Quasi-onedimentional model for chemical reacting flows in curved smooth cylindrical channels with variable cross section

A multicomponent gas mixture flows through cylindrical geometry channel have being regarded taking into account chemical reactions in voluve, inject from surface, wall heat transfer, wall friction, gravitation force and variable cross section of tube. The curvalinear coordinates $(\eta,\xi)$ have been offered. The non-steady-state Navier–Stokes equations have been overaged over laternal coorinate line $\eta$, and resulting univariation equations are correct to $\varepsilon$ order, where a small parameter $\varepsilon$ is the ratio of tube radius $f(z)$ over longitudinal curvature of wall. Under not-too-hard restrictions on the shape of channel the conversion of curvalinear coordinates $(\eta,\xi)$ in terms of the cylindrical ones $(r,z)$ has been performed in explicit form. In special cases of either the constant cross section tube or the cone shape wall channel the averaged univariation equations are accurate (interaction with surface is absent). The system of overaged equations derived here for the mean values of flow contains the expresion for the effective sources. They are generated bythe interaction of flow with wall tube surface and may be determined using boundary conditions on surface, in particularly for inject, heat transfer, wall friction ones.