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Z. Naturforsch. 66a, 481 – 488 (2011)
doi:10.5560/ZNA.2011-0011
Flow around a Triaxial Ellipsoid in a Long Circular Tube
Doo-Sung Lee
Department of Mathematics, College of Education, Konkuk University, 1, Hwayang-Dong, Kwangjin-Gu, Seoul, Korea
Received November 25, 2010 / revised April 18, 2011
Reprint requests to: D.-S. L.; E-mail: dslee@konkuk.ac.kr
This paper deals with the three-dimensional analysis of viscous fluid flow in a long circular cylinder containing an ellipsoidal obstacle. The center of the ellipsoid coincides with that of the cylinder, and the flow is confined to the space between the ellipsoid and the cylinder when the fluid velocity at the large distance from the ellipsoid is uniform. The equations of the classical theory of fluid dynamics are solved in terms of an unknown function which is then shown to be the solution of a boundary integro-differential equation. A numerical solution of the integro-differential equation is obtained and the pressure on the surface of the ellipsoid is presented in graphical forms for various values of the radius of the circular tube.
Key words: Triaxial Ellipsoid; Cylinder; Integro-Differential Equations; Reduction Formula.
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