Showing papers on "Natural convection published in 2009"

Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

Abstract: The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.

Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure

Abstract: This article presents a numerical study of natural convection cooling of a heat source embedded on the bottom wall of an enclosure filled with nanofluids. The top and vertical walls of the enclosure are maintained at a relatively low temperature. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The results indicate that adding nanoparticles into pure water improves its cooling performance especially at low Rayleigh numbers. The type of nanoparticles and the length and location of the heat source proved to significantly affect the heat source maximum temperature.

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

Abstract: This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on ...

Thermal Convection: Patterns, Evolution and Stability

Abstract: Preface . Acknowledgements . 1 Equations, General Concepts and Methods of Analysis. 1.1 Pattern Formation and Nonlinear Dynamics. 1.2 The Navier-Stokes Equations. 1.3 Energy Equality and Dissipative Structures. 1.4 Flow Stability, Bifurcations and Transition to Chaos. 1.5 Linear Stability Analysis: Principles and Methods. 1.6 Energy Stability Theory. 1.7 Numerical Integration of the Navier-Stokes Equations. 1.8 Some Universal Properties of Chaotic States. 1.9 The Maxwell Equations. 2 Classical Models, Characteristic Numbers and Scaling Arguments. 2.1 Buoyancy Convection and the Boussinesq Model. 2.2 Convection in Space. 2.3 Marangoni Flow. 2.4 Exact Solutions of the Navier-Stokes Equations for Thermal Problems. 2.5 Conductive, Transition and Boundary-layer Regimes. 3 Examples of Thermal Fluid Convection and Pattern Formation in Nature and Technology. 3.1 Technological Processes: Small-scale Laboratory and Industrial Setups. 3.2 Examples of Thermal Fluid Convection and Pattern Formation at the Mesoscale. 3.3 Planetary Structure and Dynamics: Convective Phenomena. 3.4 Atmospheric and Oceanic Phenomena. 4 Thermogravitational Convection: The Rayleigh-Benard Problem. 4.1 Nonconfined Fluid Layers and Ideal Straight Rolls. 4.2 The Busse Balloon. 4.3 Some Considerations About the Role of Dislocation Dynamics. 4.4 Tertiary and Quaternary Modes of Convection. 4.5 Spoke Pattern Convection. 4.6 Spiral Defect Chaos, Hexagons and Squares. 4.7 Convection with Lateral Walls. 4.8 Two-dimensional Models. 4.9 Three-dimensional Parallelepipedic Enclosures: Classification of Solutions and Possible Symmetries. 4.10 The Circular Cylindrical Problem. 4.11 Spirals: Genesis, Properties and Dynamics. 4.12 From Spirals to SDC: The Extensive Chaos Problem. 4.13 Three-dimensional Convection in a Spherical Shell. 5 The Dynamics of Thermal Plumes and Related Regimes of Motion. 5.1 Introduction. 5.2 Free Plume Regimes. 5.3 The Flywheel Mechanism: The 'Wind' of Turbulence. 5.4 Multiplume Configurations Originated from Discrete Sources of Buoyancy. 6 Systems Heated from the Side: The Hadley Flow. 6.1 The Infinite Horizontal Layer. 6.2 Two-dimensional Horizontal Enclosures. 6.3 The Infinite Vertical Layer: Cats-eye Patterns and Temperature Waves. 6.4 Three-dimensional Parallelepipedic Enclosures. 6.5 Cylindrical Geometries under Various Heating Conditions. 7 Thermogravitational Convection in Inclined Systems. 7.1 Inclined Layer Convection. 7.2 Inclined Side-heated Slots. 8 Thermovibrational Convection. 8.1 Equations and Relevant Parameters. 8.2 Fields Decomposition. 8.3 The TFD Distortions. 8.4 High Frequencies and the Thermovibrational Theory. 8.5 States of Quasi-equilibrium and Related Stability. 8.6 Primary and Secondary Patterns of Symmetry. 8.7 Medium and Low Frequencies: Possible Regimes and Flow Patterns. 9 Marangoni-Benard Convection. 9.1 Introduction. 9.2 High Prandtl Number Liquids: Patterns with Hexagons, Squares and Triangles. 9.3 Liquid Metals: Inverted Hexagons and High-order Solutions. 9.4 Effects of Lateral Confinement. 9.5 Temperature Gradient Inclination. 10 Thermocapillary Convection. 10.1 Basic Features of Steady Marangoni Convection. 10.2 Stationary Multicellular Flow and Hydrothermal Waves. 10.3 Annular Configurations. 10.4 The Liquid Bridge. 11 Mixed Buoyancy-Marangoni Convection. 11.1 The Canonical Problem: The Infinite Horizontal Layer. 11.2 Finite-sized Systems Filled with Liquid Metals. 11.3 Typical Terrestrial Laboratory Experiments with Transparent Liquids. 11.4 The Rectangular Liquid Layer. 11.5 Effects Originating from the Walls. 11.6 The Open Vertical Cavity. 11.7 The Annular Pool. 11.8 The Liquid Bridge on the Ground. 12 Hybrid Regimes with Vibrations. 12.1 RB Convection with Vertical Shaking. 12.2 Complex Order, Quasi-periodic Crystals and Superlattices. 12.3 RB Convection with Horizontal or Oblique Shaking. 12.4 Laterally Heated Systems and Parametric Resonances. 12.5 Control of Thermogravitational Convection. 12.6 Mixed Marangoni-Thermovibrational Convection. 12.7 Modulation of Marangoni-Benard Convection. 13 Flow Control by Magnetic Fields. 13.1 Static and Uniform Magnetic Fields. 13.2 Historical Developments and Current Status. 13.3 Rotating Magnetic Fields. 13.4 Gradients of Magnetic Fields and Virtual Microgravity. References . Index .

