Abstract
In this paper, the two-dimensional steady slip flow in microchannels is investigated. Research on micro flow, especially on micro slip flow, is very important for designing and optimizing the micro electromechanical system (MEMS). The Navier-Stokes equations for two-dimensional steady slip flow in microchannels are reduced to a nonlinear third-order differential equation by using similarity solution. The variational iteration method (VIM) is used to solve this nonlinear equation analytically. Comparison of the result obtained by the present method with numerical solution reveals that the accuracy and fast convergence of the new method.
References
He J.H.: Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput. Meth. Appl. Mech. Eng. 167(12), 69 (1998)
He J.H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Meth. Appl. Mech. Eng. 167(12), 57 (1998)
He J.H.: Variational iteration method—a kind of non-linear analytical technique: some examples. Int. J. Nonlin. Mech. 34(4), 699 (1999)
Rashidi M.M., Shahmohamadi H.: Analytical solution of three-Dimensional Navier-Stokes equations for the flow near an infinite rotating disk. Commun. Nonlin. Sci. Num. Simul. 14(7), 2999 (2009)
Rashidi, M.M., Shahmohamadi, H., Domairry, G.: Variational iteration method for solving three-dimensional Navier-Stokes equations of flow between two stretchable disks. Num. Meth. PDEs. (2009, in press)
Wazwaz A.M.: A comparison between the variational iteration method and Adomian decomposition method. J. Comput. Appl. Math. 207(1), 129 (2007)
He J.H.: The variational iteration method for eighth-order initial-boundary value problems. Phys. Scr. 76(6), 680 (2007)
Mokhtari R., Mohammadi M.: Some remarks on the variational iteration method. Int. J. Nonlin. Sci. Num. 10(1), 67–74 (2009)
He J.H.: An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int. J. Mod. Phys. B 22(21), 3487 (2008)
He J.H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20(10), 1141 (2006)
Adomian G.: A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135, 501 (1988)
He J.H., Wu G.C., Austin F.: The variational iteration method which should be followed. Nonlinear Sci. Lett. A 1, 1 (2010)
Chang C.C., Yang R.J.: Hydrodynamic focusing effect on two-unmixed-fluid in microchannels. Int. J. Nonlin. Sci. Num. 9(3), 213 (2008)
Fan J., Wang L.Q., Cheng L.: Electrokinetic effects on flow and heat transfer in parallel-plate microchannels. Int. J. Nonlin. Sci. Num. 8(3), 335 (2007)
Fan J., Wang L.Q., Cheng L.: Forced convection in rectangular microchannels: electrokinetic effects. Int. J. Nonlin. Sci. Num. 8(3), 359 (2007)
Barber, R.W., Emerson, D.R.: In: Proceedings of ECCOMAS computational fluid dynamics conference, pp. 4–7. Swansea, Wales, UK (September 2001)
Gad-el-Hak M.: The fluid mechanics of microdevices—The Freeman Scholar Lecture. J. Fluid Eng. 121, 5 (1999)
Beskok A., Karniadakis G.E.: Simulation of heat and momentum transfer in complex micro-geometries. J. Thermophys. Heat Transf. 8(4), 355 (1994)
Mohamed, G.H.: Experimental study of characteristics of distilled driven microchannel. J. Fluid Eng. 121(5) (1999)
Arkilic E.B., Schimidt M.A., Breuer K.S.: Gaseous slip flow in long microchannels. J. Microelectromech. Syst. 6, 167 (1997)
Hsieh S.S., Tsai H.H., Lin C.Y.: Gas flow in a long microchannel. Int. J. Heat Mass Transf. 47, 3877 (2004)
Weng H.C., Chen C.K.: Fully developed thermocreep-driven gas microflow. Appl. Phys. Lett. 92, 094105 (2008)
Roohi E., Darbandi M.: Extending the Navier-Stokes solutions to transition regime in two-dimensional micro- and nanochannel flows using information preservation scheme. Phys. Fluids 21(8), 082001 (2009)
Duan Z., Muzychka Y.S.: Effects of corrugated roughness on developed laminar flow in microtubes. J. Fluids Eng. 130, 031102 (2008)
Bao F.B., Lin J.Z.: Burnett simulations of gas flow in microchannels. Fluid Dyn. Res. 40, 679 (2008)
Ngoma G.D., Erchiqui F.: Heat flux and slip effects on liquid flow in a microchannel. Int. J. Therm. Sci. 46(11), 1076 (2007)
Barkhordari M., Etemad S.G.: Numerical study of slip flow heat transfer of non-Newtonian fluids in circular microchannels. Int. J. Heat Fluid Flow 28(5), 1027 (2007)
Zhang T., Jia Li., Wang Z.: Validation of Navier-Stokes equations for slip flow analysis within transition region. Int. J. Heat Mass Transf. 51, 6323 (2008)
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Rashidi, M.M., Ganji, D.D. & Shahmohamadi, H. Variational iteration method for two-dimensional steady slip flow in micro-channels. Arch Appl Mech 81, 1597–1605 (2011). https://doi.org/10.1007/s00419-010-0504-x
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DOI: https://doi.org/10.1007/s00419-010-0504-x