Showing papers on "Transport phenomena published in 1990"
01 Jan 1990
TL;DR: In this article, the authors define a porous medium and classify it based on the following properties: 1.1 The need for a continuum approach. 2.2 The general boundary condition. 3.4 The relationship between volume and areal averages.
Abstract: A General Theory.- 1 The Porous Medium.- 1.1 Definition and Classification of Porous Media.- 1.1.1 Definition of a porous medium.- 1.1.2 Classification of porous media.- 1.1.3 Some geometrical characteristics of porous media.- 1.1.4 Homogeneity and isotropy of a porous medium.- 1.2 The Continuum Model of a Porous Medium.- 1.2.1 The need for a continuum approach.- 1.2.2 Representative Elementary Volume (REV).- 1.2.3 Selection of REV.- 1.2.4 Representative Elementary Area (REA).- 1.3 Macroscopic Values.- 1.3.1 Volume and mass averages.- 1.3.2 Areal averages.- 1.3.3 Relationship between volume and areal averages.- 1.4 Higher-Order Averaging.- 1.4.1 Smoothing out macroscopic heterogeneity.- 1.4.2 The hydraulic approach.- 1.4.3 Compartmental models.- 1.5 Multicontinuum Models.- 1.5.1 Fractured porous media.- 1.5.2 Multilayer systems.- 2 Macroscopic Description of Transport Phenomena in Porous Media.- 2.1 Elements of Kinematics of Continua.- 2.1.1 Points and particles.- 2.1.2 Coordinates.- 2.1.3 Displacement and strain.- 2.1.4 Processes.- 2.1.5 Material derivative.- 2.1.6 Velocities.- 2.1.7 Flux and discharge.- 2.1.8 Gauss' theorem.- 2.1.9 Reynolds' transport theorem.- 2.1.10 Green's vector theorem.- 2.1.11 Pathlines, transport lines and transport functions.- 2.1.12 Velocity potential and complex potential.- 2.1.13 Movement of a front.- 2.2 Microscopic Balance and Constitutive Equations.- 2.2.1 Derivation of balance equations.- 2.2.2 Particular cases of balance equations.- 2.2.3 Constitutive equations.- 2.2.4 Coupled transport phenomena.- 2.2.5 Phase equilibrium.- 2.3 Averaging Rules.- 2.3.1 Average of a sum.- 2.3.2 Average of a product.- 2.3.3 Average of a time derivative.- 2.3.4 Average of a spatial derivative.- 2.3.5 Average of a spatial derivative of a scalar satisfying ?2G = 0.- 2.3.6 The coefficient T?*.- 2.3.7 Average of a material derivative.- 2.4 Macroscopic Balance Equations.- 2.4.1 General balance equation.- 2.4.2 Mass balance of a phase.- 2.4.3 Volume balance of a phase.- 2.4.4 Mass balance equation for a component of a phase.- 2.4.5 Balance equation for the linear momentum of a phase.- 2.4.6 Heat balance for a phase and for a saturated porous medium.- 2.4.7 Mass balance in a fractured porous medium.- 2.4.8 Megascopic balance equation.- 2.5 Stress and Strain in a Porous Medium.- 2.5.1 Total stress.- 2.5.2 Effective stress.- 2.5.3 Forces acting on the solid matrix.- 2.6 Macroscopic Fluxes.- 2.6.1 Advective flux of a single Newtonian fluid.- 2.6.2 Advective fluxes in a multiphase system.- 2.6.3 Diffusive flux.- 2.6.4 Dispersive flux.- 2.6.5 Transport coefficients.- 2.6.6 Coupled fluxes.- 2.6.7 Macrodispersive flux.- 2.7 Macroscopic Boundary Conditions.- 2.7.1 Macroscopic boundary.- 2.7.2 The general boundary condition.- 2.7.3 Boundary conditions between two porous media in single phase flow.- 2.7.4 Boundary conditions between two porous media in multiphase flow.- 2.7.5 Boundary between two fluids.- 2.7.6 Boundary with a 'well mixed's vector theorem.- 2.1.11 Pathlines, transport lines and transport functions.