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.
|Number of pages||1|
|Journal||Physics of Fluids|
|Early online date||17 Mar 2022|
|Publication status||E-pub ahead of print - 17 Mar 2022|