Journal of Applied Mathematics and Decision Sciences
Volume 5 (2001), Issue 2, Pages 87-104
Fluid velocity profile reconstruction for non-Newtonian shear
Biomathematics Research Centre, Department of Mathematics & Statistics, University of Canterbury, Christchurch, 1, New Zealand
Copyright © 2001 Paul R. Shorten and David J. N. Wall. 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.
An inverse problem associated with the mass transport of a material concentration down a pipe where the flowing non-Newtonian medium has a two-dimensional velocity profile is examined. The problem of determining the two-dimensional fluid velocity profile from temporally varying cross-sectional average concentration measurements at upstream and downstream locations is considered. The special case of a known input upstream concentration with a time zero step, and a strictly decreasing velocity profile is shown to be a well-posed problem. This inverse problem is in general ill-posed and mollification is used to obtain a well conditioned problem.