  A consistent description of shear flow and the accompanied viscous heating as
well the associated entropy balance is given in the framework of a
deterministic dynamical system. A laminar shear flow is modeled by a
Hamiltonian multibaker map which drives velocity and temperature fields. In an
appropriate macroscopic limit one recovers the Navier-Stokes and heat
conduction equations along with the associated entropy balance. This indicates
that results of nonequilibrium thermodynamics can be described by means of an
abstract, sufficiently chaotic and mixing dynamics. A thermostating algorithm
can also be incorporated into this framework.
