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Technical Brief

On Viscous Flow in Semi-Elliptic Ducts

[+] Author and Article Information
C. Y. Wang

Department of Mathematics and Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: cywang@mth.msu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 2, 2015; final manuscript received June 10, 2015; published online August 6, 2015. Assoc. Editor: John Abraham.

J. Fluids Eng 137(11), 114502 (Aug 06, 2015) (4 pages) Paper No: FE-15-1233; doi: 10.1115/1.4030898 History: Received April 02, 2015

The exact series solutions for the laminar flow in a semi-elliptic duct are presented. The present work studies the semi-elliptic duct with the minor axis as the straight wall, which complements that of Alassar and Abushoshah who used the major axis. Properties of the two types of semi-elliptic ducts are given, including the asymptotic Poiseuille numbers.

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Figures

Grahic Jump Location
Fig. 1

(a) The wide semi-ellipse with the major axis as the flat side. (b) The deep semi-ellipse with the minor axis as the flat side.

Grahic Jump Location
Fig. 2

Constant velocity lines for wide semi-ellipse, b = 0.5. From outside: w = 0, 0.005, 0.01, 0.015, 0.02, and 0.025.

Grahic Jump Location
Fig. 3

Constant velocity lines for “deep” semi-ellipse, b = 0.5. From outside: w = 0, 0.01, 0.02, 0.03, 0.04, and 0.05.

Grahic Jump Location
Fig. 4

Constant velocity lines for deep semi-ellipse, b = 0.2. From outside: w = 0, 0.0025, 0.005, 0.0075, 0.01, 0.0125, and 0.015. The maximum shear is at x = 0.347 and y = ±0.188 on the curved wall.

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