A perturbation solution for compressible viscous channel flows

The two-dimensional compressible Navier-Stokes equations are solved by a perturbation expansion in the parameter (Mach number)²/Reynolds number. A fortieth-order solution is generated by a computer algorithm. These series are then summed as convergent series of diagonal Padé approximants. Effectively-exact solutions have been found for Reynolds numbers between zero and 1000 and a range of subsonic Mach numbers in the case of fully-developed isothermal flow between parallel side walls. Choking of the flow is shown to occur for a moderate value of channel Reynolds number. The two-dimensional velocity and pressure fields are obtained. The engineering assumption that friction factor is sensibly independent of Mach number may lead to significant underprediction of head loss in the laminar flow regime.