Kinetic model for heat and momentum transport

Abstract

Expressions for the heat and momentum transport are obtained for a dilute gas in a steady state with both temperature and velocity gradients. The results are derived from a kinetic model recently proposed: the Liu model [Phys. Fluids A 2, 277 (1990)]. This model improves the well-known Bhatnagar-Gross-Krook (BGK) model equation. At a hydrodynamic level, the solution is characterized by a constant pressure, a linear profile of the flow velocity with respect to a space variable scaled with the local collision frequency, and a parabolic profile of the temperature with respect to the same variable. The shear viscosity and thermal conductivity coefficients are explicitly obtained. They are nonlinear functions of the shear rate and their only dependence on the temperature gradient is through their zero shear-rate values. In addition, the shear-rate dependence of the viscometric functions is also analyzed. A comparison with previous results derived from the BGK equation is carried out. © 1994 American Institute of Physics.