scholarly journals A new continuum model for general relativistic viscous heat-conducting media

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190175 ◽  
Author(s):  
E. Romenski ◽  
I. Peshkov ◽  
M. Dumbser ◽  
F. Fambri
Keyword(s):  
Hyperbolic Equations ◽  
Transport Coefficients ◽  
Irreversible Thermodynamics ◽  
Point Of View ◽  
Order System ◽  
Irreversible Processes ◽  
Heat Conducting ◽  
Causality Principle ◽  
Viscous Heat ◽  
Non Equilibrium

The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein’s special relativity and the Euler–Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as viscosity, heat conductivity, etc., are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

scholarly journals MATHEMATICAL MODELING AND CALCULATION OF GAS DYNAMIC CHARACTERISTICS OF FREE THERMAL AIR VORTEX

2017 ◽  
pp. 93-98
Author(s):  
D. D. Barannikova ◽  
A. G. Obukhov
Keyword(s):  
Gas Flow ◽  
Local Heating ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Point Of View ◽  
Underlying Surface ◽  
Heat Conducting ◽  
Gas Dynamics Equations ◽  
Viscous Heat ◽  
Flow Formation

The article analyzes experimental and analytical studies of ascending swirling air flows. In experimental works such flows are considered from the point of view of the direction of twist, the thermal regimes of heating the underlying surface, the estimation of integral parameters, the method of influence on them, and various methods of visualization. In analytical papers, by constructing solutions of the system of gas dynamics equations, the emergence of a twist of the corresponding direction is proven when there is a gas flow into a vertical cylinder of nonzero radius. In addition, in the numerical modeling of thermal ascending swirling flows, a feature was observed in the behavior of a moving gas at the initial moments of flow formation when the underlying surface was heated locally. This feature consists in the appearance on the boundary of the heating region of counter propagating gas flows with opposite directions of twist. The paper presents the results of numerical simulation of three-dimensional unsteady flows of a compressible viscous heat-conducting gas in thermal swirled vortices with local heating of the underlying surface, taking into account the action of gravity and Coriolis forces.

Nonlinear transport coefficients and plane Couette flow of a viscous, heat-conducting gas between two plates at different temperatures

1987 ◽  
Vol 65 (9) ◽  
pp. 1090-1103 ◽  
Author(s):  
Byung Chan Eu ◽  
Roger E. Khayat ◽  
Gert D. Billing ◽  
Carl Nyeland
Keyword(s):  
Boltzmann Equation ◽  
Couette Flow ◽  
Transport Coefficients ◽  
Heat Conducting ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
Plane Couette Flow ◽  
The Boltzmann Equation ◽  
Viscous Heat ◽  
Different Temperatures

By using the example of plane Couette flow between two plates maintained at different temperatures, we present a method of calculating flow profiles for rarefied gases. In the method, generalized hydrodynamic equations are derived from the Boltzmann equation. They are then solved with boundary conditions calculated by taking into consideration the interfacial interaction between the surface and the gas molecule. The nonlinear transport coefficients employed in the generalized hydrodynamic equations are obtained from the Boltzmann equation by means of the modified-moment method. The profiles calculated are in agreement with the Liu–Lees theory as long as the boundary values are in agreement. It is found that the viscous-heating effect has a significant influence on the temperature and velocity profiles. The nonlinearity of transport coefficients also has significant effects on the profiles as the Knudsen and Mach numbers increase.

ASYMPTOTIC BEHAVIOR OF THE MOTION OF A VISCOUS HEAT-CONDUCTING ONE-DIMENSIONAL GAS WITH RADIATION: THE PURE SCATTERING CASE

2013 ◽  
Vol 11 (01) ◽  
pp. 1350003 ◽  
Author(s):  
BERNARD DUCOMET ◽  
ŠÁRKA NEČASOVÁ
Keyword(s):  
Large Time ◽  
Transport Coefficients ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Large Time Behavior ◽  
Heat Conducting ◽  
Time Behavior ◽  
Static State ◽  
Viscous Heat ◽  
Initial Boundary Value