- 2.1.12 Velocity potential and complex potential.- 2.1.13 Movement of a front.- 2.2 Microscopic Balance and Constitutive Equations.- 2.2.1 Derivation of balance equations.- 2.2.2 Particular cases of balance equations.- 2.2.3 Constitutive equations.- 2.2.4 Coupled transport phenomena.- 2.2.5 Phase equilibrium.- 2.3 Averaging Rules.- 2.3.1 Average of a sum.- 2.3.2 Average of a product.- 2.3.3 Average of a time derivative.- 2.3.4 Average of a spatial derivative.- 2.3.5 Average of a spatial derivative of a scalar satisfying ?2G = 0.- 2.3.6 The coefficient T?*.- 2.3.7 Average of a material derivative.- 2.4 Macroscopic Balance Equations.- 2.4.1 General balance equation.- 2.4.2 Mass balance of a phase.- 2.4.3 Volume balance of a phase.- 2.4.4 Mass balance equation for a component of a phase.- 2.4.5 Balance equation for the linear momentum of a phase.- 2.4.6 Heat balance for a phase and for a saturated porous medium.- 2.4.7 Mass balance in a fractured porous medium.- 2.4.8 Megascopic balance equation.- 2.5 Stress and Strain in a Porous Medium.- 2.5.1 Total stress.- 2.5.2 Effective stress.- 2.5.3 Forces acting on the solid matrix.- 2.6 Macroscopic Fluxes.- 2.6.1 Advective flux of a single Newtonian fluid.- 2.6.2 Advective fluxes in a multiphase system.- 2.6.3 Diffusive flux.- 2.6.4 Dispersive flux.- 2.6.5 Transport coefficients.- 2.6.6 Coupled fluxes.- 2.6.7 Macrodispersive flux.- 2.7 Macroscopic Boundary Conditions.- 2.7.1 Macroscopic boundary.- 2.7.2 The general boundary condition.- 2.7.3 Boundary conditions between two porous media in single phase flow.- 2.7.4 Boundary conditions between two porous media in multiphase flow.- 2.7.5 Boundary between two fluids.- 2.7.6 Boundary with a 'well mixed' domain.- 2.7.7 Boundary with fluid phase change.- 2.7.8 Boundary between a porous medium and an overlying body of flowing fluid.- 3 Mathematical Statement of a Transport Problem.- 3.1 Standard Content of a Problem Statement.- 3.1.1 Conceptual model.- 3.1.2 Mathematical model.- 3.2 Multicontinuum Models.- 3.3 Deletion of Nondominant Effects.- 3.3.1 Methodology.- 3.3.2 Examples.- 3.3.3 Concluding remarks.- B Application.- 4 Mass Transport of a Single Fluid Phase Under Isothermal Conditions.- 4.1 Mass Balance Equations.- 4.1.1 The basic equation.- 4.1.2 Stationary rigid porous medium.- 4.1.3 Deformable porous medium.- 4.2 Boundary Conditions.- 4.2.1 Boundary of prescribed pressure or head.- 4.2.2 Boundary of prescribed mass flux.- 4.2.3 Semipervious boundary.- 4.2.4 Discontinuity in solid matrix properties.- 4.2.5 Sharp interface between two fluids.- 4.2.6 Phreatic surface.- 4.2.7 Seepage face.- 4.3 Complete Mathematical Model.- 4.4 Inertial Effects.- 5 Mass Transport of Multiple Fluid Phases Under Isothermal Conditions.- 5.1 Hydrostatics of a Multiphase System.- 5.1.1 Interfacial tension and capillary pressure.- 5.1.2 Capillary pressure curves.- 5.1.3 Three fluid phases.- 5.1.4 Saturation at medium discontinuity.- 5.2 Advective Fluxes.- 5.2.1 Two fluids.- 5.2.2 Two-phase effective permeability.- 5.2.3 Three-phase effective permeability.- 5.3 Mass Balance Equations.- 5.3.1 Basic equations.- 5.3.2 Nondeformable porous medium.- 5.3.3 Deformable porous medium.- 5.3.4 Buckley-Leverett approximation.- 5.3.5 Flow with interphase mass transfer.- 5.3.6 Immobile fluid phase.- 5.4 Complete Model of Multiphase Flow.- 5.4.1 Boundary and initial conditions.- 5.4.2 Complete model.