Shear flow, viscous heating, and entropy balance from dynamical systems

A consistent description of a shear ow, the accompanied viscous heating, an d the associated entropy balance is given in the framework of a determinist ic dynamical system, where a multibaker dynamics drives two fields: the vel ocity and the temperature distributions. In an appropriate macroscopic limi t their transport equations go over into the Navier-Stokes and the heat con duction equation of viscous flows. The inclusion of an artificial heat sink can stabilize steady states with constant temperatures. It mimics a thermo stating algorithm used in non-equilibrium molecular-dynamics simulations.