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 the ratio of third-order central moments Q = 〈C x3 〉 / 〈C x C 2〉. These expressions allow the equation of transfer for cx2 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.