A perturbation solution for compressible viscous channel flows
Abstract
The twodimensional compressible NavierStokes equations are solved by a perturbation expansion in the parameter (Mach number)squared/Reynolds number. A 40thorder solution is generated by a computer algorithm. These series are then summed as convergent series of diagonal Pade approximants. Effectivelyexact solutions have been found for Reynolds numbers between zero and 1000, and a range of subsonic Mach numbers, in the case of fullydeveloped isothermal flow between parallel side walls.Choking of the flow is shown to occur for a moderate value of channel Reynolds number. The twodimensional velocity and pressure fiels 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.
 Publication:

Journal of Engineering Mathematics
 Pub Date:
 1987
 DOI:
 10.1007/BF00127695
 Bibcode:
 1987JEnMa..21...69S
 Keywords:

 Channel Flow;
 Compressible Flow;
 Perturbation Theory;
 Viscous Flow;
 Friction Factor;
 Low Reynolds Number;
 Mach Number;
 NavierStokes Equation;
 Pade Approximation;
 Fluid Mechanics and Heat Transfer