Friction dominated, subsonic compressible flow in channels of slowly varying cross section

Abstract

Abstract Friction dominated, subsonic compressible flow in micro-channels of slowly varying cross-section is treated by developing a perturbation scheme which yields equations of “lubrication” approximation as the first order one. In this context several characteristic problems are encountered, such as isothermal flow, non-isothermal flow with prescribed wall temperature, and non-isothermal flow with prescribed wall heat flux, which includes the adiabatic wall problem as a special case. In all these problems pressure drops to zero while velocity components increase indefinitely at a finite distance along the channel – the phenomenon called “mathematical” choking observed for the first time in isothermal flow between parallel side walls, Schwartz, L.W., 1987. A perturbation solution for compressible viscous channel flows. J. Engrg. Math. 21, 69–86. The problem with prescribed wall heat flux is characterised, as by Shajii, A., Freidberg, J.P., 1996. Theory of law Mach number compressible flow in a channel. J. Fluid. Mech. 313, 131–145, by the existence of a critical heat flux above which the steady flow cannot be maintained. For the same mass flow rate this flux is considerably greater in divergent channels, than in convergent ones. These and other results obtained show how the prevailing viscosity may dramatically alter the flow characteristics in the problem considered, in comparison with more conventional high Reynolds number flows.