Equations for viscous gas mixture flows in curved flat channels with variable cross section

The curvilinear orthogonal system of coordinates adapted to the curved flat channel with variable cross section have been taken to writing system of hydrodynamic equations of viscous multicomponent chemical reacting gas flows in smooth ducts. The whole system of Navier–Stocks equations in adaptable system of coordinates have been transformed into parabolized type equations using common rules and laminar model of flows. In contrast to the well-known parabolized models the present one consideres the finite curvature of channel axis as well as the curvature of wall. As result the equations have got additional terms which depend on the curvature radius. In special cases the transform of the curvalinear coordinates have been working out in explicit form. When curvature of axis is much smaller than halfwide of channel our equations are transformed into those for the flow through smooth duct with variable cross sections. If the longitudinal curvature of the walls is small the equations coincide with the slender channel approximation ones [1].