Slow flows of a slightly rarefied gas under high thermal stresses are considered. The correct fluid-dynamic description of this class of flows is based on the Kogan--Galkin--Friedlander equations, containing some non-Navier--Stokes terms in the momentum equation. Appropriate boundary conditions are determined from the asymptotic analysis of the Knudsen layer on the basis of the Boltzmann equation. Boundary conditions up to the second order of the Knudsen number are studied. Some two-dimensional examples are examined for their comparative analysis. The fluid-dynamic results are supported by numerical solution of the Boltzmann equation obtained by the Tcheremissines projection-interpolation discrete-velocity method extended for nonuniform grids. The competition pattern between the first- and the second-order nonlinear thermal-stress flows has been obtained for the first time.
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