Showing papers on "Transport phenomena published in 1998"

Analysis of transport phenomena

Abstract: Preface List of Symbols CHAPTER 1. DIFFUSIVE FLUXES AND MATERIAL PROPERTIES 1.1 INTRODUCTION 1.2 BASIC CONSTITUTIVE EQUATIONS 1.3 DIFFUSIVITIES FOR ENERGY, SPECIES, AND MOMENTUM 1.4 MAGNITUDES OF TRANSPORT COEFFICIENTS 1.5 MOLECULAR INTERPRETATION OF TRANSPORT COEFFICIENTS 1.6 LIMITATIONS ON LENGTH AND TIME SCALES References Problems CHAPTER 2. FUNDAMENTALS OF HEAT AND MASS TRANSFER 2.1 INTRODUCTION 2.2 GENERAL FORMS OF CONSERVATION EQUATIONS 2.3 CONSERVATION OF MASS 2.4 CONSERVATION OF ENERGY: THERMAL EFFECTS 2.5 HEAT TRANSFER AT INTERFACES 2.6 CONSERVATION OF CHEMICAL SPECIES 2.7 MASS TRANSFER AT INTERFACES 2.8 MOLECULAR VIEW OF SPECIES CONSERVATION References Problems CHAPTER 3. FORMULATION AND APPROXIMATION 3.1 INTRODUCTION 3.2 ONE-DIMENSIONAL EXAMPLES 3.3 ORDER-OF-MAGNITUDE ESTIMATION AND SCALING 3.4 " IN MODELING 3.5 TIME SCALES IN MODELING References Problems CHAPTER 4. SOLUTION METHODS BASED ON SCALING CONCEPTS 4.1 INTRODUCTION 4.2 SIMILARITY METHOD 4.3 REGULAR PERTURBATION ANALYSIS 4.4 SINGULAR PERTURBATION ANALYSIS References Problems CHAPTER 5. SOLUTION METHODS FOR LINEAR PROBLEMS 5.1 INTRODUCTION 5.2 PROPERTIES OF LINEAR BOUNDARY-VALUE PROBLEMS 5.3 FINITE FOURIER TRANSFORM METHOD 5.4 BASIS FUNCTIONS 5.5 FOURIER SERIES 5.6 FFT SOLUTIONS FOR RECTANGULAR GEOMETRIES 5.7 FFT SOLUTIONS FOR CYLINDRICAL GEOMETRIES 5.8 FFT SOLUTIONS FOR SPHERICAL GEOMETRIES 5.9 POINT-SOURCE SOLUTIONS 5.10 MORE ON SELF-ADJOINT EIGENVALUE PROBLEMS AND FFT SOLUTIONS References Problems CHAPTER 6. FUNDAMENTALS OF FLUID MECHANICS 6.1 INTRODUCTION 6.2 CONSERVATION OF MOMENTUM 6.3 TOTAL STRESS, PRESSURE, AND VISCOUS STRESS 6.4 FLUID KINEMATICS 6.5 CONSTITUTIVE EQUATIONS FOR VISCOUS STRESS 6.6 FLUID MECHANICS AT INTERFACES 6.7 FORCE CALCULATIONS 6.8 STREAM FUNCTION 6.9 DIMENSIONLESS GROUPS AND FLOW REGIMES References Problems CHAPTER 7. UNIDIRECTIONAL AND NEARLY UNIDIRECTIONAL FLOW 7.1 INTRODUCTION 7.2 STEADY FLOW WITH A PRESSURE GRADIENT 7.3 STEADY FLOW WITH A MOVING SURFACE 7.4 TIME-DEPENDENT FLOW 7.5 LIMITATIONS OF EXACT SOLUTIONS 7.6 NEARLY UNIDIRECTIONAL FLOW References Problems CHAPTER 8. CREEPING FLOW 8.1 INTRODUCTION 8.2 GENERAL FEATURES OF LOW REYNOLDS NUMBER FLOW 8.3 UNIDIRECTIONAL AND NEARLY UNIDIRECTIONAL SOLUTIONS 8.4 STREAM-FUNCTION SOLUTIONS 8.5 POINT-FORCE SOLUTIONS 8.6 PARTICLES