Showing papers on "Transport phenomena published in 1976"
TL;DR: In this article, the authors apply virtual dissipation to nonlinear thermomechanics of continua with dissipation and heat conduction and derive field equations, constitutive equations and Lagrangian equations with generalized coordinates.
Abstract: A principle of virtual dissipation generalizing d'Alembert's principle to nonlinear irreversible thermodynamics provides a unifying foundation which leads to an extremely general variational-Lagrangian analysis of dissipative phenomena. Thus a synthesis is achieved between thermodynamics and classical mechanics. The present paper applies this principle to the nonlinear thermomechanics of continua with dissipation and heat conduction. Field equations, constitutive equations and Lagrangian equations with generalized coordinates are derived for nonlinear thermo- viscoelastcity, nonlinear thermoelasticity and heat conduction, plasticity, and com- pressible heat conducting fluids with Newtonian and non-Newtonian viscosity. The thermodynamics of instability is also analyzed from the same fundamental viewpoint. 1. Introduction. A Lagrangian-variational approach to irreversible thermo- dynamics was initiated by the author in 1954-55 (I, 21. It was developed mainly in the context of linearity and applied to thermoelasticity (3, 41 viscoelasticity (l, 2, 41, porous media (5), and initially stressed porous and continuous media (6, 71. The appli- cability of these methods to nonlinear problems was demonstrated in a variety of special cases, such as heat transfer (8), porous solids (9) and nonlinear thermoelasticity (lo). A treatment of nonlinear viscoelasticity based on a Lagrangian thermodynamic approach has also been presented by Schapery (ll). The theory embodied in the publications cited above provides a unified analysis based on Lagrangian formalism and generalized coordinates. Among many advantages, the equations have the same form in any coordinate system. Thus basic reciprocity properties of linear dissipative systems are immediately evident for a very large class of phenomena and boundary conditions. As a consequence, the proof of reciprocity properties does not have to be established for each particular case. Basic properties for systems with heredity are also obtained from the concept of internal coordinates and a general expression derived for the associated operator formalism. The corresponding
22 citations
TL;DR: In this article, the authors studied the transport phenomena occurring during the heating of a nonagitated liquid in a closed cylindrical container and revealed the existence of a boundary layer flow at the vertical sidewall of the container, together with a stratified core in the upper part and a perfectly mixed, unstratified region in the lower part.
Abstract: Transport phenomena occurring during the heating of a non-agitated liquid in a closed cylindrical container were studied. Existing literature on this and analogous problems is briefly reviewed. Special attention is devoted to studies on natural convection in environments of non-uniform temperature. Our experimental work revealed the existence of a boundary layer flow at the vertical sidewall of the container, together with a stratified core in the upper part and a perfectly mixed, unstratified region in the lower part of the container. For the heat transfer rate a dimensionless correlation is found revealing Nu to be approximately proportional to (GrPr)1/4. From the observed flow patterns and temperature profiles a simplified mathematical model is developed, with which the temperature stratification in the liquid during heating could be simulated. The model may be applied to conversion calculations of a first order chemical reaction (e.g. destruction of micro-organisms).
13 citations
TL;DR: In this paper, a finite-element numerical procedure is used for solving boundary value problems resulting from modeling of complex physical phenomena, such as heat flux from a dike and seawater intrusion in an aquifer.
Abstract: Deterministic mathematical modeling of complex geologic transport processes may require the use of odd boundary shapes, time dependency, and two or three dimensions. Under these circumstances the governing transport equations must be solved by numerical methods. For a number of transport phenomena a general form of the convective-dispersion equation can be employed. The solution of this equation for complicated problems can be solved readily by the finite-element method. Using quadrilateral isoparametric elements or triangular elements and a computational algorithm based on Galerkin's procedure, solutions to unsteady heat flux from a dike and seawater intrusion in an aquifer have been obtained. These examples illustrate that the finite-element numerical procedure is well suited for solving boundary-value problems resulting from modeling of complex physical phenomena.
