Solution of the Krook kinetic equation model and non-equilibrium thermodynamics of a rarefied gas affected by a non-linear thermal radiation field

摘要

A new approach for studying the influence of a thermal radiation field upon a rarefied neutral gas is introduced. We insert the radiation field effect in the force term of the Boltzmann equation. In a frame co-moving with the fluid, the BGK (Bhatnager–Gross–Krook) model kinetic equation is applied an-alytically. The one-dimensional steady problem is studied using the Liu–Lees model. We apply the moment method to follow the behavior of the macroscopic properties of the gas, such as the temperature and concentra-tion. They are substituted into the corresponding two-stream Maxwellian distribution functions, permitting the investigation of the non-equilibrium thermodynamic properties of the system (gas + heated plate). The entropy, entropy flux, entropy production, thermodynamic forces and the kinetic coefficients are obtained. We verify the celebrated Onsager reciprocity re-lations for the system. The ratios between the different contributions of the internal energy changes based upon the total derivatives of the extensive pa-rameters are estimated via the Gibbs formula. The results are applied to the Helium gas for various radiation field intensities due to different plate tem-peratures. Figures illustrating the calculated variables are drawn to predict their behavior and the results are discussed.