Nonlinear transport laws for low density fluids

Hydrodynamics equations derived directly from Boltzmann’s equation and specialized to sheared planar flow are shown to yield approximate nonlinear laws of heat transport and of viscous flow. The law of viscous flow predicts non-Newtonian effects including shear thinning and the law of heat transport is more general than Fourier’s law: it is not linear and it implies heat flow parallel to the isotherms. These nonlinear transport laws are faithfully corroborated by molecular dynamic simulations based on straightforward Newtonian dynamics.