Showing papers on "Natural convection published in 2004"

Fundamentals of the Finite Element Method for Heat and Fluid Flow

Abstract: Preface. 1 Introduction. 1.1 Importance of Heat Transfer. 1.2 Heat Transfer Modes. 1.3 The Laws of Heat Transfer. 1.4 Formulation of Heat Transfer Problems. 1.4.1 Heat transfer from a plate exposed to solar heat flux. 1.4.2 Incandescent lamp. 1.4.3 Systems with a relative motion and internal heat generation. 1.5 Heat Conduction Equation. 1.6 Boundary and Initial Conditions. 1.7 Solution Methodology. 1.8 Summary. 1.9 Exercise. Bibliography. 2 Some Basic Discrete Systems. 2.1 Introduction. 2.2 Steady State Problems. 2.2.1 Heat flow in a composite slab. 2.2.2 Fluid flow network. 2.2.3 Heat transfer in heat sinks (combined conduction-convection). 2.2.4 Analysis of a heat exchanger. 2.3 Transient Heat Transfer Problem (Propagation Problem). 2.4 Summary. 2.5 Exercise. Bibliography. 3 The Finite Elemen t Method. 3.1 Introduction. 3.2 Elements and Shape Functions. 3.2.1 One-dimensional linear element. 3.2.2 One-dimensional quadratic element. 3.2.3 Two-dimensional linear triangular elements. 3.2.4 Area coordinates. 3.2.5 Quadratic triangular elements. 3.2.6 Two-dimensional quadrilateral elements. 3.2.7 Isoparametric elements. 3.2.8 Three-dimensional elements. 3.3 Formulation (Element Characteristics). 3.3.1 Ritz method (Heat balance integral method-Goodman's method). 3.3.2 Rayleigh-Ritz method (Variational method). 3.3.3 The method of weighted residuals. 3.3.4 Galerkin finite element method. 3.4 Formulation for the Heat Conduction Equation. 3.4.1 Variational approach. 3.4.2 The Galerkin method. 3.5 Requirements for Interpolation Functions. 3.6 Summary. 3.7 Exercise. Bibliography. 4 Steady State Heat Conduction in One Dimension. 4.1 Introduction. 4.2 Plane Walls. 4.2.1 Homogeneous wall. 4.2.2 Composite wall. 4.2.3 Finite element discretization. 4.2.4 Wall with varying cross-sectional area. 4.2.5 Plane wall with a heat source: solution by linear elements. 4.2.6 Plane wall with a heat source: solution by quadratic elements. 4.2.7 Plane wall with a heat source: solution by modified quadratic equations (static condensation). 4.3 Radial Heat Flow in a Cylinder. 4.3.1 Cylinder with heat source. 4.4 Conduction-Convection Systems. 4.5 Summary. 4.6 Exercise. Bibliography. 5 Steady State Heat Conduction in Multi-dimensions. 5.1 Introduction. 5.2 Two-dimensional Plane Problems. 5.2.1 Triangular elements. 5.3 Rectangular Elements. 5.4 Plate with Variable Thickness. 5.5 Three-dimensional Problems. 5.6 Axisymmetric Problems. 5.6.1 Galerkin's method for linear triangular axisymmetric elements. 5.7 Summary. 5.8 Exercise. Bibliography. 6 Transient Heat Conduction Analysis. 6.1 Introduction. 6.2 Lumped Heat Capacity System. 6.3 Numerical Solution. 6.3.1 Transient governing equations and boundary and initial conditions. 6.3.2 The Galerkin method. 6.4 One-dimensional Transient State Problem. 6.4.1 Time discretization using the Finite Difference Method (FDM). 6.4.2 Time discretization using the Finite Element Method (FEM). 6.5 Stability. 6.6 Multi-dimensional Transient Heat Conduction. 