Francesca Brini

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.

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.