Showing papers on "Transport phenomena published in 1979"

Chapter 10: Movement of Solutes in Soil: Computer-Simulated and Laboratory Results

Abstract: Publisher Summary Mechanisms that determine the rate at which chemicals move through soils include processes such as diffusion/dispersion, adsorption, decay, and intra-aggregate diffusion. Exact analytical solutions can be derived for some of these processes, such as for linear adsorption and linear decay. However, for nonlinear cases, analytical methods cannot be used to obtain the exact solutions of the transport equations, and approximate methods must be employed. The use of numerical techniques helps in modeling the transport of solutes in such cases. Numerical and analytical approaches can and should complement and augment each other. For example, an analytical solution may be used to check the accuracy of a numerical program. On the other hand, a numerical solution may be used to demonstrate the appropriateness (or shortcoming) of a particular assumption necessary in the development of an analytical solution. This chapter discusses some of the transport equations currently used to describe the movement of chemicals in soils and presents solutions based on both numerical and analytical techniques. The chapter discusses the influences of several mechanisms affecting solute transport phenomena, such as nonlinear adsorption, hysteresis in the equilibrium isotherms, and decay.

The maxwell-stefan formulation of irreversible thermodynamics for simultaneous heat and mass transfer

Abstract: We consider constitutive relations for diffusion and simultaneous heat conduction in an n-coraponent non-ideal fluid mixture. Using the ideal gas treatment of Hirschfelder, Curtiss and Bird as a basis, we develop the generalization of the Maxwell-Stefan diffusion equations. The application of the second law of thermodynamics is shown to impose non-negativity constraints on the defined diffusion coefficients, D ik The practicalusefulness of the Generalized Maxwell-Stefan formulation is demonstrated by a few examples.

Transport phenomena and polymer morphology

Abstract: The presence of the crystals in the semicrystalline polymer reduces the mass fraction, determines the space distribution and modifies the transport properties of the amorphous component which is responsible for practically all the sorption, diffusion, and permeability. The conventional determination of the diffusion coefficient from the sorption or diffusion transient is strongly affected by the geometry of the sample. The spin echo method of the nuclear magnetic resonance in a pulsed magnetic field gradient measures the diffusion directly and hence reflects the anisotropy of the orientation of the amorphous component without any distortion by the shape of the sample. The anisotropy of a single amorphous layer of a thickness of less than 10 nm, however, cannot be detected by this method which measures the molecule displacement over about 300 nm. A very rough estimate of the transport properties of the volume element can be based on the fractional free volume of the polymer. This is particularly helpful in the description of the effects in elastically and plastically deformed material. The elastic tensional strain increases while the plastic strain as a rule decreases the free volume. In the latter case the amorphous component, at least at room temperature, permanently deviates from the thermodynamic equilibrium. A substantial part of this deviation can be removed by annealing. If the annealing of the fibrous material is performed with fixed ends which prevents shrinking the sample upon standing at room temperature tends to return, at least partially, to the transport properties before annealing. The sorption is proportional to the mass fraction of the amorphous component, the permeability to the square of it. The diffusion reflects the anisotropy of the morphology and of its influence on the transport properties of the amorphous component. In the fiber structure the amorphous layers parallel and perpendicular to the fiber axis differ substantially. In spite of the close connection between the morphology and the transport properties one must not forget that this connection is one-sided. A model of the structure with the proper transport parameters of the amorphous component has to yield the observed sorption and diffusion data. But these data are not sufficient for constructing unambiguously the structural model.

The generalized moment method for transport phenomena in dense fluids

Abstract: Based on the kinetic equation reported previously, the generalized moment method is presented for dense fluids in this paper. The equations of change are presented for stress tensor and heat flux in nonuniform dense fluids and by solving them up to second order by a perturbation method, constitutive relations and various linear and nonlinear transport coefficients are obtained. Comparison of the transport coefficients with the counterparts in the generalized Chapman–Enskog (GCE) method shows that two results agree with each other if the first Chapman–Enskog approximants are used for the GCE results and some potential energy contributions are neglected in the molecular expressions for fluxes. Discussions are given regarding the constitutive relation for the Stokes fluids and the non‐Newtonian behavior of real fluids.

A General Model for Turbulent Momentum and Heat Transport in Liquid Metals

Abstract: This report develops a general single-point closure scheme for calculating the local levels of turbulent fluxes of momentum and heat in liquid-metal flows. Transport effects are accounted for by way of the three scalar quantities: turbulent kinetic energy; turbulence-energy dissipation rate; and scalar energy (or half the mean temperature variance). Their values at any point in the flow are obtained from the solution of conservation equations of transport type for each of the three quantities. The turbulent momentum fluxes (Reynolds stresses) and heat-transport rates are then obtained from the algebraic formulas containing the above scalar quantities and the mean velocity and temperature fields.

