Collocation solution of creeping newtonian flow through periodically constricted tubes with piecewise continuous wall profile

Abstract

AbstractA collocation solution of creeping Newtonian flow through periodically constricted tubes is obtained. The profile of the wall of the type of tube considered is piecewise continuous, composed of symmetric parabolic segments. A transformation of the domain of interest into a rectangular one is obtained, which allows satisfaction of all boundary conditions. The collocation solution gives the stream function in terms of the new independent variables and can easily be converted to the original cylindrical coordinates. Axial and radial velocity components are obtained in analytical form, and the pressure drop is calculated from a volume integration of the viscous dissipation function as well as from line integration of the Navier‐Stokes equation. The results are compared with the finite‐difference solution by Payatakes et al. (1973b) and are found in good agreement. Differences between the two solutions are attributed mainly to discretization error in the finite‐difference solution. The analytical expressions obtained from the collocation solution can be used together with porous media models of the constricted unit cell type for the modeling of processes taking place in granular porous media.