- 5.4.3 Saturated-unsaturated flow domain.- 6 Transport of a Component in a Fluid Phase Under Isothermal Conditions.- 6.1 Balance Equation for a Component of a Phase.- 6.1.1 The dispersive flux.- 6.1.2 Diffusive flux.- 6.1.3 Sources and sinks at the solid-fluid interface.- 6.1.4 Sources and sinks within the liquid phase.- 6.1.5 Mass balance equation for a single component.- 6.1.6 Variable fluid density and deformable porous medium.- 6.1.7 Balance equations with immobile liquid.- 6.1.8 Fractured porous media.- 6.2 Boundary Conditions.- 6.2.1 Boundary of prescribed concentration.- 6.2.2 Boundary of prescribed flux.- 6.2.3 Boundary between two porous media.- 6.2.4 Boundary with a body of fluid.- 6.2.5 Boundary between two fluids.- 6.2.6 Phreatic surface.- 6.2.7 Seepage face.- 6.3 Complete Mathematical Model.- 6.4 Multicomponent systems.- 6.4.1 Radionuclide and other decay chains.- 6.4.2 Two multicomponent phases.- 6.4.3 Three multicomponent phases.- 7 Heat and Mass Transport.- 7.1 Fluxes.- 7.1.1 Advective flux.- 7.1.2 Dispersive flux.- 7.1.3 Diffusive flux.- 7.2 Balance Equations.- 7.2.1 Single fluid phase.- 7.2.2 Multiple fluid phases.- 7.2.3 Deformable porous medium.- 7.3 Initial and Boundary Conditions.- 7.3.1 Boundary of prescribed temperature.- 7.3.2 Boundary of prescribed flux.- 7.3.3 Boundary between two porous media.- 7.3.4 Boundary with a 'well mixed' domain.- 7.3.5 Boundary with phase change.- 7.4 Complete Mathematical Model.- 7.5 Natural Convection.- 8 Hydraulic Approach to Transport in Aquifers.- 8.1 Essentially Horizontal Flow Approximation.- 8.2 Integration Along Thickness.- 8.3 Conditions on the Top and Bottom Surfaces.- 8.3.1 General flux condition on a boundary.- 8.3.2 Conditions for mass transport of a single fluid phase.- 8.3.3 Conditions for a component of a fluid phase.- 8.3.4 Heat.- 8.3.5 Conditions for stress.- 8.4 Particular Balance Equations for an Aquifer.- 8.4.1 Single fluid phase.- 8.4.2 Component of a phase.- 8.4.3 Fluids separated by an abrupt interface.- 8.5 Aquifer Compaction.- 8.5.1 Integrated flow equation.- 8.5.2 Integrated equilibrium equation.- 8.6 Complete Statement of a Problem of Transport in an Aquifer.- 8.6.1 Mass of a single fluid phase.- 8.6.2 Mass of a component of a fluid phase.- 8.6.3 Saturated-unsaturated mass and component transport.- References.- Problems.
1,433 citations
Book•
01 Jan 1990
TL;DR: In this paper, the authors present a framework for simultaneous momentum, energy, and mass transfer using differential geometry, and apply it to energy and Mass transfer. But they do not discuss the application of differential geometry to momentum transfer.
Abstract: Contents: Kinematics and Conservation of Mass.- Foundations for Momentum Transfer.- Applications of the Differential Balances to Momentum Transfer.- Application of Integral Averaging to Momentum Transfer.- Foundations for Simultaneous Momentum, Energy, and Mass Transfer.- Applications of the Differen- tial Balances to Energy and Mass Transfer.- Applications of Integral Averaging to Energy and Mass Transfer.- Appendix A: Differential Geometry.- Name Index.- Subject Index.
425 citations
TL;DR: A mathematical model was developed and tested to simulate the generation and transfer of heat in solid substrate fermentation (SSF) and it was shown that conduction through the fermentation fixed bed was the main heat transfer resistance.
