KINETIC-MODEL FOR TRANSPORT AROUND UNIFORM SHEAR-FLOW

Expressions for the heat and momentum transport around the state of uniform shear flow are given for a dilute gas. The results are obtained from a kinetic model recently proposed: the Liu model. This model improves some insufficiencies of the well-known Bhatnagar, Gross and Krook (BGK) equation. It is shown that the coexistence between both velocity and temperature gradients is only possible for interaction models with uniform collision frequency. In this case, the heat flux verifies a generalized Fourier's law where the thermal conductivity tensor depends on the shear rate. When considering systems where the collision frequency is not uniform, a perturbation method around the shear flow state is proposed. The irreversible fluxes are evaluated explicitly up to first order in the expansion for Maxwell molecules. The transport coefficients obtained are highly nonlinear functions of the shear rate. The results are compared with those previously obtained from the BGK and Boltzmann equations.