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Zbl 1221.76024
Van Gorder, Robert A.; Sweet, Erik; Vajravelu, K.
Nano boundary layers over stretching surfaces. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 15, No. 6, 1494-1500 (2010). ISSN 1007-5704

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 $K$.

MSC 2000:: *76A05 Non-Newtonian fluids
34E13 Multiple scale methods
65L99 Numerical methods for ODE

Keywords: nanofluidics; Navier boundary condition; homotopy analysis method; stretching sheet

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