  The Direct Simulation Monte Carlo method is applied to solve the Boltzmann
equation in the steady planar Couette flow for Maxwell molecules and hard
spheres. Nonequilibrium boundary conditions based on the solution of the
Bhatnagar-Gross-Krook (BGK) model for the Couette flow are employed to diminish
the influence of finite-size effects. Non-Newtonian properties are
characterized by five independent generalized transport coefficients: a
viscosity function, a thermal conductivity function, two viscometric functions,
and a cross coefficient measuring the heat flux orthogonal to the thermal
gradient. These coefficients depend nonlinearly on the shear rate. The
simulation results are compared with theoretical predictions given by the Grad
method and the BGK and the ellipsoidal statistical (ES) models. It is found
that the kinetic models present a good agreement with the simulation,
especially in the case of the ES model, while the Grad method is only
qualitatively reliable for the momentum transport. In addition, the velocity
distribution function is also measured and compared with the BGK and ES
distributions.
