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RESEARCH PAPERS

A Contribution to the Numerical Solution of Developing Laminar Flow in the Entrance Region of Concentric Annuli With Rotating Inner Walls

[+] Author and Article Information
J. E. R. Coney, M. A. I. El-Shaarawi

Department of Mechanical Engineering, University of Leeds, Leeds, England

J. Fluids Eng 96(4), 333-340 (Dec 01, 1974) (8 pages) doi:10.1115/1.3447166 History: Received February 19, 1974; Online October 12, 2010

Abstract

The boundary layer simplification of the Navier-Stokes equations for hydrodynamically developing laminar flow with constant physical properties in the entrance region of concentric annuli with rotating inner walls have been numerically solved using a simple linearized finite-difference scheme. Additional results to those existing in the literature by Martin and Payne [1–2] will be presented here. An advantage of the analysis used in this paper is that it does not solve for the stream function and vorticity, but predicts the development of tangential, axial and radial velocity profiles directly, thus avoiding numerical differentiation. Results for the development of these velocity profiles, pressure drop and friction factor are presented for five annuli radii ratios (0.3, 0.5, 0.674, 0.727 and 0.90) at various values of the parameter Re2 /Ta. The paper may be considered as a direct comparison between the boundary layer solution and the complete solution of the Navier-Stokes equations [1–2] for that special case.

Copyright © 1974 by ASME
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