AND SUSPENSIONS 8.7 CORRECTIONS TO STOKES' LAW References Problems CHAPTER 9. LAMINAR FLOW AT HIGH REYNOLDS NUMBER 9.1 INTRODUCTION 9.2 GENERAL FEATURES OF HIGH REYNOLDS NUMBER FLOW 9.3 IRROTATIONAL FLOW 9.4 BOUNDARY LAYERS AT SOLID SURFACES 9.5 INTERNAL BOUNDARY LAYERS References Problems CHAPTER 10. FORCED-CONVECTION HEAT AND MASS TRANSFER IN CONFINED LAMINAR FLOWS 10.1 INTRODUCTION 10.2 PECLET NUMBER 10.3 NUSSELT AND SHERWOOD NUMBERS 10.4 ENTRANCE REGION 10.5 FULLY DEVELOPED REGION 10.6 CONSERVATION OF ENERGY: MECHANICAL EFFECTS 10.7 TAYLOR DISPERSION References Problems CHAPTER 11. FORCED-CONVECTION HEAT AND MASS TRANSFER IN UNCONFINED LAMINAR FLOWS 11.1 INTRODUCTION 11.2 HEAT AND MASS TRANSFER IN CREEPING FLOW 11.3 HEAT AND MASS TRANSFER IN LAMINAR BOUNDARY LAYERS 11.4 SCALING LAWS FOR NUSSELT AND SHERWOOD NUMBERS References Problems CHAPTER 12. TRANSPORT IN BUOYANCY-DRIVEN FLOW 12.1 INTRODUCTION 12.2 BUOYANCY AND THE BOUSSINESQ APPROXIMATION 12.3 CONFINED FLOWS 12.4 DIMENSIONAL ANALYSIS AND BOUNDARY-LAYER EQUATIONS 12.5 UNCONFINED FLOWS References Problems CHAPTER 13. TRANSPORT IN TURBULENT FLOW 13.1 INTRODUCTION 13.2 BASIC FEATURES OF TURBULENCE 13.3 TIME-SMOOTHED EQUATIONS 13.4 EDDY DIFFUSIVITY MODELS 13.5 OTHER APPROACHES FOR TURBULENT-FLOW CALCULATIONS References Problems CHAPTER 14. SIMULTANEOUS ENERGY AND MASS TRANSFER AND MULTICOMPONENT SYSTEMS 14.1 INTRODUCTION 14.2 CONSERVATION OF ENERGY: MULTICOMPONENT SYSTEMS 14.3 SIMULTANEOUS HEAT AND MASS TRANSFER 14.4 INTRODUCTION TO COUPLED FLUXES 14.5 STEFAN-MAXWELL EQUATIONS 14.6 GENERALIZED DIFFUSION IN DILUTE MIXTURES 14.7 GENERALIZED STEFAN-MAXWELL EQUATIONS References Problems CHAPTER 15. TRANSPORT IN ELECTROLYTE SOLUTIONS 15.1 INTRODUCTION 15.2 FORMULATION OF MACROSCOPIC PROBLEMS 15.3 MACROSCOPIC EXAMPLES 15.4 EQUILIBRIUM DOUBLE LAYERS 15.5 ELECTROKINETIC PHENOMENA References Problems APPENDIX A. VECTORS AND TENSORS A.1 INTRODUCTION A.2 REPRESENTATION OF VECTORS AND TENSORS A.3 VECTOR AND TENSOR PRODUCTS A.4 VECTOR-DIFFERENTIAL OPERATORS A.5 INTEGRAL TRANSFORMATIONS A.6 POSITION VECTORS A.7 ORTHOGONAL CURVILINEAR COORDINATES A.8 SURFACE GEOMETRY References APPENDIX B. ORDINARY DIFFERENTIAL EQUATIONS AND SPECIAL FUNCTIONS B.1 INTRODUCTION B.2 FIRST-ORDER EQUATIONS B.3 EQUATIONS WITH CONSTANT COEFFICIENTS B.4 BESSEL AND SPHERICAL BESSEL EQUATIONS B.5 OTHER EQUATIONS WITH VARIABLE COEFFICIENTS References Index