Abstract: A mathematical model was developed and tested to simulate the generation and transfer of heat in solid substrate fermentation (SSF). The experimental studies were realized in a 1-L static bioreactor packed with cassava wet meal and inoculated with Aspergillus niger. A simplified pseudohomogeneous monodimensional dynamic model was used for the energy balance. Kinetic equations taking into account biomass formation (logistic), sugar consumption (with maintenance), and carbon dioxide formation were used. Model verification was achieved by comparison of calculated and experimental temperatures. Heat transfer was evaluated by the estimation of Biot and Peclet heat dimensionless numbers 5-10 and 2550-2750, respectively. It was shown that conduction through the fermentation fixed bed was the main heat transfer resistance. This model intends to reach a better understanding of transport phenomena in SSF, a fact which could be used to evaluate various alternatives for temperature control of SSF, i.e., changing air flow rates and increasing water content. Dimensionless numbers could be used as scale-up criteria of large fermentors, since in those ratios are described the operating conditions, geometry, and size of the bioreactor. It could lead to improved solid reactor systems. The model can be used as a basis for automatic control of SSF for the production of valuable metabolites in static fermentors.
209 citations
TL;DR: For dynamical systems of large spatial extension giving rise to transport phenomena, like the Lorentz gas, a relationship between the transport coefficient and the difference between the positive Lyapunov exponent and the Kolmogorov-Sinai entropy per unit time is established.
Abstract: For dynamical systems of large spatial extension giving rise to transport phenomena, like the Lorentz gas, we establish a relationship between the transport coefficient and the difference between the positive Lyapunov exponent and the Kolmogorov-Sinai entropy per unit time, characterizing the fractal and chaotic repeller of trapped trajectories. Consequences for nonequilibrium statistical mechanics are discussed.
201 citations
TL;DR: In this article, the effects of operating conditions, reactor geometry, and heat transfer characteristics on flow patterns and growth rate uniformity in vertical, axisymmetric reactors for metalorganic vapor phase epitaxy (MOVPE) are described.
149 citations
TL;DR: In this article, the results of Hughes, France, and Mallet are generalized to conservation law systems taking into account high-temperature effects, and a general divariant gas is studied; it can be specialized to the usual Navier-Stokes equations, as well as to situations where the gas is vibrationally excited and undergoes equilibrium chemical reactions.
71 citations
TL;DR: In this paper, an extensive study on the fluidized bed combustion behavior of a single carbon particle was carried out with a newly developed transient model, the ASPC model, and also with the much simpler progressive conversion model.
65 citations
TL;DR: In this article, the Hamiltonian formulation of equations in continuum mechanics through a generalized bracket operation is shown to reproduce a variety of incompressible viscoelastic fluid models, including the Giesekus model, the upper-convected Maxwell and the Oldroyd-B models, the FENE-P dumbbell, the Phan-Thien/Tanner, the Leonov, the Bird/DeAguiar, and the bead-spring chain models.
Abstract: The Hamiltonian formulation of equations in continuum mechanics through a generalized bracket operation is shown here to reproduce a variety of incompressible viscoelastic fluid models, including the Giesekus model (with particular cases the upper‐convected Maxwell and the Oldroyd‐B models), the FENE–P dumbbell, the Phan‐Thien/Tanner, the Leonov, the Bird/DeAguiar, and the bead–spring chain models. The analysis allows comparison of the differential models on a more fundamental level than previously possible by reformulating the equations in terms of the Hamiltonian (system energy) and the dissipation of the system expressed as functionals involving the velocity vector and structural parameter(s). In fact, all of these models involve only slight variations of the same general Hamiltonian and the dissipation tensor. An advantage of this formulation is the establishment of thermodynamic admissibility criteria which in complex flows can shed light on the range of validity and/or faithfulness of the numerical calculations involving the above models. The usefulness of the generalized bracket formulation lies in the systematic approach that it provides in addressing one of the fundamental problems that the engineer working with complex materials has to deal with: how to transfer information that has been painstakingly provided by the physical chemist, addressing fundamental problems on a molecular level, from the microscopic scale to the macroscopic level where the engineer actually needs the model in dealing with everyday industrial problems. It is hoped that this new formulation can be used in the future to systematically generate continuum constitutive models, which are thermodynamically consistent, and based on microscopic analysis. Thus, it is the purpose here to narrow the gap between detailed (molecular) microscopic descriptions of the motions of polymer chains and (macroscopic phenomenological) continuum approaches. We believe that the generalized bracket formulation, due to its inherent simplicity and symmetry, has the potential to provide an answer to very complex situations, such as multicomponent structured media and coupled transport phenomena.
