Showing papers on "Transport phenomena published in 1970"

The mathematical theory of non-uniform gases : an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases

Abstract: Foreword Introduction 1. Vectors and tensors 2. Properties of a gas: definitions and theorems 3. The equations of Boltzmann and Maxwell 4. Boltzmann's H-theorem and the Maxwellian velocity-distribution 5. The free path, the collision-frequency and persistence of velocities 6. Elementary theories of the transport phenomena 7. The non-uniform state for a simple gas 8. The non-uniform state for a binary gas-mixture 9. Viscosity, thermal conduction, and diffusion: general expressions 10. Viscosity, thermal conduction, and diffusion: theoretical formulae for special molecular models 11. Molecules with internal energy 12 Viscosity: comparison of theory with experiment 13. Thermal conductivity: comparison of theory with experiment 14. Diffusion: comparison of theory with experiment 15. The third approximation to the velocity-distribution function 16. Dense gases 17. Quantum theory and the transport phenomena 18. Multiple gas mixtures 19. Electromagnetic phenomena in ionized gases Historical summary Name index Subject index References to numerical data for particular gases (simple and mixed).

FEFLOW: A Finite Element Code For Simulating Groundwater Flow, Heat Transfer And Solute Transport

Abstract: The FEFLOW code is a finite element program package developed at VTT Energy to model flow, solute transport and heat transfer in coupled and non-coupled, steady-state and transient situations, as well as in deterministic and stochastic modes. The code offers a novel finite element technique to model groundwater phenomena in fractured crystalline rock. Linear and bi-quadratic one-, twoand threedimensional finite elements can be used for describing engineered and natural bedrock structures. One of the solute transport models implemented in the package is capable of taking into account matrix diffusion as well. Highly convective cases are handled with different kinds of upwind schemes. The system of linear algebraic equations emerging from the standard Galerkin approximation can be solved with a direct frontal solver, as well as with an array of iterative solvers partly from the NSPCG package. The nonlinear algebraic equations resulting from coupled cases are solved with the Picard iterative approach with options for relaxation. The discretization of time is based on a simple finite difference scheme. For each result quantity to be determined, the code offers a wide selection of nodal boundary conditions including prescribed values, sources, sinks and/or fluxes. These may be constant or a function of time. Hydraulic properties of the bedrock features may also be constant or vary with depth. Besides the finite element analysis code the FEFLOW package comprises several programs to compute derived quantities (like flow paths and flow rates) and to facilitate generic modelling tasks. The code has been tested in a series of test cases, and verified in the international HYDROCOIN project. Main application areas of the FEFLOW package have been site investigations and safety analyses undertaken by the Finnish power company Teollisuuden Voima/Posiva Oy operating two nuclear power plants. It has also been employed to simulate various hydraulic disturbances and solute transport phenomena in the Aspo Hard Rock Laboratory, Sweden. Transactions on Ecology and the Environment vol 10, © 1996 WIT Press, www.witpress.com, ISSN 1743-3541

Transport Mechanics in Systems of Orientable Particles. II. Kinetic Theory of Orientation Specific Transport for Hard‐Core Models

Abstract: The role of orientation and polarization in the transport phenomena of hard‐core polyatomic gases is developed in detail from the standpoint of the Boltzmann equation. A rigorous orientation specific Chapman and Enskog scheme is used to establish linear constitutive relations and anisotropic transport coefficients for orientation‐specific translational and rotational diffusion and for the orientation‐summed fluxes of mass, momentum, and heat. Calculations are reported for the effect of polarization upon the shear viscosity and thermal conductivity tensors of loaded spheres. The anisotropic expressions for rotational and translational thermal diffusion, shear diffusion, and concentration diffusion coefficient tensors are determined for a dilute system of loaded spherocylinders in a bath of rigid spheres. With the use of time reversal invariance, a microscopic reciprocal theorem is established and employed to prove Onsager reciprocal relations among the transport coefficient tensors.