Two‐dimensional model for proton exchange membrane fuel cells

Abstract: A 2-D mathematical model for the entire sandwich of a proton-exchange membrane fuel cell including the gas channels was developed The self-consistent model for porous media was used for the equations describing transport phenomena in the membrane, catalyst layers, and gas diffusers, while standard equations of Navier-Stokes, energy transport, continuity, and species concentrations are solved in the gas channels A special handling of the transport equations enabled us to use the same numerical method in the unified domain consisting of the gas channels, gas diffusers, catalyst layers and membrane It also eliminated the need to prescribe arbitrary or approximate boundary conditions at the interfaces between different parts of the fuel cell sandwich By solving transport equations, as well as the equations for electrochemical reactions and current density with the membrane phase potential, polarization curves under various operating conditions were obtained Modeling results compare very well with experimental results from the literature Oxygen and water vapor mole fraction distributions in the coupled cathode gas channel-gas diffuser were studied for various operating current densities Liquid water velocity distributions in the membrane and influences of various parameters on the cell performance were also obtained

Introduction to Catalytic Combustion

Abstract: Thermodynamics, Kinetics and Transport Phenomena. Modelling of Catalytic Combustion Reactors. Homogeneous Gas Phase Reactions. Experimental Studies. Combustion Applications: Examples of Modelling Studies

Basic Transport Phenomena in Biomedical Engineering

Abstract: Introduction Review of Units and Dimensions Dimensional Equation Tips for Solving Engineering Problems Conservation of Mass A Review of Thermodynamic Concepts The First Law of Thermodynamics The Second Law of Thermodynamics Properties The Fundamental Property Relations Single Phase Open Systems Phase Equilibrium Physical Properties of the Body Fluids and the Cell Membrane Body Fluids Fluid Compositions Capillary Plasma Protein Retention Osmotic Pressure Formation of the Interstitial Fluid Net Capillary Filtration Rate Lymphatic System Solute Transport Across the Capillary Endothelium The Cell Membrane Ion Pumps The Physical and Flow Properties of Blood Physical Properties of Blood Cellular Components Rheology Relationship Between Shear Stress and Shear Rate Hagan-Poiseuille Equation Other Useful Flow Relationships Rheology of Blood The Casson Equation Using the Casson Equation The Velocity Profile for Tube Flow of a Casson Fluid Tube Flow of Blood at Low Shear Rates The Effect of The Diameter at High Shear Rates Marginal Zone Theory Using the Marginal Zone Theory Boundary Layer Theory Generalized Mechanical Energy Balance Equation Capillary Rise and Capillary Action Solute Transport in Biological Systems Description of Solute Transport in Biological Systems Capillary Properties Capillary Flowrates Solute Diffusion Solute Transport by Capillary Filtration Solute Diffusion Within Heterogeneous Media Solute Permeability The Irreversible Thermodynamics of Membrane Transport Transport of Solutes Across the Capillary Wall Transport of Solute Between a Capillary and the Surrounding Tissue Space Oxygen Transport in Biological Systems The Diffusion of Oxygen In Multicellular Systems Hemoglobin The Hemoglobin-Oxygen Dissociation Curve Oxygen Levels in Blood The Hill Equation Other Factors That Can Affect the Oxygen Dissociation Curve Tissue Oxygenation Oxygen Transport in Bioartificial Organs and Tissue Engineered Constructs Steady State Oxygen Transport in a Perfusion Bioreactor Oxygen Transport in the Krogh Tissue Cylinder An Approximate Solution for Oxygen Transport in the Krogh Tissue Cylinder Artificial Blood Pharmacokinetic Analysis Terminology Entry Routes for Drugs Modeling Approaches Factors that Affect Drug Distribution Drug Clearance A Model for Intravenous Injection of Drug Accumulation of Drug in the Urine Constant Infusion of Drug First Order Drug Absorption and Elimination Two Compartment Models Extracorporeal Devices Applications Contacting Schemes Membrane Solute Transport Estimating the Mass Transfer Coefficients Estimating the Solute Diffusivity in Blood Hemodialysis Blood Oxygenators Immobilized Enzyme Reactors Affinity Adsorption Tissue Engineering Introduction Cell Transplantation The Extracellular Matrix (ECM) Cellular Interactions Polymeric Support Structures Biocompatibility and the Initial Response to an Implant Tissue Ingrowth in Porous Polymeric Structures Measuring the Blood Flow Within Scaffolds Used for Tissue Engineering Cell Transplantation into Polymeric Support Structures Bioreactor Design for Tissue Engineering Bioartificial Organs Background Some Immunology Immunoisolation Permeability of Immunoisolation Membranes Membrane Sherwood Number Bioartificial Organs The Bioartificial Liver The Bioartificial Kidney Design Considerations for Bioartificial Organs References Index

