Viscous Gas Flow between Vertical Walls

Abstract

A new solution for the Navier–Stokes equations has been found for a plane steady-state shear flow of a viscous gas in the gravity field between two vertical walls. For the temperature dependence of the viscosity factor, Sutherland’s formula is accepted; for the heat conductivity factor, two formulas with the same accuracy are used: a known formula for low temperatures (170–1000 K) and a first-proposed formula for high temperatures (800–1500 K). In each of these temperature ranges, a general solution for the Navier–Stokes equations has been obtained. The solution is expressed in terms of a function which satisfies an ordinary second order differential equation having different forms for low and high temperatures depending on the chosen formula for heat conductivity. For low temperatures, the solution of this equation is obtained numerically; for high temperatures, owing to using the new formula for heat conductivity, analytically. Examples of exact solutions are presented.