On the thermodynamics of nonlinear constitutive relations in gasdynamics

Thermodynamic arguments are used to derive the nonlinear Burnett equations for a monatomic gas, thus avoiding the complicated kinetic theory by which the equations were discovered and which somewhat obscures the origin of the various terms in the equations. Expressions are given for the entropy, its flux, and its production rate correct to second-order in Knudsen number. The theory involves five phenomenological parameters; and as there are 11 coefficients in the second-order terms of Burnett's equations, it is possible to deduce several necessary constraints between these coefficients. The present theory is used to draw some general conclusions concerning the second law of thermodynamics.