International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 4, Pages 765-784
doi:10.1155/S016117128400079X
Asymptotic solution of the low Reynolds-number flow between two co-axial cones of common apex
Mechanical Engineering Department, Faculty of Engineering, Cairo university, Cairo, Egypt
Received 29 March 1979
Copyright © 1984 M. A. Serag-Eldin and Y. K. Gayed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The paper is concerned with the axi-symmetrlc, incompressible, steady, laminar and Newtonian flow between two, stationary, conical-boundaries, which exhibit a common apex but may include arbitrary angles. The flow pattern and pressure field are obtained by solving the pertinent Navier-Stokes' equations in the spherical coordinate system. The solution is presented in the form of an asymptotic series, which converges towards the creeping flow solution as a cross-sectional Reynolds-number tends to zero. The first term in the series, namely the creeping flow solution, is given in closed form; whereas, higher order terms contain functions which generally could only be expressed in infinite series form, or else evaluated numerically. Some of the results obtained for converging and diverging flows are displayed and they are demonstrated to be plausible and informative.