Stationary heat transfer in helicoidal flows of a rarefied gas

¹ Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina V.le F. D'Alcontres 31, 98166 Messina, Italy
² Department of Mathematics and Alma Mater Research Center on Applied Mathematics AM 2, University of Bologna via Saragozza 8, 40123 Bologna, Italy

Received: 17 November 2017
Accepted: 1 January 2018

Abstract

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.