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Nano boundary layers over stretching surfaces. (English) Zbl 1221.76024
Summary: We present similarity solutions for the nano boundary layer flows with Navier boundary condition. We consider viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface. The resulting nonlinear ordinary differential equations are solved analytically by the Homotopy Analysis Method. Numerical solutions are obtained by using a boundary value problem solver, and are shown to agree well with the analytical solutions. The effects of the slip parameter K and the suction parameter s on the fluid velocity and on the tangential stress are investigated and discussed. As expected, we find that for such fluid flows at nano scales, the shear stress at the wall decreases (in an absolute sense) with an increase in the slip parameter K.
76A05Non-Newtonian fluids
34E13Multiple scale methods (ODE)
65L99Numerical methods for ODE
[1]Navier, C. L. M.H.: Mémoire sur LES lois du mouvement des fluids, Mém acad R sci inst France 6, 389 (1823)
[2]Shikhmurzaev, Y. D.: The moving contact line on a smooth solid surface, Int J multiphase flow 19, 589 (1993) · Zbl 1144.76452 · doi:10.1016/0301-9322(93)90090-H
[3]Choi CH, Westin JA, Breuer KS. To slip or not to slipwater flows in hydrophilic and hydrophobic microchannels. In: Proceedings of IMECE 2002, New Orleans, LA, Paper No. 2002-33707.
[4]Matthews, M. T.; Hill, J. M.: Nano boundary layer equation with nonlinear Navier boundary condition, J math anal appl 333, 381 (2007) · Zbl 1207.76050 · doi:10.1016/j.jmaa.2006.08.047
[5]Wang, C. Y.: Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear anal real world appl 10, 375 (2009) · Zbl 1154.76330 · doi:10.1016/j.nonrwa.2007.09.013
[6]Wang, C. Y.: Flow due to a stretching boundary with partial slip – an exact solution of the Navier – Stokes equations, Chem eng sci 57, 3745 (2002)
[7]Xu, H.; Liao, S. J.; Wu, G. X.: A family of new solutions on the wall jet, Eur J mech B/fluid 27, 322-334 (2008) · Zbl 1154.76335 · doi:10.1016/j.euromechflu.2007.07.002
[8]Liao, S. J.: A new branch of boundary layer flows over a permeable stretching plate, Int J non-linear mech 42, 819-830 (2007) · Zbl 1200.76046 · doi:10.1016/j.ijnonlinmec.2007.03.007
[9]Liao, S. J.: A new branch of solutions of boundary-layer flows over an impermeable stretched plate, Int J heat mass transfer 48, 2529-2539 (2005) · Zbl 1189.76142 · doi:10.1016/j.ijheatmasstransfer.2005.01.005
[10]Crane, L. J.: Flow past a stretching plate, Z angew math phys 21, 645 (1970)
[11]Liao SJ. On the proposed homotopy analysis techniques for nonlinear problems and its application. Ph.D. dissertation, Shanghai Jiao Tong University; 1992.
[12]Liao, S. J.: Beyond perturbation: introduction to the homotopy analysis method, (2003)
[13]Liao, S. J.: An explicit, totally analytic approximation of Blasius viscous flow problems, Int J non-linear mech 34, 759 (1999)
[14]Liao, S. J.: On the homotopy analysis method for nonlinear problems, Appl math comput 147, 499 (2004) · Zbl 1086.35005 · doi:10.1016/S0096-3003(02)00790-7
[15]Liao, S. J.; Tan, Y.: A general approach to obtain series solutions of nonlinear differential equations, Stud appl math 119, 297 (2007)
[16]Liao, S. J.: Notes on the homotopy analysis method: some definitions and theorems, Commun nonlinear sci numer simul 14, 983 (2009) · Zbl 1221.65126 · doi:10.1016/j.cnsns.2008.04.013
[17]U. Ascher, R. Mattheij, and R. Russell, Numerical solution of boundary value problems for ordinary differential equations, In: SIAM Classics in Applied Mathematics, No. 13; 1995. · Zbl 0843.65054
[18]Ascher, U.; Petzold, L.: Computer methods for ordinary differential equations and differential-algebraic equations, (1998) · Zbl 0908.65055