Dilute gas Couette flow: Theory and molecular dynamics simulation

Explicit analytic nonlinear laws of heat transport and of viscous flow are derived from Grad's approximate solution of Boltzmann's equation and they are shown to describe quite well the observations made in molecular dynamics simulations. With this aim a planar Couette flow is studied analytically and by means of microscopic molecular dynamics techniques for the case of a bidimensional gas of hard disks. The fluid develops a nonuniform temperature profile, shows a non-Newtonian behavior, and there is a heat current which obeys Fourier's law with a tensorial shear rate-dependent thermal conductivity.