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Unsteady gaseous Poiseuille slip flow in rectangular microchannels

  • Dennis A. SiginerEmail author
  • F. Talay Akyildiz
  • Mhamed Boutaous
Technical Paper
  • 46 Downloads

Abstract

Unsteady slip flow of an incompressible gaseous fluid in a rectangular microchannel subject to a sudden time-dependent pressure drop is investigated via the generalized integral transform method. Three novel analytical solutions of the governing partial differential equations corresponding to first- and second-order slip models are derived. These can be used in the experimental determination of the constant slip length for any fluid–solid combination. All unsteady flow patterns asymptotically reach the fully developed state for each problem considered in the present investigation.

Keywords

Microfluidics First-order slip Second-order slip Rectangular microchannel Experimental determination of slip lengths Integral transform method 

Notes

References

  1. 1.
    Barber RW, Emerson DR (2008) Optimal design of microfluidic networks using biologically inspired principles. Microfluid Nanofluid 4:179–191CrossRefGoogle Scholar
  2. 2.
    Duan ZP, Muzychka YS (2008) Slip flow heat transfer in annular microchannels with constant heat flux. J. Heat Transf 130:092401.1–092401.8Google Scholar
  3. 3.
    Bahrami H, Bergman TL, Faghri A (2012) Forced convective heat transfer in a microtube including rarefaction, viscous dissipation and axial conduction effects. Int J Heat Mass Transf 5:6665–6675CrossRefGoogle Scholar
  4. 4.
    Larrode FE, Housiadas C, Drossinos Y (2000) Slip-flow heat transfer in circular tubes. Int J Heat Mass Transf 43:2669–2680CrossRefGoogle Scholar
  5. 5.
    Renksizbulut M, Niazmand H, Tercan G (2006) Slip-flow and heat transfer in rectangular microchannels with constant wall temperature. Int J Therm Sci 45:870–881CrossRefGoogle Scholar
  6. 6.
    Eckert EGR, Drake RM Jr (1972) Analysis of heat and mass transfer. McGraw-Hill, New York, pp 467–486zbMATHGoogle Scholar
  7. 7.
    Liu JQ, Tai YC, Ho CM (1995) MEMS for pressure distribution studies of gaseous flows in microchannels. In: Proceedings of IEEE micro-electromechanical systems, pp 209–215Google Scholar
  8. 8.
    Arkilic EB, Breuer KS, Schmidt MA (1994) Gaseous flow in microchannels, application of micro-fabrication to fluid mechanics. ASME FED 197:57–66Google Scholar
  9. 9.
    Thompson PA, Troian SM (1997) A general boundary condition for liquid flow at solid surfaces. Nature 389:25Google Scholar
  10. 10.
    Wu L (2008) A slip model for rarefied gas flows at arbitrary Knudsen number. Appl Phys Lett 93:253103CrossRefGoogle Scholar
  11. 11.
    Duartea ASR, Miranda AIP, Oliveira PJ (2008) Numerical and analytical modelling of unsteady viscoelastic flows: the start-up and pulsating test case problems. J Non Newton Fluid Mech 154:153–169CrossRefGoogle Scholar
  12. 12.
    Akyildiz FT, Jones RS (1993) The generation of steady flow in a rectangular duct. Rheol Acta 32(5):499–504CrossRefGoogle Scholar
  13. 13.
    Matthews MT, Hill JM (2009) On three simple experiments to determine slip lengths. Microfluid Nanofluid 6:611–619CrossRefGoogle Scholar
  14. 14.
    Aubert C, Colin S (2001) High-order boundary conditions for gaseous flows in rectangular microducts. Microscale Thermophys Eng 5:41–54CrossRefGoogle Scholar
  15. 15.
    Ng C-O, Wang CY (2011) Oscillatory flow through a channel with stick-slip walls: Complex Navier’s slip length. J Fluids Eng 133(1):014502–014502-6CrossRefGoogle Scholar
  16. 16.
    Karniadakis GE, Beskok A, Aluru N (2005) Microflows and nanoflows: fundamentals and simulations. Springer, New York, pp 51–74zbMATHGoogle Scholar
  17. 17.
    Cotta RM (1998) The integral transform method in thermal and fluid sciences and engineering. Bagell House Inc, New YorkzbMATHGoogle Scholar
  18. 18.
    Avramenko AA, Tyrinov AI, Shevchuk IV (2015) Start-up slip flow in a microchannel with a rectangular cross section. Theor Comput Fluid Dyn 29(5):351–371CrossRefGoogle Scholar
  19. 19.
    Kaoullas G, Georgiou GC (2013) Slip yield stress effects in start-up Newtonian Poiseuille flows. Rheol Acta 52(10):913–925CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Dennis A. Siginer
    • 1
    • 2
    • 3
    Email author
  • F. Talay Akyildiz
    • 4
  • Mhamed Boutaous
    • 5
  1. 1.Departamento de Ingeniería Mecánica, Centro de Investigación en Creatividad y Educación SuperiorUniversidad de Santiago de ChileSantiagoChile
  2. 2.Department of Mathematics and Statistical SciencesBotswana International University of Science and TechnologyPalapyeBotswana
  3. 3.Department of Mechanical, Energy and Industrial EngineeringBotswana International University of Science and TechnologyPalapyeBotswana
  4. 4.Department of Mathematics and Statistics, Faculty of ScienceAl-Imam UniversityRiyadhSaudi Arabia
  5. 5.UMR5008, CETHIL, INSA-Lyon, CNRSUniversité de LyonVilleurbanneFrance

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