61 citations
01 May 1990
TL;DR: The hydrodynamic transport model based fin the generalized momentum and energy equations is used to simulate a n + -n-n + one-dimensional silicon device and the results are compared with Monte Carlo calculations, which are generally in good agreement.
Abstract: The hydrodynamic transport model based fin the generalized momentum and energy equations is used to simulate a n + -n-n + one-dimensional silicon device and the results are compared with Monte Carlo calculations. The non-local effects are shown to become important for lengths of the order of a few tenths of a micrometer at applied voltages around 1.0–1.5 V. The hydrodynamic and Monte Carlo velocity and energy are generally in good agreement. Finally, the effects of the thermal conductivity and of the convective terms, in regions where large gradients are present, are investigated.
49 citations
TL;DR: In this paper, the influence of surface mass transfer on mixed convection over horizontal plates in saturated porous media was investigated and the limiting cases of free and forced convection were also examined, where the surface temperature, free stream velocity and injection, or withdrawal, velocity are a prescribed power function of distance.
34 citations
15 Aug 1990-JSME international journal. Series 2, Fluids engineering, heat transfer, power, combustion, thermophysical properties
01 Jan 1990
TL;DR: In this paper, the authors studied the transport phenomena of the extended Graetz problem with three different entrance boundary conditions and showed that the expansion coefficients of the solution corresponding to the different conditions play an important role in effecting the solution form.
Abstract: The transport phenomena of the extended Graetz problem with three different entrance boundary conditions are discussed. The expansion coefficients of the solution corresponding to the different conditions play an important role in effecting the solution form. The solution, assuming that the entrance boundary conditions for both temperature and energy flux (TFBC) are continuous, is the same as that for the problem in which the downstream region was considered infinite. Among all the procedures used, the computational procedures for TFBC are the simplest. The TFBC condition is recommended for use in analyzing the problem. Results show that temperature profiles and local Nussell number are influenced by Piclet number and different entrance boundary conditions. In addition, it is also shown that the asymptotic Nussell numbers for the three different conditions are the same.
TL;DR: In this article, a model has been presented to describe crystal growth and dissolution kinetics from a mother liquid referred to as the bulk, which takes surface integration kinetics as well as transport of heat and mass to (or from) the bulk from (or to) the crystal surface into account.
TL;DR: In this article, the transport properties of networks filled with carbon black have been studied in order to obtain information on the rubber-filler interactions and the results show that the filling particles can be completely or partially excluded from the transport phenomena which occur mainly in the rubberlike matrix.
Abstract: The transport properties of networks filled with carbon black have been studied in order to obtain information on the rubber–filler interactions. The obtained results show that the filling particles can be completely or partially excluded from the transport phenomena which occur mainly in the rubberlike matrix. The transport properties of the pure components, compared with the filled system, allow to obtain a possible evaluation of the interphase phenomena.
TL;DR: In this paper, the influence of the Prandtl number on buoyancy-induced transport phenomena was investigated through two-dimensional steady-state computations for flow in a square enclosure at two different vertical wall temperatures, both with and without solidification.
TL;DR: In this paper, the authors investigate experimentally the effects of the container aspect ratio and width ratio on the onset of thermal instability and the oscillation phenomenon in a typical crystal growth configuration.
Abstract: Lately, natural convection in low Prandtl number (Pr) fluids has gained importance because of growing interest in the transport phenomena in crystal growth processes. It is known that some of the undesirable striations encountered in crystals grown from the melt are caused by thermal instabilities associated with natural convection in the melt. In a typical crystal growth configuration the container aspect ratio Ar (depth/length ratio) is not very small (typically 0.1 to 1) nor is the width ratio Wr (width/depth ratio) very large (typically 1 to 10), so the instability is expected to be influenced by the parameters Ar and Wr. Thus the objective of the present work is to investigate experimentally the effects of Ar and Wr on the onset of thermal instability and the oscillation phenomenon.
01 Jan 1990
TL;DR: In this article, the authors investigate experimentally the effects of the container aspect ratio and width ratio on the onset of thermal instability and the oscillation phenomenon in a typical crystal growth configuration.
