Journal of Applied Mathematics
Volume 2005 (2005), Issue 4, Pages 341-364

Potential flow of a second-order fluid over a tri-axial ellipsoid

F. Viana,1 T. Funada,2 D. D. Joseph,1 N. Tashiro,2 and Y. Sonoda2

1Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union Street SE, Minneapolis 55455, MN, USA
2Department of Digital Engineering, Numazu National College of Technology, 3600 Ooka, Numazu-shi, Shizuoka 410-8501, Japan

Received 8 October 2004; Revised 17 August 2005

Copyright © 2005 F. Viana et al. 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.


The problem of potential flow of a second-order fluid around an ellipsoid is solved, and the flow and stress fields are computed. The flow fields are determined by the harmonic potential but the stress fields depend on viscosity and the parameters of the second-order fluid. The stress fields on the surface of a tri-axial ellipsoid depend strongly on the ratios of principal axes and are such as to suggest the formation of gas bubble with a round flat nose and two-dimensional cusped trailing edge. A thin flat trailing edge gives rise to a large stress which makes the thin trailing edge thinner.