Nonlinear dissipation and nonequilibrium gas flows.

Abstract

Rayleigh and Onsager showed that in the regime where the flows are small and the thermodynamic forces vary slowly, the entropy generation rate is linearly related to the flows, and the flows are related to the gradient of the forces. Hence, the Rayleigh-Onsager dissipation is only applicable to linear irreversible thermodynamics. We introduce the extension of Rayleigh-Onsager dissipation to highly nonlinear dissipation to treat nonlinear irreversible thermodynamics. This extension fulfills the positive entropy generation criterion. To demonstrate this nonlinear dissipation, we apply it to obtain the generalized hydrodynamics from the kinetic theory according to Eu theory. Specifically, it provides an alternative evolution for a stress tensor and heat flux. The challenging problems of nonlinear irreversible thermodynamics, as represented by nonequilibrium flows, are investigated. The result implies that this study provides a promising alternative to obtain a unified framework for modeling both equilibrium and nonequilibrium gas flows.