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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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References

Alassar, R. S. , and Abushoshah, M. , 2012, “Hagen–Poiseuille Flow in Semi-Elliptic Microchannels,” ASME J. Fluids Eng., 134(12), p. 124502. [CrossRef]
Wang, C. Y. , 1991, “Exact Solutions of the Steady-State Navier–Stokes Equations,” Ann. Rev. Fluid Mech., 23, pp. 159–177. [CrossRef]
Velusamy, K. , Garg, V. K. , and Vaidyanathan, G. , 1995, “Fully Developed Flow and Heat Transfer in Semi-Elliptical Ducts,” Int. J. Heat Fluid Flow, 16(2), pp. 145–152. [CrossRef]
Lei, Q. M. , and Trupp, A. C. , 1989, “Maximum Velocity Location and Pressure Drop of Fully Developed Laminar Flow in Circular Sector Ducts,” ASME J. Heat Transfer, 111(4), pp. 1085–1087. [CrossRef]
Wang, C. Y. , 2008, “Analytical Solution for Forced Convection in a Semi-Circular Channel Filled With a Porous Medium,” Transp. Porous Medium, 73(3), pp. 369–378. [CrossRef]
Alassar, R. S. , 2014, “Fully Developed Forced Convection Through Semicircular Ducts,” J. Thermophys. Heat Transfer, 28(3), pp. 560–565. [CrossRef]
Shah, R. K. , and London, A. L. , 1978, Laminar Forced Convection in Ducts, Academic, New York.
Sparrow, E. M. , and Haji-Seikh, A. , 1966, “Flow and Heat Transfer in Ducts of Arbitrary Shape With Arbitrary Thermal Conditions,” ASME J. Heat Transfer, 88(4), pp. 351–358. [CrossRef]
Ben-Ali, T. M. , Soliman, H. M. , and Zariffeh, E. K. , 1989, “Further Results for Laminar Heat Transfer in Annular Sector and Circular Sector Ducts,” ASME J. Heat Transfer, 111(4), pp. 1090–1093. [CrossRef]
Etemad, H. G. , and Majumdar, A. S. , 1995, “Effects of Variable Viscosity and Viscous Dissipation on Laminar Convection Heat Transfer of a Power Law Fluid in the Entrance Region of a Semi-Circular Duct,” Int. J. Heat Mass Transfer, 38(2), pp. 2225–2238. [CrossRef]
Bahrami, M. , Yovanovich, M. M. , and Culham, J. R. , 2007, “A Novel Solution for Pressure Drop in Singly Connected Microchannels of Arbitrary Cross Section,” Int. J. Heat Mass Transfer, 50(13–14), pp. 2492–2502. [CrossRef]

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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