Temperature jump and Knudsen layer in rarefied molecular gas

Abstract

The temperature jump problem in rarefied molecular (diatomic and polyatomic) gases is investigated based on a one-dimensional heat conduction problem. The gas dynamics is described by a kinetic model, which is capable of recovering the general temperature and thermal relaxation processes predicted by the Wang-Chang Uhlenbeck equation. Analytical formulations for the temperature jump coefficient subject to the classical Maxwell gas-surface interaction are derived via the Chapman-Enskog expansion. Numerically, the temperature jump coefficient and the Knudsen layer function are calculated by matching the kinetic solution to the Navier-Stokes prediction in the Knudsen layer. Results show that the temperature jump highly depends on the thermal relaxation processes: the values of the temperature jump coefficient and the Knudsen layer function are determined by the relative quantity of the translational thermal conductivity to the internal thermal conductivity; and a minimum temperature jump coefficient emerges when the translational Eucken factor is 4/3 times of the internal one. Due to the exclusion of the Knudsen layer effect, the analytical estimation of the temperature jump coefficient may possess large errors. A new formulation, which is a function of the internal degree of freedom, the Eucken factors, and the accommodation coefficient, is proposed based on the numerical results.