Nonlinear transport coefficients from Grad’s 13–moment approximation

In this work we use Grad’s 13–moment approximation to study a stationary shock wave in dilute gases. The conservation equations valid across the shock wave profile depend on the constitutive relations for the viscous tensor and the heat flux. The Grad’s 13-moment equations are taken to obtain the set of constitutive equations and the conservation equations are closed and solved. In addition, such constitutive equations can be written in terms of nonlinear transport coefficients depending on the velocity gradient. Their structure shows that the temperature gradient and the gradient of velocity produce non-trivial contributions in the heat flux as well as in the viscous tensor. A comparison with experiments and some other models is done.