Boundary layer control of rotating convection systems

Abstract: Turbulent rotating convection is an important dynamical process occurring on nearly all planetary and stellar bodies, influencing many observed features such as magnetic fields, atmospheric jets and emitted heat flux patterns. For decades, it has been thought that the importance of rotation's influence on convection depends on the competition between the two relevant forces in the system: buoyancy (non-rotating) and Coriolis (rotating). The force balance argument does not, however, accurately predict the transition from rotationally controlled to non-rotating heat transfer behaviour. New results from laboratory and numerical experiments suggest that the transition is in fact controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. Turbulent rotating convection controls many observed features in stars and planets, such as magnetic fields. It has been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force. This paper presents results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. Turbulent rotating convection controls many observed features of stars and planets, such as magnetic fields, atmospheric jets and emitted heat flux patterns1,2,3,4,5,6. It has long been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force7,8,9,10,11,12. Here, however, we present results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. We formulate a predictive description of the transition between the two regimes on the basis of the competition between these two boundary layers. This transition scaling theory unifies the disparate results of an extensive array of previous experiments8,9,10,11,12,13,14,15, and is broadly applicable to natural convection systems.

Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh-Bénard convection

Abstract: For given aspect ratio and given geometry, the nature of Rayleigh Benard convection (RBC) is determined by the Rayleigh number Ra = bg DL3 / (kn)Ra=gL3() and by the Prandtl number Pr = n/ kPr= is the thermal expansion coefficient, g the gravitational acceleration D = Tb - Tt=Tb−Tt the difference between the imposed temperatures Tb and Tt at the bottom and the top of the sample, respectively, and v and k the kinematic viscosity and the thermal diffusivity, respectively. The rotation rate Ω (given in rad/s) is used in the form of the Rossby number Ro = O{bg D/ L / (2 W)}Ro=gL(2)

Origin of the Temperature Oscillation in Turbulent Thermal Convection

Abstract: We report an experimental study of the three-dimensional spatial structure of the low-frequency temperature oscillations in a cylindrical Rayleigh-Benard convection cell. Through simultaneous multipoint temperature measurements it is found that, contrary to the popular scenario, thermal plumes are emitted neither periodically nor alternately, but randomly and continuously, from the top and bottom plates. We further identify a new flow mode-the sloshing mode of the large-scale circulation (LSC). This sloshing mode, together with the torsional mode of the LSC, are found to be the origin of the oscillation of the temperature field.

Transitions between turbulent states in rotating Rayleigh-Bénard convection.

Abstract: Weakly rotating turbulent Rayleigh-Benard convection was studied experimentally and numerically. With increasing rotation and large enough Rayleigh number a supercritical bifurcation from a turbulent state with nearly rotation-independent heat transport to another with enhanced heat transfer is observed at a critical inverse Rossby number 1/Ro_c≃0.4. The strength of the large-scale convection roll is either enhanced or essentially unmodified depending on parameters for 1/Ro < 1/Ro_c, but the strength increasingly diminishes beyond 1/Ro_c where it competes with Ekman vortices that cause vertical fluid transport and thus heat-transfer enhancement.

Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption

Abstract: The problem of magneto-hydrodynamic mixed convective flow and heat transfer of an electrically conducting, power-law fluid past a stretching surface in the presence of heat generation/absorption and thermal radiation has been analyzed. After transforming the governing equations with suitable dimensionless variables, numerical solutions are generated by an implicit finite-difference technique for the non-similar, coupled flow. The solution is found to be dependent on the governing parameters including the power-law fluid index, the magnetic field parameter, the modified Richardson number, the radiation parameter, the heat generation parameter, and the generalized Prandtl number. To reveal the tendency of the solutions, typical results for the velocity and temperature profiles, the skin-friction coefficient, and the local Nusselt number are presented for different values of these controlling parameters.

Enhanced Mass Transfer of CO2 into Water: Experiment and Modeling

Abstract: Concern over global warming has increased interest in quantification of the dissolution of CO2 in (sub-)- surface water. The mechanisms of the mass transfer of CO2 in aquifers and of transfer to surface water have many common features. The advantage of experiments using bulk water is that the underlying assumptions to the quantify mass-transfer rate can be validated. Dissolution of CO2 into water (or oil) increases the density of the liquid phase. This density change destabilizes the interface and enhances the transfer rate across the interface by natural convection. This paper describes a series of experiments performed in a cylindrical PVT- cell at a pressure range of pi ) 10-50 bar, where a fixed volume of CO2 gas was brought into contact with a column of distilled water. The transfer rate is inferred by following the gas pressure history. The results show that the mass-transfer rate across the interface is much faster than that predicted by Fickian diffusion and increases with increasing initial gas pressure. The theoretical interpretation of the observed effects is based on diffusion and natural convection phenomena. The CO2 concentration at the interface is estimated from the gas pressure using Henry's solubility law, in which the coefficient varies with both pressure and temperature. Good agreement between the experiments and the theoretical results has been obtained. tion of CO2 in the atmosphere, geological storage of CO2 is considered. 2-4 When CO2 is injected into an aquifer, the competition between viscous, capillary, and buoyancy forces determines the flow pattern. Eventually, due to buoyancy forces CO2 will migrate upward and be trapped under the cap rock due to capillary forces. In this case an interface between a CO2- rich phase and brine exists. Subsequently, CO2 starts to dissolve into water by molecular diffusion when it is in contact with the brine. The dissolution of CO2 increases the density of brine. 5 This density increase together with temperature fluctuations in the aquifer (which may be only partially compensated by pressure gradients 6 ) destabilize the CO2-brine interface and accelerate the transfer rate of CO2 into the brine by natural convection. 5-10 The occurrence of natural convection signifi- cantly increases the total storage rate in the aquifer since convection currents bring the fresh brine to the top. Hence, the quantification of CO2 dissolution in water and understanding the transport mechanisms are crucial in predicting the potential and long-term behavior of CO2 in aquifers. Unfortunately there are only a few experimental data in the literature, involving mass transfer between water and CO2 under elevated pressures. Weir et al. 11 were the first to point out the importance of natural convection for sequestration of CO2. Yang and Gu 8 performed experiments in bulk where a column of CO2 at high pressure was in contact with water. The procedure was similar to the established approach in which the changes in gas pressure relate the gas to the transfer rate. 12-15 A modified diffusion equation with an effective diffusivity was used to describe the mass-transfer process of CO2 into the brine. Good agreement between the experiments and the model was observed by choosing effective diffusion coefficients 2 orders of mag- nitude larger than the molecular diffusivity of CO2 into water. However, the authors pointed out that the accurate modeling of the experiments should consider natural convection effects. Farajzadeh et al. 9,10 reported experimental results for the same system, in a slightly different geometry, showing initially enhanced mass transfer followed by a classical diffusion behavior in long times. A physical model based on Fick's second law and Henry's law was used to interpret the experimental data. It was found that the mass-transfer process cannot be modeled with a modified Fick's second law with a single effective diffusion coefficient for the CO2-water system at high pressures. Nevertheless, the initial stages and later stages of the experiments can be modeled individually with the described model. Arendt et al. 16 applied a Schlieren method and a three- mode magnetic suspension balance connected to an optical cell to analyze the mass transfer of the CO2-water system up to 360 bar. Good agreement between their model (linear superposi- tion of free conVection and Marangoni convection) and the experiment was obtained. The addition of surfactant suppressed the Marangoni convection in their experiments, while in the experiments of ref 9, addition of surfactant did not have a significant effect on the transfer rate of CO2. A similar mass- transfer enhancement was observed for the mass transfer between a gaseous CO2-rich phase with two hydrocarbons (n- decane and n-hexadecane) 9,10 due to the fact that CO2 increases the hydrocarbon density. 17 The effect becomes less significant with increasing oil viscosity. This has implications for oil recovery. Indeed in geological storage of CO2 the early time behavior is governed by diffusion before the onset of the natural