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Technical Briefs

Hagen–Poiseuille Flow in Semi-Elliptic Microchannels

[+] Author and Article Information
Rajai S. Alassar

e-mail: alassar@kfupm.edu.sa

Mohammed Abushoshah

King Fahd University of Petroleum and Minerals,
Department of Mathematics and Statistics,
Dhahran 31261, Saudi Arabia

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 6, 2012; final manuscript received September 14, 2012; published online November 20, 2012. Assoc. Editor: Michael G. Olsen.

J. Fluids Eng 134(12), 124502 (Nov 20, 2012) (4 pages) doi:10.1115/1.4007900 History: Received April 06, 2012; Revised September 14, 2012

In this paper, an exact solution of Hagen–Poiseuille flow in microchannels with semi-elliptic cross sections is obtained. The velocity, shear stress distribution, and the friction factor are calculated and compared to known approximate solutions in the literature. The solution is also verified by comparing the limiting case when the axis ratio approaches unity to the exact solution obtained for semicircular channels.

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References

Figures

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Fig. 1

Problem configuration

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Fig. 2

Velocity distribution for the case b/a=1/2

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Fig. 3

Maximum and average dimensionless velocity

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Fig. 4

Shear stress for the case b/a=3/4

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Fig. 5

The product of Fanning friction factor and Reynolds number, exact (solid line) versus the approximate expression of Bahrami (circles)

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Fig. 6

Correction factor versus compactness number

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