10 citations
8 citations
01 Jan 1976
7 citations
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5 citations
TL;DR: In this paper, a fundamental inequality is derived for thermodynamic systems which exchange heat and mass with their surroundings, which is mainly a consequence of the Second Law of Thermodynamics.
Abstract: A Fundamental Inequality is derived for Thermodynamic Systems which exchange heat and mass with their surroundings. This inequality is mainly a consequence of the Second Law of Thermodynamics. It serves as a basis for the derivation of rather general constitutive equations which describe the heat and mass transfer of the system. We consider a multi-phase, multi-component thermodynamic system with internal energy U, volume V = const and masses Μί? i = 1 ... n. The system undergoes a thermodynamic process during which heat (dQ) at the temperature Te and mass dm*> = Σ dmP , α = 1 ... A i = l with temperature T, Pressure P, chemical potentials μ[, i = 1 ... n, specific enthalpy h and entropy s is transfered to it from its surroundings. For sake of simplicity we exclude chemical reactions among the components and neglect the influence of external forces on the system. The system is assumed to start its process at t = — °° in an equilibrium state Z~~ and to end up at t = OP in another equilibrium state Z. For such a process the Second Law of Thermodynamics reads [ 1—3]. Z* f\\C*\\ A S-S~> / {~^+ Σ sdm<>}. (1) Zle a=l Here S* is the (well defined) entropy of the system in the equilibrium states Z*, respectively. The inequality sign holds for both quasi-static-irreversible and natural processes, i. e. processes during which the system not only assumes equilibrium but also non-equilibrium states. The equality sign is valid for quasi-static-reversible processes only. The temperature Te is that of the surroundings of the system. J. Non-Equilib. Thermodyn., Vol. 1, 1976, No. 1
5 citations
01 Jan 1976
TL;DR: In this paper, the authors studied the effect of fluctuation in the output of solid state electronic devices (SSE devices) and showed that fluctuations can be present in SSE devices even if their frequency is not in the acoustic domain, and no sound waves are generated.
Abstract: Various fluctuations can be present in the output of solid state electronic devices. The study of fluctuation phenomena is important both for practical applications and theoretical considerations. Electrical fluctuations are known as noise in general, even if their frequency is not in the acoustic domain, and no sound waves are generated.
4 citations
TL;DR: A review of the literature on heat transfer can be found in this article, where a number of papers have been published in various fields of heat transfer during the 1970s and early '80s.
TL;DR: The Fontenay-aux-Roses code allows testing of the existing theories and deduction of empirical rules and coefficients and examples of a few applications of this code are given.
TL;DR: In this paper, the so-called bubbling and weeping effects observed with porous semihydrophobic fuel cell electrodes are discussed in terms of gas transport in porous media, and it is shown that the bubbling of gas on the electrolyte side can be accounted for by transport equations valid in the intermediate region between ordinary and Knudsen diffusion.
TL;DR: In this paper, a physical model based on the analysis of the physical properties of liquid surfaces and on the kinetic theory of gases and liquids is presented, which gives a detailed picture, on a molecular scale, of the phase transition and transport phenomena at the interface between liquid and vapour.
Abstract: This paper deals with a physical model, based on the analysis of the physical properties of liquid surfaces and on the kinetic theory of gases and liquids, which gives a detailed picture, on a molecular scale, of the phase-transition and transport phenomena at the interface between liquid and vapour. Some numerical calculations relating to water-vapour systems and comparisons with experimental results have been performed.
TL;DR: In this article, experimental data concerning Hall effect, Seebeck effect and electrical conductivity in bulk samples of Pb1−xCdxS solid solutions, in the temperature range 100-360 K, were presented.
TL;DR: In this article, a simplified yet adequate model for electrochemical transport, compatible with the practical model of mass transport generally adopted to solve engineering problems, is presented, and brief comparisons to alternative models are also included.