6.7 Phase Change Problems-Solidification and Melting. 6.7.1 The governing equations. 6.7.2 Enthalpy formulation. 6.8 Inverse Heat Conduction Problems. 6.8.1 One-dimensional heat conduction. 6.9 Summary. 6.10 Exercise. Bibliography. 7 Convection Heat Transfer 173 7.1 Introduction. 7.1.1 Types of fluid-motion-assisted heat transport. 7.2 Navier-Stokes Equations. 7.2.1 Conservation of mass or continuity equation. 7.2.2 Conservation of momentum. 7.2.3 Energy equation. 7.3 Non-dimensional Form of the Governing Equations. 7.3.1 Forced convection. 7.3.2 Natural convection (Buoyancy-driven convection). 7.3.3 Mixed convection. 7.4 The Transient Convection-diffusion Problem. 7.4.1 Finite element solution to convection-diffusion equation. 7.4.2 Extension to multi-dimensions. 7.5 Stability Conditions. 7.6 Characteristic-based Split (CBS) Scheme. 7.6.1 Spatial discretization. 7.6.2 Time-step calculation. 7.6.3 Boundary and initial conditions. 7.6.4 Steady and transient solution methods. 7.7 Artificial Compressibility Scheme. 7.8 Nusselt Number, Drag and Stream Function. 7.8.1 Nusselt number. 7.8.2 Drag calculation. 7.8.3 Stream function. 7.9 Mesh Convergence. 7.10 Laminar Isothermal Flow. 7.10.1 Geometry, boundary and initial conditions. 7.10.2 Solution. 7.11 Laminar Non-isothermal Flow. 7.11.1 Forced convection heat transfer. 7.11.2 Buoyancy-driven convection heat transfer. 7.11.3 Mixed convection heat transfer. 7.12 Introduction to Turbulent Flow. 7.12.1 Solution procedure and result. 7.13 Extension to Axisymmetric Problems. 7.14 Summary. 7.15 Exercise. Bibliography. 8 Convection in Porous Media. 8.1 Introduction. 8.2 Generalized Porous Medium Flow Approach. 8.2.1 Non-dimensional scales. 8.2.2 Limiting cases. 8.3 Discretization Procedure. 8.3.1 Temporal discretization. 8.3.2 Spatial discretization. 8.3.3 Semi- and quasi-implicit forms. 8.4 Non-isothermal Flows. 8.5 Forced Convection. 8.6 Natural Convection. 8.6.1 Constant porosity medium. 8.7 Summary. 8.8 Exercise. Bibliography. 9 Some Examples of Fluid Flow and Heat Transfer Problems. 9.1 Introduction. 9.2 Isothermal Flow Problems. 9.2.1 Steady state problems. 9.2.2 Transient flow. 9.3 Non-isothermal Benchmark Flow Problem. 9.3.1 Backward-facing step. 9.4 Thermal Conduction in an Electronic Package. 9.5 Forced Convection Heat Transfer From Heat Sources. 9.6 Summary. 9.7 Exercise. Bibliography. 10 Implementation of Computer Code. 10.1 Introduction. 10.2 Preprocessing. 10.2.1 Mesh generation. 10.2.2 Linear triangular element data. 10.2.3 Element size calculation. 10.2.4 Shape functions and their derivatives. 10.2.5 Boundary normal calculation. 10.2.6 Mass matrix and mass lumping. 10.2.7 Implicit pressure or heat conduction matrix. 10.3 Main Unit. 10.3.1 Time-step calculation. 10.3.2 Element loop and assembly. 10.3.3 Updating solution. 10.3.4 Boundary conditions. 10.3.5 Monitoring steady state. 10.4 Postprocessing. 10.4.1 Interpolation of data. 10.5 Summary. Bibliography. A Green's Lemma. B Integration Formulae. B.1 Linear Triangles. B.2 Linear Tetrahedron. C Finite Element Assembly Procedure. D Simplified Form of the Navier-Stokes Equations. Index.