Abstract: Lately, natural convection in low Prandtl number (Pr) fluids has gained importance because of growing interest in the transport phenomena in crystal growth processes. It is known that some of the undesirable striations encountered in crystals grown from the melt are caused by thermal instabilities associated with natural convection in the melt. In a typical crystal growth configuration the container aspect ratio Ar (depth/length ratio) is not very small (typically 0.1 to 1) nor is the width ratio Wr (width/depth ratio) very large (typically 1 to 10), so the instability is expected to be influenced by the parameters Ar and Wr. Thus the objective of the present work is to investigate experimentally the effects of Ar and Wr on the onset of thermal instability and the oscillation phenomenon.
TL;DR: In this paper, a mathematical representation is developed to describe heat and fluid flow phenomena inside the plasma torch for a non-transferred arc system, where a joule heating pattern is postulated for the arc column and then the heat flow and fluidflow equations are solved rigorously.
Abstract: A mathematical representation is developed to describe heat and fluid flow phenomena inside the plasma torch for a non-transferred arc system. In the model a joule heating pattern is postulated for the arc column and then the heat flow and fluid flow equations are solved rigorously. The resultant solutions give information on the temperature and the velocity fields in the plasma gas inside and outside the torch. By postulating “reasonable” values for the heat generation pattern, very good agreement has been obtained between measurements and predictions for a laminar system, used by the INEL researchers. The agreement was less satisfactory with measurements obtained using a Metco torch, where the flow was turbulent. These findings indicate that this is a promising avenue for research, but a great deal more needs to be done before a model of general validity can be developed.
TL;DR: In this paper, the authors focus on how the transport phenomena of migration, convection, and turbulent diffusion have been approximated by the donor cell technique, and compare this model with other computational approaches.
01 Jan 1990
TL;DR: A complete understanding of the interrelationships between rheology, kinetics, and transport phenomena is a very critical part of food process design and analysis.
Abstract: A complete understanding of the interrelationships between rheology, kinetics, and transport phenomena is a very critical part of food process design and analysis. The need to understand the mechanisms underlying the interactions of these three areas cannot be overemphasized. To establish a common ground for discussion, the following definitions are presented.
TL;DR: In this paper, a macroscopic theory that includes Ostwald ripening, a process occurring in solid-liquid phase mixtures whereby the size scale of the solid phase tends to grow so as to decrease interfacial energy.
Abstract: This paper develops a macroscopic theory that includes Ostwald ripening, a process occurring in solid-liquid phase mixtures whereby the size scale of the solid phase tends to grow so as to decrease interfacial energy. The dynamic mixture theory presented is also capable of dealing with transport phenomena and phase redistribution effects that arise from relative flow between the phases. The presence of the interfacial energy means that the pressures of the liquid and solid in the phase mixture are not equal and the ripening process is directly related to the relaxation of the system to a state of local thermodynamic equilibrium with a common pressure for the phases.
01 Jan 1990
TL;DR: In this article, a model consisting of a balance equation for each extensive quantity that is being transported, constitutive relations, describing the properties of the particular phases involved, source functions of the extensive quantities, and initial and boundary conditions, all stated at the macroscopic level.
Abstract: The objective of this chapter is to develop the mathematical models that describe transport phenomena in porous media at the macroscopic level. As will be shown, a model consists of a balance equation for each extensive quantity that is being transported, constitutive relations, describing the properties of the particular phases involved, source functions of the extensive quantities, and initial and boundary conditions, all stated at the macroscopic level.
TL;DR: In this paper, the authors consider suspensions of rigid particles under flow conditions such that the fluid and particle velocity fluctuations can be neglected, and they analyze the dynamic behaviour of such suspensions from a macroscopic point of view, with the help of irreversible thermodynamics.
Abstract: We consider suspensions of rigid particles under flow conditions such that the fluid and particle velocity fluctuations can be neglected. We analyzed the dynamic behaviour of such suspensions from a macroscopic point of view, with the help of irreversible thermodynamics. We pay special attention to the differences that exist between transport phenomena in suspensions and those in a classical binary mixture. Our analysis reveals the existence of a coupling between barycentric and relative motions. This coupling involves both inertial and viscous forces. When inertia and concentration diffusion are neglected, we get a set of equations somewhat similar to the one recently suggested by Nozieres.