Mathematical Simulation on Coupled Flow, Heat, and Solute Transport in Slab Continuous Casting Process

Abstract: A three-dimensional comprehensively coupled model has been developed to describe the transport phenomena, including fluid flow, heat transfer, solidification, and solute redistribution in the continuous casting process. The continuous casting process is considered as a solidification process in a multicomponent solid-liquid phase system. The porous media theory is used to model the blockage of fluid flow by columnar dendrites in the mushy zone. The relation between flow pattern and the shape of the solid shell is demonstrated. Double diffusive convection caused by thermal and concentration gradients is considered. The change in the liquidus temperature with liquid concentration is also considered. The formation mechanism of macrosegregation is investigated. Calculated solid shell thickness and temperature distribution in liquid core are compared with the measured quantities for validating the model.

Study of Transport Phenomena in Chromatographic Columns by Pulsed Field Gradient NMR

Abstract: Pulsed field gradient NMR has been applied to study mass transfer, flow, and dispersion in packed chromatographic columns. A single measurement allows the determination of the full displacement probability distribution of all fluid particles located in the measurement volume. Depending on the orientation of the pulsed magnetic field gradient with respect to the net flow direction, the so-called averaged propagator is obtained independently and quantitatively for either the axial or the transverse fluid particle displacements, over an experimentally adjustable observation time. Thus, this technique can act on a dynamic time scale ranging from a few to several hundred milliseconds. This enabled us to detect the stagnant mobile phase in packed chromatographic columns and to follow the mass transfer between the stagnant solvent and the stream of mobile phase percolating through the column bed. With field gradients in the direction of net flow velocity, mean fluid particle displacements ranging between 0.07 an...

Modeling of 2D Density-Dependent Flow and Transport in the Subsurface

Abstract: A 2-dimensional finite-element model for density-dependent flow and transport through saturated-unsaturated porous media has been developed. The combined flow and transport model can handle a wide range of real-world problems, including the simulations of flow alone, contaminant transport alone, and combined flow and transport. The conventional finite-element methods and a hybrid Lagrangian-Eulerian finite-element method were incorporated in the transport module. Saltwater intrusion problems and instability caused by denser water on the top were investigated in this paper. Because the fundamental mechanism causing saltwater intrusion most likely is caused by density-induced convection and dispersion, the developed model was used to assess the interplay between density-driven flow and the subsurface media through which the saltwater intrusion occurs. The mathematical formulation of the model is comprised of fluid flow and solute transport equations, coupled by fluid density. In the specific case of saltwater intrusion and unstable brine transport problems, this set of governing equations is nonlinear and requires iterative methods to solve them simultaneously. Three case studies, which include a wide spectrum of physical conditions, show the verification and effectiveness of the model by comparing previously published solutions from other researchers with the simulation results of the present model. Two demonstrated problems examine the model capabilities to handle saltwater intrusion problems through unsaturated-saturated porous media and density-dependent flow and transport under unstable conditions.

Full nonlinear closure for a hydrodynamic model of transport in silicon

Abstract: The increasing miniaturization of modern electronic devices requires an accurate modelization of transport in semiconductors. This is of great importance for describing phenomena such those due to hot electrons, i.e., the conditions very far from thermodynamic equilibrium caused by strong electric fields and field gradients. The most general approach to the simulation of charge transport in semiconductors employes the semiclassical Boltzmann transport equation ~BTE! coupled with Poisson equation. A numerical solution of such system of equations with traditional techniques is extremely complex, and then approximate methods based on kinetic and fluid dynamic ~FD! models are often preferred. The most accurate kinetic description is given by Monte Carlo ~MC! methods, which can take into account explicitly both the band structure and the various scattering phenomena. 1,2 This method permits us to compute directly all the quantities relative to transport ~such as the distribution function, density of carriers, velocity, mean energy, and so on! but at a cost of long computation times and stochastic noise in data. The results obtained from MC simulations permit us also to calculate transport coefficients , which are used as an input to more simplified FD models. Other kinetic approaches are based on the choice of particular forms of the nonequilibrium distribution function of carriers. Common examples are the simple shifted Maxwellian 3 or an expansion of the distribution in spherical harmonics. 4 The cylindrical symmetry constraint in momentum space and the reduced number of terms of the expansion that can be practically used do not permit, however, to describe transport properties of carriers in conditions very far from equilibrium. 5

Collective transport in locally asymmetric periodic structures.

