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

Abstract

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.