Diffusion-convection Problems Using Boundary-domain Integral Formulation For Non-uniform Flows

Abstract: The paper presents a new numarical approach for diffusion-convection problems in non-uniform velocity field employing fundamental solution of the corresponding steady-state difusion-convection equation with constant coefficients and an extreme concept of subdomain technique. Numerical example of steady state flow in two-dimensions is included to demostrate the accuracy present numerical technique. Introduction The diffusion-convection equation is one of the most basic governin equation describing the transport phenomena in classical physic. However, it is still very difficult to numerically solve this type of equation, when the convection term is dominant. Most of the common numerical methods give emphasis on algorithms to suppress the well-known problems of oscillation in numerical solution for high PC number values [4]. Applications of the boundary-domain integral formulation is free from these problems due to the correct degree of "upwind" presented in the fundamental solution of the convection-diffusion equation [8]. A substantial number of different formulations by BEM for the diffusionconvection equation has appeared in the literature. Some of them have employed the elliptic or parabolic fundamental solution and treated the convective term as pseudo-sources [6], but they are useful only for low PC, number values. Alternatively, the velocity field can be decomposed into an average and a variable part and the fundamental solution of the diffusion-convection equation used incorporating the average velocity. The variable part of field can be accented for either by domain diskretization [5] or through DRM technique [7]. This approach is applicable for moderate PC number values. For high PC number values only for constant velocity field the BEM technique is developed [1]. Transactions on Modelling and Simulation vol 9, © 1994 WIT Press, www.witpress.com, ISSN 1743-355X 76 Boundary Element Methods for Fluid Dynamics II In the new algorithm for high Pe number values, the main restriction of the formulation, fact that the fundamental solution are only available for equations with constant coefficients, is overcome by decomposition of the domain under consideration into subdomains, which allows the use of constant coefficients [9]. Such formulation drastically cuts down the computation of integrals and allows the use of the alternative solvers for sparse matrices. Governing equation Let us consider a general unsteady state nonlinear diffusion-convection equation describing time dependent transfer of an arbitrary scalar function w(r, t) in a homogeneous and isotropic medium defined in solution domain R = ft x / representing the product of space 0 and time interval 1(1^^1) -^-itef-*-"*'-^ '"*• w where Vj(r ) is the local solcnoidal velocity field. The variable w(r&) can be interpreted, e.g. as a temperature in heat transfer problems, concentration in dispersion processes, vorticity in fluid dynamics problems, turbulent kinetic energy in its transport equation etc., and will be refered to as a potential. The effective diffusivity (Ze(r&,%), the effective reaction constant ke(rk,u) and the source term /u(^fc?w) are some monotonic space and potential dependent functions. The effective diffusivity # can be always partitioned into a constant a t^ , -—nj = — on F2 for t > , (5) OXj on #% , \ r f , , ——nj — ««(« — Uf) on I 3 for t > t^ , Transactions on Modelling and Simulation vol 9, © 1994 WIT Press, www.witpress.com, ISSN 1743-355X

Observations of transport phenomena and of atomic motion in the liquid phase

Abstract: Some compounds, Sb2Se3, InSe and CuSbSe2 have been studied which have relatively low electrical conductivities (

High field transport phenomena in n-InSb at high temperatures

Abstract: Earlier theories of transport phenomena in n -InSb have been extended to include medium-high electron concentrations at high lattice temperatures (300° to 500°K) in presence of high electric fields. Polar optical mode of electron-phonon scattering has been considered to be the sole mechanism of electron scattering at these temperatures. The steady state electron distribution function has been chosen to be the Fermi-Dirac distribution function appropriate to the effective electron temperature which is determined by the energy balance condition. Nonparabolicity of the conduction band has been taken care of by the Kane's model. It is seen that the effective electron temperature is not far above the lattice temperature even at the highest attainable fields and that the Galvano-thermo-magnetic transport coefficients do not exhibit any marked dependence on the strength of electric field under the present conditions. Some limitations and approximations have also been mentioned.

