Constitutive relations associated with the Mott-Smith distribution function

It is shown that the distribution function assumed by Mott-Smith determines a unique relation between heat flux, stress, and fluid velocity given by q = (3/2)_τu, i.e., it provides a constitutive relation for heat flux, and it also determines a simple expression for this ratio of third-order central moments Q = (C³_{x) /} C_xC². These expressions allow the equation of transfer for c x2 to be cast in a form that yields a nonlinear constitutive relation for stress. The results obtained from the Mott-Smith ansatz are compared with the theory of Baganoff and Nathenson and results from a numerical solution of the Boltzmann equation for shock-wave structure obtained by Hicks and Yen.