is the buoyancy force (Archimedean thrust) or temperaturedependent surface tension in homogeneities (Marangoni effect). Also, the general mathematical formulation (for instance, in the Bénard problem  heated from below) and the effect of free surface deformation are taken into account. In the case of atmospheric thermal convection, the Coriolis force and stratification effects are also considered. This volume gives a rational and analytical analysis of the above mentioned physical effects on the basis of the full unsteady NavierStokes and Fourier (NSF) equations  for a Newtonian compressible viscous and heatconducting fluid  coupled with the associated initials (at initial time), boundary (lowerat the solid plane) and free surface (upperin contact with ambiant air) conditions. This, obviously, is not an easy but a necessary task if we have in mind a rational modelling process, and work within a numerically coherent simulation on a high speed computer.
Table of Contents (provisional) Preface and Acknowledgments 1 Short Preliminary Comments and Summary of Chapters 2 to 10 1 . 1 Introduction 1.2 Summary of the chapters 2 to 10 2 The NavierStokes and Fourier Problem 2. 1 Some relations of the thermodynamics 2.2 The case of a thermally perfect gas 2.3 The case of an expansible liquid 2.4 The NSF starting problem 2.4.1 Equations 2.4.2 Initial and boundary conditions 2.5 SQme comments 3 The Simple Rayleigh (1916) Thermal Convection Problem 3. 1 Formulation of the exact simplified (a la Rayleigh) problem 3.2 Dimensionless dominant Rayleigh problem and the Boussinesq approximation 3.3 The RayleighBénard (RB), rigidrigid, problem as a leadingorder approximate model 3.4 Associated, to RB problem, secondorder model problem 4 The Bénard (1900, 1901), Heated from Below, Convection Problem 4.1 The mathematical formulation of the full Bénard convection problem heated from below 4. 1 . 1 Bénard, basic motionless conduction, effect 4. 1 .2 Marangoni, temperature dependent surface tension, effect 4. 1 .3 Biot, heat flux through the upper surface, effect 4.4.4 Boussinesq, buoyancy, effect 4.2 Dimensionless analysis and reduced parameters 4.3 Dominant equations 4.4 Dominant boundary conditions 4.5 An 'alternative' 4.6 Three significant cases: 4.6. 1 Shallow convection 4.6.2 Deep convection 4.6.3 Marangoni convection 5 Thermal Shallow Convection Problem, 'a la RayleighBénard' 5. 1 The RB rigidfree instability problem as a significant leadingorder model problem 5.2 The free surface, Marangoni and Biot effects 5.3 Secondorder non Boussinesq and viscous dissipation effects 5.4 Linear classical theory 5.5 Some comments and complements 6 The Deep Thermal Convection Problem, 6. 1 The viscous dissipation effect and the 'depth' parameter 6.2 The deep thermal convection problem, 'a la Zeytounian' 6.3 The Charki, Errafyi and Zeytounian results: 6.3.1 Linear theory 6.3.2 Routes to chaos, 6.3.3 Lorenz system 6.3.4 Landau Ginzburg equation 6 6.4 The Straughan and Charki rigorous mathematical results 6.5 The Hills and Roberts approach 7 The Thermocapilary, Marangoni, Convection Problem 7. 1 The free surface effects and the ' 'Biot paradox" 7.2 The BénardMarangoni model problem 7.3 The longwave approximation and the lubrication evolution equation for the thickness of the film 7.4 Freely falling vertical film 7.5 The KS and KSKdV approximate equations 7 . 6 Stability results 7.7 Complements 8 Summing Up of the Three Cases Related with the Bénard, Heated from Below, Convection Problem 8. 1 The consistent conditions for the RayleighBénard model problem 8. 1 . 1 Constraints on the thickness of the fluid layer 8. 1 .2 The role of the viscous dissipation term 8. 1 .3 An equation for the free surface deformation 8.2 The particularity of the deep thermal convection model problem 8.2. 1 The role of the 'depth' parameter and the effect of the viscous dissipation 8.2.2 The variation of the critical Rayleigh numbers as a function of the depth parameter 8.3 The thin viscous liquid film, Marangoni, case 8.3.1 Constraints on the thickness of the liquid layer 8.3.2 The role of the free surface deformation 8.3..3 Constraints for a reduced long wave film problem 9 Atmospheric Thermal Convection Problems 9. 1 The Coriolis force and stratification effects 9.2 A rigorous formulation of the atmospheric free thermal convection 9.3 The Boussinesq approximation and the breeze problem 9.4 Infuence of a local temperature field in an atmospheric Ekman layer; a tripledeck approach 9.5 A periodic thermal freeconvection problem over a curvilinear wall; the 'double boundarylayer' effect 'a la StuartRiley' 9.6 Complements 10 Miscellaneous: Various Convection Model Problems 10. 1 Convection in the Eart's outer core 10.2 Electro, Ferro, Solar, mantle, planetary and Magneto hydrodynamic convections 10.3 Averaged integral boundary layer models; the results of Shkadov, Zeytounian and RuyerQuil 10.4 Coupled system of two evolution equations for the two dimensional free films. 10.5 Ultrathin films 10.6 Convection in ocean  thermosolutal convection 10.7 Some recent results References Index
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