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

Abstract

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.