Elvira Barbera

On the Temperature of a Rarefied Gas in Non‐Equilibrium

This paper addresses the problem of the proper definition of temperature of a gas in non‐equilibrium. It shows that the mean kinetic energy of the atoms of a rarefied gas is not a good measure for thethermodynamic temperature, because in general it jumps at a wall, and because it is non‐monotone in a one‐dimensional process of stationary heat conduction. The jump of the ‘kinetic temperature’ is calculated and found to be about 5 K in a rarefied gas. The basis for the calculations is provided by the arguments of extended thermodynamics of 14 moments. An essential tool is the minimax principle of entropy production recently postulated by Struchtrup Weiss [1], because it furnishes one important boundary condition.Sommario. Il lavoro riguarda la corretta definizione della temperatura di un gas in condizioni di non‐equilibrio. Si mostra come l’energia cinetica media degli atomi di un gas rarefatto non sia una buona misura della temperatura termodinamica poiché in generale, essa risulta discontinua su una parete e non‐monotona in un processo unidimensionale di conduzione stazionaria del calore. Viene calcolato il salto della ‘temperatura cinetica’ che risulta pari a circa 5 K in un gas rarefatto. La base per il calcolo è fornita dal contesto della termodinamica estesa di 14 momenti. Uno strumento essenziale è rappresentato dal principio di minimax di produzione di entropia recentemente postulato da Struchtrup and Weiss [1], che fornisce un’importante condizione alcontorno.

Some non-linear effects of stationary heat conduction in 3D domains through extended thermodynamics

We describe stationary heat conduction in an ideal gas at rest between three-dimensional manifolds. To this aim, we refer to the field equations of extended thermodynamics. The solution is determined through a 3rd-order asymptotic expansion with respect to the Knudsen number. As illustrative examples, we show the results for a gas enclosed between two non-coaxial circular cylinders or two confocal elliptical cylinders. With respect to the classical thermodynamics, we obtain corrections on the temperature, stress tensor and heat flux, that give rise to more complex behaviors of these variables. The dependence on the parameters is also analyzed.

Heat Conduction in a Non-Inertial Frame

Stationary heat conduction is considered in a monatomic gas between two co-axial cylinders which are at rest in a non-inertial frame. Instead of the usual Navier-Stokes-Fourier theory we employ the more reliable 13-moment theory of extended thermodynamics. Three surprising observations are made: There is a tangential heat flux between the cylinders. No rigid rotation of the heat conducting gas is possible. There is a normal pressure field in the axial direction.

A two or three compartments hyperbolic reaction-diffusion model for the aquatic food chain.

Two hyperbolic reaction-diffusion models are built up in the framework of Extended Thermodynamics in order to describe the spatio-temporal interactions occurring in a two or three compartments aquatic food chain. The first model focuses on the dynamics between phytoplankton and zooplankton, whereas the second one accounts also for the nutrient. In these models, infections and influence of illumination on photosynthesis are neglected. It is assumed that the zooplankton predation follows a Holling type-III functional response, while the zooplankton mortality is linear. Owing to the hyperbolic structure of our equations, the wave processes occur at finite velocity, so that the paradox of instantaneous diffusion of biological quantities, typical of parabolic systems, is consequently removed. The character of steady states and travelling waves, together with the occurrence of Hopf bifurcations, is then discussed through linear stability analysis. The governing equations are also integrated numerically to validate the analytical results herein obtained and to extract additional information on the population dynamics.

Stationary heat transfer in helicoidal flows of a rarefied gas

The paper focuses on a stationary problem in a rarefied gas confined between two coaxial cylinders kept at different constant temperatures. It is assumed that the external cylinder is at rest, while the internal one rotates around its axis and contemporaneously moves upwards with a constant axial velocity, so that a helicoidal motion of the fluid is generated. The equations of Rational Extended Thermodynamics are introduced to study the physical effects due to the combination of both helicoidal flow and heat transfer. It turns out that, although only a radial temperature gradient is prescribed, both the tangential and the axial components of the heat flux do not vanish. Moreover, all the components of the stress tensor are not null, even though the radial and the axial velocity of the gas depend only on the radial coordinate. The results are compared with the prediction of the corresponding Classical Thermodynamics model and significative differences are observed. The role of the helicoidal motion is also analyzed through a comparison with the cases of only rotation or only axial flows.

Non-isothermal axial flow of a rarefied gas between two coaxial cylinders

A stationary problem of heat transfer in a rarefied gas confined between two coaxial cylinders is presented. The two cylinders are maintained at two different constant temperatures, so that a radial temperature gradient is created. The external cylinder is at rest, while the internal one moves in the axial direction with a constant velocity. A flow of the gas in the z -direction, orthogonal to the temperature gradient, is created by the motion of the internal boundary. Instead of the classical Navier-Stokes and Fourier theory, the field equations of extended thermodynamics with 13 moments are used in order to describe this physical problem. It turns out that, although only a radial temperature difference is imposed, the heat flux presents also an axial component. Moreover, some components of the stress tensor do not vanish, even though the axial velocity of the gas depends only on the radial coordinate r . The solution here obtained is compared with the classical one. Furthermore, the dependence of the solution on the boundary velocity is investigated.

Some 2D heat transfer problems in metals described by a linearized extended thermodynamics model

We describe qualitatively some 2D stationary problems for metal electrons in the presence of a temperature gradient and a magnetic field. To this aim we refer to a linearized Extended Thermodynamics model that allows a semianalytical construction of the solutions. The results are in agreement with the thermomagnetic effects already known in the literature.

WEAKLY NONLINEAR INTERACTION OF TWO WAVES IN RADIATIVE GASDYNAMICS

The interaction of two weakly nonlinear waves in radiative gasdynamics is investigated following the perturbation analysis developed by He and Moodie. Explicit solutions are given and the two waves interactions are graphically shown.