Study of the Kinetic Anomalous Transport Effects in Nonequilibrium Flows

Abstract

AbstractThe second law of thermodynamics is one of the basic physical principals. The expression of the law in the macroscopic thermodynamics is the well-known Fourier equation. However, the question can be asked whether the validity of this equation for microscopic scales is confirmed by the kinetic description by means of the Boltzmann and other equations. We introduce the new classes of flows caused by nonequilibrium distribution functions, in other words, on the microscopic level related to molecular velocity (or inner energy) distributions. These nonequilibrium flows are realized by introducing new types of boundary conditions. For these flows, the Fourier equation for the thermal conduction is invalid (the Newton-Stokes relationships for the stress transport are also invalid for some physical situations). The anomalous nonclassical transport effects, in which in fact negative viscosity and thermal conductivity coefficients appear, are observed in computer simulations on the basis of direct solutions of the Boltzmann kinetic equation. The validity of results is verified by comparison with the simulations by means of a popular Direct Simulation Monte Carlo (DSMC) method, and the results are found to be in good agreement. The second law of thermodynamics is treated in terms of the H-theorem, and it is valid. Although Fourier equation in the scales of the mean free path can be invalid, the Clausius formulation of the second law can be true—as heat is transferred from a cooler region of the flow to a warmer one, the nonequilibrium boundary conditions must be maintained that requires permanent energy flux and provides the total increase of entropy. Possible experiments for testing the effects are also discussed.KeywordsNonequilibrium flowsBoltzmann equationAnomalous transfer