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Zbl 1231.35155
Talay Akyildiz, F.; Bellout, Hamid; Vajravelu, Kuppalapalle; Van Gorder, Robert A.
Existence results for third order nonlinear boundary value problems arising in nano boundary layer fluid flows over stretching surfaces. (English)
[J] Nonlinear Anal., Real World Appl. 12, No. 6, 2919-2930 (2011). ISSN 1468-1218

Summary: Solutions for a class of degenerate, nonlinear, nonlocal boundary value problems, arising in nano boundary layer fluid flows over a stretching surface, are obtained. Viscous flows over a two-dimensional stretching surface and an axisymmetric stretching surface are considered. Using the Schauder fixed point theorem, existence and uniqueness results are established. The effects of the slip parameter $k$ and the suction parameter a on the fluid velocity and on the tangential stress are investigated and discussed (through numerical results). We find that for fluid flows at nanoscales, the shear stress at the wall decreases (in an absolute sense) with an increase in the slip parameter $k$.

MSC 2000:: *35Q30 Stokes and Navier-Stokes equations
76D10 Boundary-layer theory (incompressible fluids)
35A01
35A02

Keywords: nanofluids; Navier boundary condition; existence and uniqueness results; Schauder fixed point theorem; stretching surface

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