Abstract: In this paper we give an overview of the cooperative effects in fluctuation driven transport arising from the interaction of a large number of particles. (i) First, we study a model with finite-sized, overdamped Brownian particles interacting via hard-core repulsion. Computer simulations and theoretical calculations reveal a number of novel cooperative transport phenomena in this system, including the reversal of direction of the net current as the particle density is increased, and a very strong and complex dependence of the average velocity on both the size and the average distance of the particles. (ii) Next, we consider the cooperation of a collection of motors rigidly attached to a backbone. This system possesses dynamical phase transition allowing spontaneous directed motion even if the system is spatially symmetric. (iii) Finally, we report on an experimental investigation exploring the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits complex collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. (c) 1998 American Institute of Physics.

Combustion and heat transfer interaction in a pore-scale refractory tube burner

Abstract: An axisymmetric two-dimensional model of chemical reaction and heat transfer that accounts for the transport of mass, momentum, heat, and species in radial and axial directions has been developed to provide a fundamental understanding of the transport phenomena relevant to porous radiant burners made from ported ceramics. The passage geometry of practical porous media is modeled as a cylindrical tube in which combustion stakes place. This enables treatment of the chemical reactions and transport processes in the gas phase, of heat conduction in the tube wall, and of radiation exchange on the inside surface of the tube to account for the conjugate heat transfer effects. The predictions are compared with available experimental data for the purpose of model validation. Parametric calculations are performed using the model to improve understanding of the phenomena.

Thermo-Flow Structure and Epitaxial Uniformity in Large-Scale Metalorganic Chemical Vapor Deposition Reactors with Rotating Susceptor and Inlet Flow Control

Abstract: The transport phenomena in large-scale metalorganic chemical vapor deposition (MOCVD) reactors with a rotating susceptor are investigated by numerical simulation of thin-film epitaxial growth of gallium arsenide. We are mainly concerned with the thermo-flow structure, its influence on epitaxial growth rate, and the means of improving epilayer flatness. The effects of susceptor rotation and thermo-flow conditions on gas flow, temperature and concentration fields are studied. The present results show the flow structure and transport characteristics in various flow regimes. A parameter map and the associated correlations of boundary curves of the flow-mode transition are proposed. It is demonstrated that the epilayer flatness can be tuned either by properly controlling the vortex strength in a rotation-dominated flow regime and/or by employing an inlet flow control technique proposed in the present work.

Similarity solutions of mixed convection heat and mass transfer in combined stagnation and rotation-induced flows over a rotating disk

Abstract: The objective of the present study is to develop a novel similarity model for analysis of mixed convection heat and mas transfer in combined stagnation and rotation-induced flows over a rotating disk. Thermal and concentration (solutal) buoyancy effects stemmed from temperature and concentration gradients in rotational as well as gravitational forces fields are all taken into account. The influences of the forced flow, disk rotation, thermal buoyancy, buoyancy ratio and the fluid properties, i.e. Prandtl and Schmidt numbers, on the flow, temperature and concentration fields and the associated friction factors, heat and mass transfer rates are investigated. The present results reveal the effects of various buoyancy modes with combined forces on the transport phenomena in rotating-disk flows, and the analysis is also useful in understanding the mechanisms of mixed convection in the class of rotating fluids.

Transport phenomena through porous screens and openings: from theory to greenhouse practice.

Abstract: The study of transport phenomena in multi-zone enclosures with permeable boundaries is fundamental for indoor climate control management. In this study, aspects concerning the air exchange through porous screens and openings, and heat transfer between the enclosure surface and inside air, were analysed. Basic physical laws were the starting point during the construction of the models. To illustrate the practical side of the research performed, the formulation developed was applied to the study of convective heat exchange within screened greenhouses, as well as to the study of airflow through greenhouse screens and window apertures. Concerning the airflow through porous screens and window openings, the results obtained thoroughly demonstrate the importance of inertia and viscous effects, as well as window openings' geometry effects, on fluid flow. The airflow characteristics of porous screens and the structure of fluctuation of wind velocity, were quantified. Regarding the study of free convection heat transfer within a screened greenhouse, the convective heat transfer coefficients between the air and the downward and the upward surfaces of the screen were obtained, among other results. The results obtained from this study can greatly contribute, in general, to a better climate control management of multi-zone enclosures, and specifically, to an improved application of porous screens and window apertures.

