Abstract
In this paper, we investigate the effect of nano-flow on vibration of nano-pipe conveying fluid using Knudsen (Kn). We use Euler–Bernoulli plug-flow beam theory. We modify no-slip condition of nano-pipe conveying fluid based on Kn. We define a Kn-dependent flow velocity. We consider effect of slip condition, for a liquid and a gas flow. We reformulate Navier–Stokes equations, with modified versions of Kn-dependent flow velocity. We observe that for passage of gas through nano-pipe with nonzero Kn, the critical flow velocities decreased considerably as opposed to those for zero Kn. This can show that ignoring Kn effect on a gas nano-flow may cause non-conservative design of nano-devices. Furthermore, a more impressive phenomenon happens in the case of clamped-pinned pipe conveying gas fluid. While we do not observe any coupled-mode flutter for a zero Kn, we can see the coupled-mode flutter, accompanying the second-mode divergence, for a nonzero Kn.
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References
Iijima S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)
Karniadakis G., Beskok A., Aluru N.: Microflows and Nanoflows: Fundamentals and Simulation. Springer, NY (2005)
Yoon J., Ru C.Q., Mioduchowski A.: Vibration and instability of carbon nano-tubes conveying fluid. Compos. Sci. Technol. 65, 1326–1336 (2005)
Wang L., Ni Q., Li M.: Buckling instability of double-wall carbon nano-tubes conveying fluid. Comp. Mater. Sci. 44, 821–825 (2008)
Chang W.J., Lee H.L.: Free vibration of a single-walled carbon nano-tube containing a fluid flow using the Timoshenko beam model. Phys. Lett. A 373, 982–985 (2009)
Wang L., Ni Q.: A reappraisal of the computational modeling of carbon nano-tubes conveying viscous fluid. Mech. Res. Commun. 36, 833–837 (2009)
Zhen Y., Fang B.: Thermal-mechanical and nonlocal elastic vibration of single-walled carbon nano-tubes conveying fluid. Comp. Mater. Sci. 49, 276–282 (2010)
Hannon L., Lie G.C., Clementi E.: Molecular dynamics simulation of channel flow. Phys. Lett. A 119, 174–177 (1986)
Sun M., Ebner C.: Molecular-dynamics simulation of compressible fluid flow in two-dimensional channels. Phys. Rev. A 46, 4813–4819 (1992)
Thompson P.A., Troia S.M.: A general boundary condition for liquid flow at solid surfaces. Nature 389, 360–362 (1997)
Ellisab J.S., Thompson M.: Slip and coupling phenomena at the liquid-solid interface. Phys. Chem. 6, 4928–4938 (2004)
Miguel A.F., Serrenho A.: On the experimental evaluation of permeability in porous media using a gas flow method. J. Phys. D Appl. Phys. 40, 6824–6828 (2007)
Beskok A., Karniadakis G.E.: A model for flows in channels, pipes, and ducts at micro and nano scales. Microscale Thermophys. Eng. 3, 43–77 (1999)
Shokouhmand H., Isfahani A.H.M., Shirani E.: Friction and heat transfer coefficient in micro and nano channels filled with porous media for wide range of Knudsen number. Int. Commun. Heat Mass 37, 890–894 (2010)
Shames I.H.: Mechanics of Fluids. McGraw-Hill, NY (1982)
Polard W.G., Present R.D.: On gaseous self-diffusion in long capillary tubes. Phys. Rev. 73, 762–774 (1948)
Paidoussis M.D.: Fluid-Structure Interactions: Slender Structures and Axial Flow, vol. 1. Academic Press, London (1998)
Weaver W., Timoshenko S.P., Young D.H.: Vibration Problems in Engineering. Wiley, NY (1990)
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Mirramezani, M., Mirdamadi, H.R. The effects of Knudsen-dependent flow velocity on vibrations of a nano-pipe conveying fluid. Arch Appl Mech 82, 879–890 (2012). https://doi.org/10.1007/s00419-011-0598-9
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DOI: https://doi.org/10.1007/s00419-011-0598-9