Abstract: Publisher Summary The chapter formulates a simplified yet adequate model for electrochemical transport, compatible with the practical model of mass transport generally adopted to solve engineering problems. For the purpose of elucidation, brief comparisons to alternative models are also included. Transport of ionic species is directly related to passage of electric current and to associated parameters like electric field, conductivity, mobilities, and transport numbers. The complete, quantitative description of electrochemical systems is composed of a number of algebraic and partial differential equations, their parameters, and their boundary conditions. Electrical charge is very simply related to atoms and molecules, and the use of molar units is most usual. As transport phenomena involve the fluid velocity, it is necessary in the description of mass transport to determine the velocity function from the fluid mechanical equations of continuity. The chapter presents general transport equation, electrical current by mass transport, and conservation of energy. Electrokinetic phenomena such as electroosmosis, electrophoresis, electroosmotic counterpressure, the Dorn effect, electrosorption, isoelectric point, and momentum transfer are also discussed. The chapter also presents the thermodynamic approach of electrochemical transport followed by the summarization of the Nemst–Einstein relation and generalization of Stefan–Maxwell equation.
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01 Jan 1976
01 Jun 1976
TL;DR: In this article, two dimensional PIC methods are used to simulate the flux limitation and thermal flux in simulations is shown to approach the theoretical value when the phenomena approaches the steady state.
Abstract: Laser energy absorbed in an irradiated pellet is converted to high energy parts of the electron distribution. The contribution of these electrons to the transport phenomena is investigated. The flux limited theory is discussed. Another theory is presented which limits electron thermal conduction due to ion acoustic instability. Two dimensional PIC methods are used to simulate the flux limitation. Initial calculations are given. Thermal flux in simulations is shown to approach the theoretical value when the phenomena approaches the steady state.
01 Jan 1976
TL;DR: The steady and one-dimensional heat conduction process is studied in this paper, where the authors present a precise derivation of the governing differential equations, and review the boundary conditions that must be imposed at phase interfaces.
Abstract: This chapter discusses the steady and one-dimensional heat conduction process. The chapter focusses on the simplest possible type of heat transfer process, that is, energy transport in the absence of convection and radiation, steady, and only one component of the heat flux vector being non-zero or one-dimensional. However, the practical applications of the process are significant. The chapter presents a precise derivation of the governing differential equations, and reviews the boundary conditions that must be imposed at phase interfaces. Problems in cylindrical and spherical coordinates are analyzed, and the use of extended surfaces (fins) to enhance overall heat transfer rates is presented. When the overall heat transfer rate is limited by a low rate of heat transfer between a solid surface and a surrounding fluid, extended surfaces , or fins, may often be used to improve the overall transfer rate .
TL;DR: In this article, a perturbation theory for transport phenomena in a simple fluid is applied to a real binary mixture, and the results are explicitly only for the diffusion coefficient, which is defined as the sum of the diffusion coefficients of all the components of the mixture.
01 Jan 1976
TL;DR: In this article, the authors provide an overview of the basic equations of momentum and energy transfer, including steady and transient heat conduction for a variety of important processes, and provide an expression for the total time derivative.
Abstract: This chapter provides an overview of the basic equations of momentum and energy transfer. It reviews both steady and transient heat conduction for a variety of important processes. Throughout the analysis of these problems, a variety of flux boundary conditions are encountered, which are often specified in terms of a film heat transfer coefficient. To carefully analyze systems in which fluid motion is taking place, one must understand some concepts of kinematics. The chapter discusses the time derivatives of point functions and time derivatives of volume integrals when the limits of integration are the functions of time. Study of the kinematics of point functions leads to an expression for the total time derivative. In the analysis of a continuous medium, there are two laws of mechanics, the linear momentum principle and the angular momentum principle. It must be remembered that for a continuum these two laws stand as separate fundamental postulates.