Influence of gravity on nonlinear transport in the planar Couette flow

Abstract

The effect of gravity on a dilute gas subjected to the steady planar Couette flow with arbitrarily large velocity and temperature gradients is analyzed. The results are obtained from the Bhatnagar–Gross–Krook kinetic model by means of a perturbation expansion in powers of the external field. The reference state corresponds to the pure (nonlinear) Couette flow solution, which retains all the hydrodynamic orders in the shear rate and the thermal gradient. To first order in the gravity field, we explicitly obtain the hydrodynamic profiles and the five relevant nonlinear transport coefficients; the shear viscosity η, the two viscometric functions Ψ1,2, and the two nonzero elements, κxy and κyy, of the thermal conductivity tensor. The results show that, in general, the influence of gravity on the rheological properties η and Ψ1,2 tend to decrease as the shear rate increases, while this influence is especially important in the case of the thermal conductivity coefficient, κyy, which measures the heat flux parallel to the temperature gradient.