Derivation of the equations of slow nonisothermal gas flows

In recent years, some new phenomena have been predicted theoretically on the basis of the Burnett approximation. These include thermal-stress and concentration-stress convection [1–3], and also effects due to the influence of a magnetic field in a multiatomic gas (viscomagnetic heat flux, etc., [4]). It has been shown theoretically (see [5]) that under certain conditions various terms of the Burnett approximation must be taken into account in the expression for barodiffusion. The conclusions relating to a viscomagnetic heat flux have recently been confirmed experimentally [4]. The predicted phenomena follow rigorously from the Burnett equations. However, many hydrodynamicists adopt a sceptical attitude to these equations, which is due partly perhaps to attachment to the classical Navier-Stokes equations, which have served theoreticians without fail for a century and a half. In this connection, we discuss the evolution of ideas relating to the validity of the Burnett approximation. We discuss the minimal assumptions which must be made in order to derive the equations of slow [Reynolds number R = 0(1)], essentially nonisothermal [ ln T = 0(1)] flows of a gas as a continuous medium (Knudsen number K O) in the case when the derivatives of the thermal Burnett stresses in the momentum equation have the same order of magnitude as the Euler and Navier-Stokes terms of this equation [1–3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 77–84, November–December, 1979.We thank G. I. Petrov and L. I. Sedov for discussions that stimulated the above analysis.