TL;DR: In this article, a mean field approximation is used to derive hydrodynamic equations for the system and the expression for the rotational viscosity, which is shown to be proportional to the volume fraction.
Abstract: Here we analyze transport phenomena in suspensions of magnetic dipoles in a Newtonian nonpolar solvent (ferrofluid). A continuum or mean field approximation is used to derive hydrodynamic equations for the system and the expression for a new transport coefficient: the rotational viscosity, which is shown to be proportional to the volume fraction. From these equations we discuss two problems: the relaxation of the internal degrees of freedom and the viscoelastic character of the suspension. We then compare our results with previous theoretical and experimental analyses.
TL;DR: In this paper, a formalism of Extended Irreversible Thermodynamics (EIT) is used to study the physical aspects of heat, momentum and mass transport through porous media, and the thermodynamic space is enlarged with respect to that of classical linear irreversible thermodynamics (LIT) to include the mass, heat and momentum fluxes as independent variables.
Abstract: A formalism of extended irreversible thermodynamics (EIT) is used to study the physical aspects of heat, momentum and mass transport through porous media. The thermodynamic space is enlarged with respect to that of classical linear irreversible thermodynamics (LIT) to include the mass, heat and momentum fluxes as independent variables. The time evolution equations for such variables are derived self-consistently and reduce to the usual constitutive equations of LIT when the appropriate limits are taken. Equations that involve effects characterized by terms of second order in the gradients of conserved variables (such as the Darcy-Brinkman law) may also be derived within the same formalism. Finally, EIT provides the natural framework beyond LIT to introduce non-isothermal effects in the study of transport phenomena in porous media.
01 Jan 1990
TL;DR: The papers contained in this volume represent a wide range of current research interests in processes such as food and polymer processing, casting, welding, machining, laser cutting, and superconductor processing.
Abstract: The papers contained in this volume represent a wide range of current research interests in processes such as food and polymer processing, casting, welding, machining, laser cutting, and superconductor processing. This volume includes papers presented in four sessions: Heat Transfer in Materials Processing; Thermal Phenomena in Superconductor Processing; Heat Transfer in Food and Polymer Processing; Heat Transfer in CAsting and Welding.
TL;DR: In this paper, a general purpose computer model for describing the transport phenomena and resulting rate of deposition has been described, and the model can be used as a tool for design optimization of such reactors.
Abstract: A general purpose computer model for describing the transport phenomena and resulting rate of deposition has been described. Partial differential equations describing the conservation of mass, momentum, energy, and chemical species are solved by a computer program employing the finite difference method. The system considered in this paper is deposition of silicon in a vertical stagnation flow reactor by the reaction of silicon tetrachloride and hydrogen. The program allows for multiple chemical species and natural convection effects. Predicted silicon deposition rates along the substrate are in reasonable agreement with experimental values available in the literature. The effect of gas inlet configuration on the uniformity of deposition has been studied. The model can be used as a tool for design optimization of such reactors.
01 Aug 1990-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, a mathematical representation of the velocity and concentration fields in a three-dimensional (3D) horizontal chemical vapor deposition (CVD) reactor in the mass transfer-controlled regime was developed.
Abstract: A mathematical representation has been developed describing the velocity and concentration fields in a three-dimensional (3-D) horizontal chemical vapor deposition (CVD) reactor in the mass transfer-controlled regime. The theoretical predictions for the deposition rate were found to be in excellent agreement with measurements reported by Park and Chun. [17] A parametric study conducted examining the effects of the key process parameters has shown the following: the transport problems in horizontal CVD reactors are definitely 3-D; the concentration of the gaseous reactant at the inlet may have an important effect on the uniformity of the deposition rate; the imposition of a positive pressure gradient on the gas will improve the uniformity of the deposition rate; and the uniformity of the deposition rate may also be promoted by operating at a reduced pressure.
TL;DR: In this paper, the application of CVD technologies for coating of fibrous substrates is addressed, and the transport phenomena occurring in the reactor chamber are modeled in terms of conservation laws.