Porous and Complex Flow Structures in Modern Technologies

Abstract: Contents Preface 1 Porous Media Fundamentals 1.1 Structure 1.1.1 Microporous Media 1.1.2 Mesoporous Media 1.1.3 Macroporous Media 1.2 Mass Conservation 1.3 Darcy Flow and More Advanced Models 1.4 Energy Conservation 1.5 Heat and Mass Transfer 1.5.1 Fluid Flow 1.5.2 Heat Flow 2 Flows in Porous Media 2.1 Use Simple Methods First 2.2 Scale Analysis of Forced Convection Boundary Layers 2.3 Sphere and Cylinder with Forced Convection 2.4 Channels with Porous Media and Forced Convection 2.5 Scale Analysis of Natural Convection Boundary Layers 2.6 Thermal Stratification and Vertical Partitions 2.7 Horizontal Walls with Natural Convection 2.8 Sphere and Horizontal Cylinder with Natural Convection 2.9 Enclosures Heated from the Side 2.10 Enclosures Heated from Below 2.11 The Method of Intersecting the Asymptotes 2.11.1 The Many Counterflows Regime 2.11.2 The Few Plumes Regime 2.11.3 The Intersection of Asymptotes 3 Energy Engineering 3.1 Thermodynamics Fundamentals: Entropy Generation or Exergy Destruction 3.2 Exergy Analysis 3.3 Thermal Energy Storage 3.4 Sensible Heat Storage 3.5 Aquifer Thermal Energy Storage 3.6 Latent Heat Storage 3.7 Cold Thermal Energy Storage 3.8 Porous Medium Model of a Storage System with Phase-Change Material 3.9 Fuel Cell Principles and Operation 3.10 Fuel Cell Structure and Performance 3.11 The Concept of Exergy-Cost-Energy-Mass (EXCEM) Analysis 3.12 Exergy, Environment, and Sustainable Development 4 Environmental and Civil Engineering 4.1 The Energy-Environment Interface 4.2 Wakes: Concentrated Heat Sources in Forced Convection 4.3 Plumes: Concentrated Heat Sources in Natural Convection 4.4 Penetrative Convection 4.5 Aerosol Transport and Collection in Filters 4.6 Filter Efficiency and Filtration Theories 4.7 Pressure Drop, Permeability,and Filter Performance 4.8 Ionic Transport 4.9 Reactive Porous Media 4.10 Electrodiffusion 4.11 Tree-Shaped Flow Networks 4.12 Optimal Size of Flow Element 4.13 Hot Water Distribution Networks 4.14 Minimal Resistance Versus Minimal Flow Length 5 Compact Heat Transfer Flow Structures 5.1 Heat Exchangers as Porous Media 5.2 Optimal Spacings in Natural Convection 5.3 Optimal Spacings in Forced Convection 5.4 Pulsating Flow 5.5 Optimal Packing of Fibrous Insulation 5.6 Optimal Maldistribution: Tree-Shaped Flows 5.7 Dendritic Heat Exchangers 5.7.1 Elemental Volume 5.7.2 First Construct 5.7.3 Second Construct 5.8 Constructal Multiscale Structure for Maximal Heat Transfer Density 5.8.1 Heat Transfer 5.8.2 Fluid Friction 5.8.3 Heat Transfer Rate Density: The Smallest Scale 5.9 Concluding Remarks 6 Living Structures 6.1 Respiratory System 6.1.1 Airflow Within the Bronchial Tree 6.1.2 Alveolar Gas Diffusion 6.1.3 Particle Deposition 6.2 Blood and the Circulatory System 6.3 Biomembranes: Structure and Transport Mechanisms 6.3.1 Cell Membrane 6.3.2 Capillary Wall 6.4 Transport of Neutral Solutes Across Membranes 6.5 Transport of Charged Solutes Across Membranes 6.5.1 Membrane Potential 6.5.2 Electrical Equivalent Circuit 6.6 The Kidney and the Regulation of Blood Composition 6.6.1 Kidney Failure and Dialysis 6.6.2 Pumping Blood Through Semipermeable Membranes 7 Drying of Porous Materials 7.1 Introduction 7.2 Drying Equipment 7.3 Drying Periods 7.4 Basic Heat and Moisture Transfer Analysis 7.5 Wet Material 7.6 Types of Moisture Diffusion 7.7 Shrinkage 7.8 Modeling of Packed-Bed Drying 7.9 Diffusion in Porous Media with Low Moisture Content 7.10 Modeling of Heterogeneous Diffusion in Wet Solids 7.10.1 Mass Transfer 7.10.2 Heat Transfer 7.10.3 Boundary Cond

Fluctuations in turbulent Rayleigh-Bénard convection: The role of plumes

Abstract: Our unifying theory of turbulent thermal convection [Grossmann and Lohse, J. Fluid. Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001); Phys. Rev. E 66, 016305 (2002)] is revisited, considering the role of thermal plumes for the thermal dissipation rate and addressing the local distribution of the thermal dissipation rate, which had numerically been calculated by Verzicco and Camussi [J. Fluid Mech. 477, 19 (2003); Eur. Phys. J. B 35, 133 (2003)]. Predictions for the local heat flux and for the temperature and velocity fluctuations as functions of the Rayleigh and Prandtl numbers are offered. We conclude with a list of suggestions for measurements that seem suitable to verify or falsify our present understanding of heat transport and fluctuations in turbulent thermal convection.

