An extended macroscopic transport model for rarefied gas flows in long capillaries with circular cross section

Abstract

Pressure-driven and thermally driven rarefied gas flows in long capillaries with circular cross sections are investigated. For both Poiseuille and thermal transpiration flows, a unified theoretical approach is presented based on the linear form of regularized 13-moment (R13) equations. The captured nonequilibrium effects in the processes are compared to available kinetic solutions, and the shortcomings of classical hydrodynamics, i.e., the Navier–Stokes–Fourier equations, are highlighted. Breakdown of Onsager’s symmetry is proposed as a criterion to determine the range of applicability of extended macroscopic models. Based on Onsager’s reciprocity relation it is shown that linearized R13 equations provide agreement with kinetic data for moderate Knudsen numbers, Kn≤0.25. Two-way flow pattern and thermomolecular pressure difference in simultaneous pressure-driven and temperature-driven flows are analyzed. Moreover, second-order boundary conditions for velocity slip and temperature jump are derived for the Navier–Stokes–Fourier system. The proposed boundary conditions effectively improve classical hydrodynamics in the transition flow regime.