We study the large-time behavior of the solution of an initial-boundary value problem for the equations of 1D motions of a compressible viscous heat-conducting gas coupled with radiation through a radiative transfer equation. Assuming only scattering processes between matter and photons (neglecting absorption and emission) and suitable hypotheses on the transport coefficients, we prove that the unique weak solution of the problem converges toward the static state.

scholarly journals Conservation-dissipation formalism of irreversible thermodynamics

2015 ◽  
Vol 40 (2) ◽  
Author(s):  
Yi Zhu ◽  
Liu Hong ◽  
Zaibao Yang ◽  
Wen-An Yong
Keyword(s):  
Evolution Equations ◽  
Maxwell Fluid ◽  
Irreversible Thermodynamics ◽  
Rigid Bodies ◽  
Heat Fluxes ◽  
Coarse Grained ◽  
Irreversible Processes ◽  
State Variables ◽  
Long Time ◽  
Non Equilibrium

AbstractWe propose a conservation-dissipation formalism (CDF) for coarse-grained descriptions of irreversible processes. This formalism is based on a stability criterion for non-equilibrium thermodynamics. The criterion ensures that non-equilibrium states tend to equilibrium in long time. As a systematic methodology, CDF provides a feasible procedure in choosing non-equilibrium state variables and determining their evolution equations. The equations derived in CDF have a unified elegant form. They are globally hyperbolic, allow a convenient definition of weak solutions, and are amenable to existing numerics. More importantly, CDF is a genuinely nonlinear formalism and works for systems far away from equilibrium. With this formalism, we formulate novel thermodynamics theories for heat conduction in rigid bodies and non-isothermal compressible Maxwell fluid flows as two typical examples. In these examples, the non-equilibrium variables are exactly the conjugate variables of the heat fluxes or stress tensors. The new theory generalizes Cattaneo's law or Maxwell's law in a regularized and nonlinear fashion.

Non-Equilibrium Thermodynamics

1994 ◽  
Author(s):  
Antony N. Beris ◽  
Brian J. Edwards
Keyword(s):  
Time Scales ◽  
Irreversible Thermodynamics ◽  
Transport Processes ◽  
Irreversible Processes ◽  
Internal Variables ◽  
Equilibrium Thermodynamics ◽  
System P ◽  
The Subject ◽  
Thermodynamic Variables ◽  
Non Equilibrium

After having devoted five chapters of this book to the discussion of equilibrium thermodynamics and conservative dynamic phenomena, it is now high time that we entered into the realm of irreversible transport processes. As mentioned in chapter 1, most of the physical systems which engineers wish to model exhibit dissipative phenomena. Therefore, although the techniques touched upon in the previous chapters are mathematically profound and well-suited for diverse analyses for conservative systems, it is in this chapter and the next that the major engineering applications will find their foundation. Granted, in describing irreversible phenomena on the continuum level a certain amount of phenomenology is necessarily introduced; yet we hope to illustrate here how the application of thermodynamic knowledge to the irreversible system can reduce this phenomenology to the bare minimum. The objective of this chapter is similar to that of chapter 4; we wish to present a brief, yet sufficiently thorough, discussion concerning the theory of non-equilibrium thermodynamics applied to irreversible processes. There already exist several outstanding references on the subject [De Groot and Mazur, 1962; Yourgrau et al., 1966; Prigogine, 1967; Gyarmati, 1970; Woods, 1975; Lavenda, 1978; Truesdell, 1984]. Thus, the objective of our discussion here is mainly to introduce the principles that are subsequently used to formulate the dissipative bracket, as outlined in the next chapter. Moreover, the presentation of the subject is biased towards the presentation of the concepts that we consider as most helpful to continuum modeling. For example, the notion of internal variables is introduced early on, in §6.2. As we shall see, the inclusion of internal variables in the non-equilibrium description of the system has profound implications concerning the roles of the various thermodynamic variables and the definitions of the various state functions, in particular, the entropy. Indeed, the definitions of these functions hinge upon the notion of time scales which become of chief importance in the discussion of irreversible thermodynamics. In the philosophy of equilibrium thermodynamics, it is assumed that the time scale for changes in the system is sufficiently large as compared to the intrinsic time scales of any internal variables within the system.