Smolder Spread Through Thin Horizontal FuelLayers

Abstract: Two-dimensional smoldering combustion of a thin layer of cellulosic particles, in quiescent air, is numerically simulated. The mathematical model describes pressure and velocity variations through the Darcy law. Mass and energy balance equations are used to describe convective and diffusive transport of chemical species and convective, radiative and conductive heat transfer. In conjuction with transport phenomena, chemical processes are also taken into account to describe endothermic pyrolytic and exothermic oxidative degradation of the solid to volatiles and char and further exothermic oxidation of char. The solution is computed numerically through a finite difference formulation of the model equations, based on the hybrid scheme. The splitting of the operators allows the solution to be computed into three steps, the first dealing with chemistry and the remaining two with physics. The structure of the leading edge of the smoldering wave is dominated by oxygen diffusion from the surrounding environment. However, as heat losses from the bottom surface increase, the length of the smolder wave is successively reduced and quenching of some partially charred solid occurs. INTRODUCTION Noticeable progress has been made in the last 50 years towards the understanding of heat and momentum transport through porous media. Studies have been motivated by direct technological applications which include [1] pollutant dispersion across the soil, heat exchanger and chemical reactor design and optimization, drying processes and insulation of buildings and pipes. In this case, cellulosic materials (newsprint) are widely used for their efficacy and low cost. Further to transport phenomena, these highly permeable materials can allow smoldering combustion. Smoldering is essentially a non-flaming, exothermic, reacting surface propagating through the porous solid. It is particularly important in the fire safety science because it is associated with the emission of toxic gases (mainly carbon monoxide) and it is often the first step of fire initiation. The determination of the controlling mechanisms is thus of great importance for fire prevention and control. As appears from experimental observation [2,3], the reaction zone is multi-dimensional and is characterized by different stages. The cellulosic material undergoes pyrolytic and oxidative degradation with the formation Transactions on Engineering Sciences vol 5, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533

Dynamics of Multi-Component Plasma with Transport Phenomena

Abstract: Fundamental equations for a multi-component plasma with transport phenomena for the case of no magnetic field are proposed. Each component of the plasma is electrically charged or neutral, and has its own velocity and temperature, as well as its density and partial pressure. As the transport phenomena, the “velocity relaxations” and the “temperature relaxations” between components are taken into account, as well as the viscosities and the thermal conductivities. These fundamental equations can be confirmed on the basis of the Boltzmann equations, using the “mean free time approximation.” For the typical examples, the Rayleigh- and the oscillating plate-problems for two-component plasma, etc. are examined.

Transport phenomena in partially ionized cesium.

Abstract: An analysis of electron and ion transport phenomena in cesium plasma is developed in a form consistent with experimental conditions typical of those in thermionic and magnetohydrodynamic energy converters and other cesium discharges. Particular attention is given to electron collision processes which are shown to influence significantly both electron and ion transport phenomena. Using available electron cross‐section data, electron and ion transport coefficients are evaluated as a function of electron temperature and fractional ionization. Results are then applied to the plasma of a low‐pressure nonuniform thermionic arc. Experimentally determined spatial variations of electron density and electron temperature are analyzed numerically and quantitative estimates are made of the spatial variation of electric field intensity, ion current density, and net charged particle production rate. The inferred production rate is compared with that evaluated using a nonequilibrium kinetic analysis developed by Norcross and Stone.

Closed-form Analytical Solutions For Steady-stateDensity-dependent Flow And Transport In A LayeredVertical Soil Column

Abstract: Closed-form analytical solutions are derived for steady-state ground water flow and solute transport phenomena when the ground water density depends on the solute concentration. The flow and transport under consideration are one dimensional vertical as they occur in a vertical soil column. The soil column can be inhomogeneous, consisted of two layers where transport related properties are uniform within each layer, but there can be jump discontinuities across the layer interface. Transport mechanisms considered are advection, molecular diffusion, and velocitydependent mechanical dispersion. Therefore, all relevant transport mechanisms are accounted for. The closed-form solutions derived herein can be used to assess accuracies of various numerical codes which simulate density-dependent flow and transport.

A!ID pH PMFILES WITH AtQCENTED DDTUSION IN CAPILlARY BLOOD OXYGENATORS

Abstract: The mathema;cical analysis and modeling of the steady flow capillary tube blood gas exchanger has been attempted by earlier investigators with varying degrees of success Analysis of the data and theoretical prediction of earlier researchers led us to conclude that a phenomenon other than ordinary diffusion was also occuring in the gas exchanger Figure 1 shows the data collected by Buckles (1, 2) using fresh human blood and his theoretical prediction It is evident in this figure that at the lowest flows the theoretical curve falls well below the data points Rotation induced diffusion has been suggested previously in the literature (3) although its existence in flowing blood has not been proven conclusively This paper presents a mathematical analysis of the gas transport phenomena including the diffusion augmentation due to the mixing effect of the rotating erythrocytes Blood is considered a fluid continuum with reversible gas sinks in instantaneous local equilibrium wi th the plasma surrounding thetn The equilibrium between the gas contained in the sinks and that dissolved in the plasma is given by the well known blood gas dissociation curves for oxygen (figure 2) as well as for carbon dioxide The resistance of the wall to the transport of the gases is also conSidered, although the axial transport in the wall is neglected