Frame dependence of stationary heat transfer in an inert mixture of ideal gases

Abstract

This paper is devoted to the study of a stationary heat transfer problem in an inert binary mixture of ideal gases. The mixture is enclosed between two coaxial cylinders, kept at two different constant temperatures and at rest in a non-inertial frame. In particular, the frame is assumed to rotate with a constant angular velocity around the cylinder axes. The phenomenon is described by the linearized equations of extended thermodynamics with 13 moments. Integration of the field equations requires the assignment of non-controllable boundary values, which are determined through a fluctuation principle. It turns out that the temperature field presents boundary layers. Moreover, in agreement with the predictions of the kinetic theory, the tangential components of the heat and of the diffusion fluxes cannot vanish. We also show that the mixture and its constituents cannot be at rest in the rotating frame. An analysis is proposed concerning the combined effects of thermo-diffusion and rotation in the separation of mixture components. A comparison between classical and extended thermodynamics predictions is also proposed.