Chemical engineering for chemists

Abstract: INTRODUCTION TO CHEMICAL ENGINEERING PRINCIPLES: Interface Between Chemistry and Chemical Engineering What's in this Book Mass Balances Energy Balances Heat Transfer in Industrial Chemical Processes Fluid Flow and Chemical Processing Mass Transfer in Separation, Purification, and Heterogeneous Systems EXAMPLES OF MASS TRANSFER: Chemical Engineering Kinetics, Process Control, and Engineering Economics Basic Steps for Scaling Up a Process Design The Principles of Fluid Flow, Heat Transfer, and Mass Transfer Chemical Engineering Principles Applied to New Technologies APPLIED THERMODYNAMIC: Terms Temperature and Heat Definition of Work Conservation of Energy-The First Law of Thermodynamics The Second Law of Thermodynamics-The Limits of Efficiency Gibbs Free Energy, Chemical Potential, Fugacity, and Activity Applied Phase Equilibrium and the Distribution Coefficient Activity Coefficients FLUID FLOW: Fluid Statics Buoyancy Fluid Dynamics-The Character of Flowing Fluids Flow and the First Law of Thermodynamics-Bernoulli's Equation Friction Losses in Fluid Flow Types of Pumps and Their Uses Flow Around Submerged Objects-Calculating a Drag Force Non-Newtonian Fluid Flow Mixing Fluids Flow Through Packed Beds, Porosity, and Sphericity HEAT TRANSFER: Conduction Convection-Heat Transfer with Motion Radiation-Heat Transfer Through a Vacuum Steady-State Heat Conduction-q Steady with Time Steady-State Heat Conduction with a Heat Source-Heated Wires, Chemical Reactors, and Phase Changes Unsteady-State Heat Conduction Convective Heat Transfer-Forced and Free Dimensionless Number for Comparing Conduction and Convection-The Nusselt Number The Overall Heat Transfer Coefficient, U-Combining Conductive and Convective Heat Transfer Effects Heat Transfer with Flow Around Objects Radiative Heat Transfer How an Object's Shape Affects Radiation An Introduction to Heat Exchangers MASS TRANSFER: Steady-State Molecular Diffusion Unsteady-State Molecular Diffusion-Time Dependence Mass Transfer at a Phase Boundary Mass Transfer for Different Geometrics Equilibrium Stage Operations, the Ideal Stage, and Phase Equilibria Mechanical Separation Processes APPLIED REACTION KINETICS AND REACTOR DESIGN: A Review of Chemical Kinetics and Chemical Equilibrium Chemical Reaction Kinetics Categories Chemical Reactor Design PROCESS CONTROL AND DATA ACQUISITION: Control Applications and Types of Systems Types of Control Basics of Control Systems Process Control Equipment Process Dynamics-Determining Control Response Mathematically Process Dynamics Design Methods Additional and Advanced Control Methods Data Acquisition by Computer ENGINEERING ECONOMICS AND PROCESS DESIGN: Time Value of Money Depreciation and Salvage Value: Depreciation Methods and Sinking Funds Economic Alternatives Guidelines for Comparing Investment Alternatives Cost Indexes-Estimating Process Costs from Existing Operations Equipment Cost-Capacity and Scaling Factors, Six-Tenths Rule Capital Investment Estimating Techniques Pricing Chemical Products Process Design Conclusion

Transpiration mass spectrometry of high temperature vapors

Abstract: Material transport via vapor phase species at high temperature and pressure is an important phenomenon in materials science and technology The preparation of high purity semiconductor and ceramic materials utilizes vapor transport to advantage, whereas the corrosion of power plant boilers, gas turbines and other advanced energy devices results from reactive vapor transport To understand and control these transport phenomena, it is essential to be able to identify and measure the key chemical species present in the vapor phase systems However, in the past, classical characterization methods such as transpiration and Knudsen or Langmuir effusion have been limited because they do not establish the molecular identity of transport species or because low pressures are necessary to make effusion measurements Transpiration Mass Spectrometry (TMS) overcomes both of these limitations by combining the basic features of transpiration and mass spectrometry With this technique, it is possible to sample reactive gases directly from high-temperature, high-pressure atmospheres for qualitative and quantitative characterization with a mass spectrometer To demonstrate the method, the thermodynamic equilibrium vaporization of the salts Na/sub 2/SO/sub 4/ and NaCl was studied at total pressures up to an atmosphere using N/sub 2/ or Ar as carrier gases

Equations of motion for electrons, phonons, and librons in one-dimensional conductors

Abstract: Phenomenological equations of motion for electrons, phonons, and librons are developed to describe the transport phenomena in one-dimensional conductors above the Peirels transition. These equations provide a unified framework for explaining all the experimental data for the dc conductivity, its frequency dependence, the optical conductivity, and the effect of radiation on the dc and the optical conductivity.