From laminar plumes to organized flows: the onset of large-scale circulation in turbulent thermal convection

Abstract: We report an experimental study on the onset of the large-scale coherent mean flow in Rayleigh–Benard turbulent convection. Shadowgraph and particle image velocimetry techniques are used to visualize the motion of thermal plumes and measure the velocity of the plumes and of the ‘background’ flow field, as the fluid motion evolves from quiescent to steady state. The experiment reveals the dynamical origin of the initial horizontal motion required by the large-scale flow: the fluid entrainment caused by the plume's vertical motion generates vortices surrounding the plume itself. These vortices in turn generate the initial horizontal motion of the flow field. Two types of interactions have been identified: (i) direct plume–vortex interaction; and (ii) plume–plume interaction via vortices. These interactions and the interaction and merging of the vortices from neighbouring plumes lead to groupings and/or merging of plumes, which in turn generate vortices of even larger scale. As a result of these interactions, the convective flow evolves into a coherent rotatory motion consisting of mainly the plumes themselves and spanning the whole convection box. This study clearly demonstrates that it is the thermal plumes that initiate the horizontal large-scale flow across the top and bottom conducting plates.

The temperature dependence of effective thermal conductivity of open-celled steel alloy foams

Abstract: The effective thermal conductivity of steel alloy FeCrAlY (Fe—20 wt.% Cr—5 wt.% Al—2 wt.% Y—20 wt.%) foams with a range of pore sizes and porosities was measured between 300 and 800 K, under both vacuum and atmospheric conditions. The results show that the effective thermal conductivity increases rapidly as temperature is increased, particularly in the higher temperature range (500–800 K) where the transport of heat is dominated by thermal radiation. The effective conductivity at temperature 800 K can be three times higher than that at room temperature (300 K). Results obtained under vacuum conditions reveal that the effective conductivity increases with increasing pore size or decreasing porosity. The contribution of natural convection to heat conduction was found to be significant, with the effective thermal conductivity at ambient pressure twice the value of vacuum condition. The results also show that natural convection in metal foams is strongly dependent upon porosity.

Experimental Investigation of Natural Convection Heat Loss From a Model Solar Concentrator Cavity Receiver

Abstract: Natural convection heat loss inevitably occurs in cavity-type receivers in high concentrating solar dishes, downward focusing systems and solar towers. In most applications, it can contribute a significant fraction of total energy loss, and hence it is an important determining factor in system performance. To investigate natural convection losses from cavity type receivers, an electrically heated model receiver, was tested at inclinations varying from -90 deg (cavity facing up) to 90 deg (cavity facing straight down), with test temperatures ranging from 450 to 650 deg C. Ratios of the aperture diameter to cavity diameter of 0.5, 0.6, 0.75, 0.85 and 1.0, were used. In addition to measurements of overall heat loss, the Synthetic Schlieren technique was used to visualize the flow pattern out of the cavity. Numerical modeling of the convection losses from the cavity was carried out for positive angles with the commercial computational fluid dynamics software package, Fluent 6.0. Good agreement was found between the numerical flow patterns at the aperture region with the schlieren images and between measured and predicted values for heat loss. Of the previously published work that has been reviewed, a model proposed by Clausing, A. M., 1981, An Analysis of Convective Losses from Cavity Solar Central Receivers, Sol. Energy 27 (4) pp. 295-300 shows the closest prediction to both numerical and experimental results for downward facing cavities despite its original use for bigger-scale central receivers.

