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Numerical Study of Skin Friction Coefficient and Reattachment Length for a Slip Flow Encountered in a Partially Blocked Channel

[+] Author Affiliations
Eiyad Abu-Nada, AbdelSalam Al-Sarkhi

Hashemite University, Zarqa, Jordan

Paper No. ICMM2004-2350, pp. 313-318; 6 pages
doi:10.1115/ICMM2004-2350
From:
  • ASME 2004 2nd International Conference on Microchannels and Minichannels
  • ASME 2nd International Conference on Microchannels and Minichannels
  • Rochester, New York, USA, June 17–19, 2004
  • Conference Sponsors: Nanotechnology Institute
  • ISBN: 0-7918-4164-2
  • Copyright © 2004 by ASME

abstract

The current research investigates the effect of Reynolds number and Knudsen number on the coefficient of skin friction and reattachment length for a micro-scale fluid flow over a step mounted on a lower wall of a micro-channel. Five Reynolds numbers are studied Re = 1, 10, 25, 50, and 75 and the Knudsen number is varied from 1×10−3 to 0.1. Finite difference method with non-uniform grid is used to solve the incompressible Navier Stokes equations accompanied with velocity slip boundary condition. As Knudsen number (Kn) decreases the magnitude of modified local shear stress (1/2 Cf Re), on the upper wall of the channel, increases. In the circulation zone behind the step and for the case of high Reynolds number (Re = 50 and Re = 75) the modified local shear stress increases as Knudsen number increases. Results show that the modified total skin friction (1/2 CD Re) decreases as the Knudsen number increases. The modified total skin friction drops significantly with Knudsen number for Kn >= 1 × 10−2 . However, (1/2 CD Re) is relatively independent of Knudsen number for Kn < 1 × 10−2 . Finally, for 1 × 10−2 < Kn < 0.1, as Knudsen number increase the reattachment length increases.

Copyright © 2004 by ASME

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