The steady-state one-dimensional flow of a gas between two parallel plates moving with relative velocity and maintained at different temperatures is examined on the basis of the nonlinear Bhatnagar-Gross-Krook (BGK) model equation, subject to Maxwell diffuse boundary conditions. The computational scheme is based on the discrete velocity method. Results are provided for the bulk quantities of the flow in the whole range of the Knudsen number from the free molecular through the transition and slip regimes all the way up to the hydrodynamic limit. Several interesting issues related to the combined momentum and heat transfer effects are examined including the presence of a heat flux parallel to the plates, induced by the shear flow. This is a cross effect, which is absent in the Navier-Stokes-Fourier regime. The validity of the results is confirmed in several ways including the recovery of the analytical solutions at the free molecular limit.

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