Thermal Transport in High Porosity Cellular Metal Foams

Abstract: The heat dissipation capability of highly porous cellular metal foams with open cells subject to forced air convection is studied using a combined experimental and analytical approach. The cellular morphologies of six FeCrAlY (an iron-based alloy) foams and six copper alloy foams with a range of pore sizes and porosities are quantified with the scanning electronic microscope and image analysis. Experimental measurements on pressure drop and heat transfer for copper foams are carried out. A numerical model for forced convection across opencelled metal foams is subsequently developed, and the predictions are compared with those measured. Reasonably good agreement with test data is obtained, given the complexity of the cellular foam morphology and the associated momentum/energy transport. The results show that cell size has a more significant effect on the overall heat transfer than porosity. An optimal porosity is obtained based on the balance between pressure drop and overall heat transfer, which decreases as the Reynolds number is increased. Nomenclature ˜ a = specific surface area per unit volume C f = heat capacity of fluid C I = inertial coefficient d f = diameter of cell edge ligament d p = pore size FI = inertial variable f = friction factor H = channel height h sf = interfacial heat transfer coefficient

Estimation of Surface Turbulent Fluxes through Assimilation of Radiometric Surface Temperature Sequences

Abstract: A model of land surface energy balance is used as a constraint on the estimation of factors characterizing land surface influences on evaporation and turbulent heat transfer from sequences of radiometric surface temperature measurements. The surface moisture control on evaporation is captured by the dimensionless evaporative fraction (ratio of latent heat flux to the sum of the turbulent fluxes), which is nearly constant for near-peak radiation hours on days without precipitation. The dimensionless parameter capturing the turbulent transfer characteristics (bulk heat transfer coefficient) includes the impacts of both forced and free convection. The mean diurnal pattern and seasonal trends are interpreted in the context of expected surface air layer static stability variations. The approach is tested over the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) site (Kansas) where verification data on surface fluxes are available. It is shown that sequent...

Mixed convection and density-dependent seawater circulation in coastal aquifers

Abstract: [1] Density-dependent circulation of seawater in coastal aquifers results in submarine groundwater discharge (SGD) across the seabed that is a mixture of terrestrial groundwater and former marine water In this study, the controls of the relative amount of seawater to freshwater in SGD were investigated numerically using the FEFLOW and SUTRA codes It was found that the key controls could be expressed in the form of a single nondimensional recirculation number that incorporates the combined effects of free convection, forced convection, and hydrodynamic dispersion on convective overturn within the coastal salt wedge Anisotropy effects were incorporated into the recirculation number with limited success based on the principle of equivalent isotropic hydraulic conductivity The type of boundary condition employed along the seabed was shown to be important Convective overturn was substantially increased if backward dispersion of salt into the aquifer from along the outflowing portion of the seabed boundary was prevented Overall, the results demonstrated a strong dependence of convective overturn on the aquifer dispersivities, suggesting that results from numerical simulations are problematic to apply to real aquifer systems that typically exhibit uncertain, scale-dependent dispersion properties

Heat and mass transfer in MHD flow by natural convection from a permeable, inclined surface with variable wall temperature and concentration

Abstract: An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a permeable, inclined surface with variable wall temperature and concentration, taking into consideration the effects of ohmic heating and viscous dissipation. Power-law temperature and concentration variations are assumed at the inclined surface. The resulting governing equations are transformed using suitable transformations and then solved numerically by an implicit finite-difference method. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Eckert number, the buoyancy ratio between species and thermal diffusion, Prandtl number, Schmidt number, wall temperature and concentration exponent, the inclination angle from the vertical direction, and the injection parameter. A parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions as well as the local friction coefficient, local Nusselt number, and the local Sherwood number.

Experimental study of a pulsating heat pipe using fc-72, ethanol, and water as working fluids

Abstract: Experimental studies were performed on a pulsating heat pipe (PHP), consisting of a heating section, an adiabatic section, and a condensation section incorporating a heat sink. The capillary tube used in this study has an inside diameter of 1.18 mm and a wall thickness of 0.41 mm. The experiments were conducted under the condition of pure natural convection, for heating powers from 5 to 60 W, fill ratios from 60% to 90%. Three working fluids—FC-72, ethanol, and deionized water—were used. The thermal oscillation of the thin wall surface was recorded by a high-speed data acquisition system. Such thermal oscillation waves are random for some run cases due to the randomly distributed vapor plug and liquid slugs inside the PHP. The thermal oscillation amplitude is much smaller for FC-72, due to its lower surface tension, than for ethanol and water, while the oscillation cycle period for FC-72 is shorter than for the other two fluids, indicating the faster oscillation movement in the channels, possibly due to t...