Interlayer Diffusive Transfer and Transport of Contaminants in Stratified Formation. II: Analytical Solutions

Abstract: Transverse diffusive transfer of solute mass between regions of mobile and immobile water is a key mechanism causing tailing and reduced peak concentrations. In Part 1, we developed a two-dimensional first-order rate model that describes reactive solute transport averaged across the thickness of a two-layer system. The model describes the capacitance effect of low-permeability layers to store and release solute by diffusive-type mass transfer, under quasi-steady conditions. In this paper, we develop two-dimensional analytical solutions for the first-order rate model in an infinite porous medium, using the methods of Fourier and Laplace transforms and superposition. The solutions consider a rectangular source with (1) an instantaneous release of a contaminant mass and (2) an exponentially decaying source applied at a fixed rate. Simulations show that increased pore-water velocity produces a more dispersed mobile solute and pronounced tailing. Comparison of the theory with the Borden aquifer data indicates ...

Transient combustion response of homogeneous solid propellant to acoustic oscillations in a rocket motor

Abstract: Interactions between acoustic waves and the transient combustion response of a double-base homogeneous propellant in a rocket motor have been analyzed numerically. The analysis extends the previous work on gas-phase flame dynamics to include the coupling with condensed-phase processes. Consequently, a more complete description of propellant combustion response to imposed acoustic oscillations can be obtained. Emphasis is placed on the near-surface flame-zone physiochemistry and its coupling with unsteady propellant burning in an oscillatory environment. The formulation treats complete conservation equations and the finite-rate chemical kinetics in both the gas-phase and subsurface regions. The instantaneous propellant burning rate is predicted as part of the solution. Various distinct features of unsteady heat release arising from propellant combustion response in a motor with forced oscillations are studied systematically. As in the pure gas-phase dynamics of the previous case, the dynamic behavior of the luminous flame plays a decisive role in determining the motor stability characteristics. However, the propellant combustion response may qualitatively modify the temporal evolution of heat-release distribution in the luminous flame and as a result exerts a significant influence on the global stability behavior. The primary flame structure adjacent to the propellant surface is usually little affected by flow oscillation. This may be attributed to the large thermal inertial of the condensed phase, which tends to restrain the temperature variation in the near-surface zone in the present study of laminar flows. The situation with a turbulent flow may be drastically different, as turbulence may penetrate directly into the, primary flame and substantially change the local flame dynamics and transport phenomena.

Recent advances in fluid mechanics

Abstract: Section I - Flow Problems 1. Magnetohydrodynamics 2. Solution to a Class of Integral Equation with an Application to Vortex Sheets in Plane Strain and the Finite Structure of Turbulence 3. Particle Aggregation and Unsteady Pipe Flow Characteristics of Magnetic Fluids Section II - Convection and Transport Phenomena 1. Interfacial Tension Between Miscible Liquids 2. Heat and Mass Transfer in Vertical Annuli 3. Asymptotic Methods in Magnetoconvection 4. The Earth's Dynamo Section III - Dynamics of Atmosphere 1. Turbulent Diffusion in the Natural Environment 2. Dynamic Modelling of the Global Change Section IV - Wave Propagation 1. Propagation of Alfen Waves In an Isothermal Compressible Atmosphere When the Displacement Current Is Not Neglected 2. Simple Waves Are Not so Simple!

Analogy between heat and momentum transfer

Abstract: Analogy between heat and momentum transfer—the concepts as developed by O. Reynolds and L. Prandtl—are based on certain hypotheses about the mechanism of turbulent transport phenomena. Therefore, heat transfer equations based on these concepts are semi-empirical. In addition, a new heat transfer equation is presented which applies to non-developed turbulent flow e.g. in plate heat exchangers. This equation can be derived from the classical differential equations for viscous flow and heat conduction which are not bound to any modeling concept of turbulent transport phenomena whatsoever, and may be taken as rigorous.

Transient transport phenomena induced by cold pulses in W7-AS

Abstract: Cold-pulse experiments were carried out in the W7-AS stellarator for the first time. Carbon was injected by a laser blow-off system into the plasma edge. The electron density increase due to the injected carbon is found to be responsible for the edge electron temperature drop. In all cases, the propagation of the edge temperature perturbation to the plasma centre could be modelled with a local parameter-dependent electron heat diffusivity. Unlike in tokamaks, non-local transport effects were not observed in these experiments.