Heat and momentum transport far from equilibrium

Explicit expressions for the heat and momentum transport are given for a gas in a stationary state with temperature and velocity gradients. The results are obtained from a formally exact analysis of the normal solution to the Bhatnagar-Gross-Krook model for the nonlinear Boltzmann equation, and are not restricted to small gradients. The irreversible momentum and heat fluxes are found to be nonanalytic functions of the velocity gradients, indicating that the Chapman-Enskog expansion does not converge for this state. However, these fluxes are analytic in the temperature gradients; in particular, the heat flux is simply proportional to the temperature gradient so that Fourier's law applies even for large gradients. The space dependence of the thermodynamic and velocity fields is determined as a function of the interaction potential, and the results for Maxwell molecules and hard spheres are compared.