boundary value problem in extended thermodynamics - one-dimensional steady flows with heat conduction

One-dimensional steady flows with heat conduction, treated by the 13moment theory of extended thermodynamics are considered. The usual well-posed boundary conditions for the corresponding problems in the Navier-Stokes-Fourier (NSF) theory are insufficient to give unique solutions. In order to have unique physically sensible solutions, minimization of the deviation of iterative approximations from the exact solutions, proposed in [1], is used as a criterion. Moreover, the solutions are shown to be invariant with respect to change of consistent boundary conditions - a requirement abide by our physical intuition. In the problems of plane shearing flow and Couette flow, the minimization with respect to two uncontrollable parameters is involved. The examples are carried out numerically, and the results are compared with the classical results of NSF theory.