scholarly journals Variational multi-fluid dynamics and causal heat conductivity

2009 ◽  
Vol 466 (2117) ◽  
pp. 1373-1387 ◽  
Author(s):  
N. Andersson ◽  
G. L. Comer
Keyword(s):  
Heat Conductivity ◽  
Fluid Model ◽  
Thermal Relaxation ◽  
Irreversible Thermodynamics ◽  
Heat Propagation ◽  
Point Of View ◽  
Heat Conducting ◽  
Massive Fluid ◽  
Non Local ◽  
Two Fluid Model

We discuss heat conductivity from the point of view of a variational multi-fluid model, treating entropy as a dynamical entity. We demonstrate that a two-fluid model with a massive fluid component and a massless entropy can reproduce a number of key results from extended irreversible thermodynamics. In particular, we show that the entropy entrainment is intimately linked to the thermal-relaxation time that is required to make heat propagation in solids causal. We also discuss non-local terms that arise naturally in a dissipative multi-fluid model, and relate these terms to those of phonon hydrodynamics. Finally, we formulate a complete heat-conducting two-component model and discuss briefly the new dissipative terms that arise.

scholarly journals A Priori Estimates of the Conjugate Problem Describing an Axisymmetric Thermocapillary Motion for Small Marangoni Number

2019 ◽  
pp. 483-495 ◽  
Author(s):  
Victor K. Andreev ◽  
Evgeniy P. Magdenko
Keyword(s):  
A Priori Estimates ◽  
Solid Wall ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Conjugate Problem ◽  
Point Of View ◽  
Heat Conducting ◽  
Priori Estimates ◽  
Viscous Heat

This paper is devoted to the study of equations solution describing the axisymmetric motion of a viscous heat-conducting liquid. The motion is interpreted as a two-layer flow of viscous heat-conducting liquids in a cylinder with a solid wall and a common movable non-deformable interface. From a mathematical point of view, the arising initial-boundary value problem is nonlinear and inverse. Under certain assumptions concerning to apply the problem is replaced by a linear one. As a result, the unimprovable uniform priori estimates for solutions of the problems posed are obtained

scholarly journals Theories and heat pulse experiments of non-Fourier heat conduction

2016 ◽  
Vol 7 (2) ◽  
pp. 150-166 ◽  
Author(s):  
Péter Ván
Keyword(s):  
Heat Conduction ◽  
Heat Pulse ◽  
Theoretical Background ◽  
Point Of View ◽  
Experimental Basis ◽  
Equilibrium Thermodynamics ◽  
Fourier Heat Conduction ◽  
Non Equilibrium

Abstract The experimental basis and theoretical background of non-Fourier heat conduction is shortly reviewed from the point of view of non-equilibrium thermodynamics. The performance of different theories is compared in case of heat pulse experiments.

Spin down problem of rotating stratified fluid in thermally insulated circular cylinders

1969 ◽  
Vol 37 (4) ◽  
pp. 689-699 ◽  
Author(s):  
Takeo Sakurai
Keyword(s):  
Steady State ◽  
Time Scale ◽  
Boussinesq Approximation ◽  
Circular Cylinders ◽  
Heat Conducting ◽  
Quasi Steady State ◽  
Homogeneous Fluid ◽  
Time Duration ◽  
Viscous Heat ◽  
Final Approach

A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing thermally insulated circular cylinder under the existence of stable distribution of the temperature is investigated within the framework of the Boussinesq approximation for a time duration of the order of the homogeneous-fluid spin down time in order to resolve the Holton-Pedlosky controversy. The explicit expression of the solution is obtained by the standard method and Holton's conclusion is confirmed. The secondary meridional current induced by the Ekman layers spins the fluid down to a quasi-steady state within the present time scale. However, unlike the homogeneous case, the quasi-steady state is not one of solid body rotation. The final approach to the state of rigid rotation is achieved via the viscous diffusion in the time scale of the usual diffusion time.

Sign in / Sign up

Export Citation Format

Share Document