Tokamak Fuelling with Pellets: Effect of Transport Phenomena on the Injection Requirements

Abstract: Abstract Results of calculations on pellet-plasma interaction that take into account transport phenomena inherent in tokamak plasmas are analyzed. It is shown that the results obtained by different authors on the optimum pellet penetration depth and required pellet injection frequencies, which are partly contradictory, can be explained by means of the different transport processes taken into account or neglected in the calculations concerned.

On the mathematical formulation of the first principle of thermodynamics for non-uniform temperature processes

Abstract: 2014 In a system at non-uniform temperature some of the heat which flows from hotter regions to colder ones can produce non-thermal energy, quite apart from whether the system undergoes changes in its state or not. In this paper a general mathematical formulation of the first principle of thermodynamics is given which takes account explicitly of the non-thermal energy originating from the heat flow. Moreover, some restrictions imposed by the second principle of thermodynamics on this production of non-thermal energy are determined. Once the present formulation is adopted, it is shown that the energy of an amount of calories in motion in a non-uniform temperature field cannot be obtained simply by multiplying the number of calories times the Joule’s equivalent of heat. An explicit expression of this energy is deduced for steady-state situation. Finally, the consequences of the proposed formulation on heat conduction problems are discussed, and some experimental evidence is given in support of the present approach. RÉSUMÉ. Dans un systeme a temperature non uniforme une partie de la chaleur qui s’ecoule de zones plus chaudes a des zones plus froides peut produire de l’énergie non calorifique, même lorsque Ie systeme ne subit pas de changements d’etat. Dans cet article on donne une formulation mathematique generate du premier principe de la thermodynamique qui tient compte de l’énergie non calorifique produite par Ie flux de chaleur. On determine en outre certaines restrictions que Ie deuxieme principe de Ia thermodynamique impose a cette production d’énergie non calorifique. Une fois que la presente formulation est adoptee, on montre que l’énergie Annales de l’Institut Henri Poincaré Section A Vol. XXX, 0020-2339/1979/61/$ 4.00/ @ Gauthier-Villars.

Thermo-fluid mechanics of liquid or gas-cooled tubular first walls

Abstract: An analysis for hydrodynamically and thermally, fully developed heat transfer in a circular tube coupled with heat conduction in the tube wall is presented. Anisotropy of turbulent energy transport has been taken into account employing theoretical results for eddy diffusivity in the various directions. The energy equations for the fluid and solid body are solved simultaneously and are subject to continuity in heat flux and temperature at the interface. Solutions of the equations are found by separation of variables. Indicative of the analysis is that neglecting radial conduction but allowing circumferential conduction results in underestimating the wall temperature for relatively thin-wall structures and also the fluid temerature. In addition, a comparison of the dimensionless tube wall temperatue equation derived from the coupled analysis with that based on a constant heat transfer coefficient indicates that the constant heat transfer analysis can be made identical with the present case by renormalizing the heat transfer coefficient. The analysis provides the designer with a simple set of analytical design equations for the coupling of solid and fluid temperature distributions for obtaining the Nusselt numbers.

The kinetic theory of multicomponent dilute gases under electro-magnetic field

Abstract: In this article the transport phenomena of multicomponent dilute gases under electromagnetic and gravity fields are treated by the thirteen-moment method of Grad An approximate solution of the Boltzmann equation and expressions for the transport coefficients are obtained An expression for the electrical conductivity of partly ionized gases is derived Finally, conditions for the validity of the results are discussed

Modeling of silane pyrolysis in a continuous flow reactor. Low-Cost Solar Array Project

Abstract: Silane pyrolysis in a continuous flow pyrolyzer is a simple process that is currently being developed for producing solar cell grade silicon. The process involves complex phenomena, however, including thermal decomposition of silane, nucleation and growth of silicon particles, and mass and heat transfer. Modeling the effects of transport phenomena on silane pyrolysis in a continuous flow pyrolyzer is discussed. One- and two-dimensional models are developed to predict velocity, temperature, and concentration profiles in the reactor. The one-dimensional model has been implemented as a computer code.

Turbulent heat transfer for pipe flow with uniform heat generation

Abstract: An Analytic solution is presented of the problem of turbulent heat transfer in pipes with internal heat generation and insulated wall by applying a recently-developed eddy conductivity model. The results agree closely with available experimental data for a wide range of Prandtl number (0.02–10.5).

Transport phenomena in a knudsen molecular gas in a magnetic field

Abstract: We consider the behavior of a strongly rarefied (Knudsen) polyatomic gas between two surfaces that have different temperatures in a magnetic field. We show that in the magnetic field H there can arise a flux of gas and a heat flux along the surfaces (odd functions in H), and also normal and tangential forces on the walls.