Non-classical thermal physics in force-driven micro-channel gas flows

Abstract

The fundamental physics of non-classical thermal characteristics in micro-channel gas flows is investigated on the basis of non-Fourier law embedded in moment equations derived from the kinetic Boltzmann equation. First, the effects of the force-stress coupling term on thermal behavior are examined in both Navier non-Fourier and non-Navier non-Fourier laws. It is shown that the ultimate source behind the non-monotonic temperature distribution is the force-stress coupling term in the constitutive equation of heat flux, irrespective of the constitutive equations of viscous stress, classical or non-classical. Second, the thermal characteristics such as the temperature and heat flux distributions for various Knudsen numbers are investigated in order to understand the complex interaction between the force and the rarefaction effects. It is shown that the central temperature reaches minimum in whole flow field after a critical Knudsen number in case of non-Navier non-Fourier law. Lastly, it is demonstrated that the force-stress coupling term in the non-Fourier law is solely responsible for the so-called Knudsen minimum of mass flow rate in the force-driven compressible Poiseuille gas flow, which is against intuition obtained from classical theory and indicates a dominant role of non-classical thermal physics in gas flow far from thermal nonequilibrium.