Existence results for third order nonlinear boundary value problems arising in nano boundary layer fluid flows over stretching surfaces

Abstract

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 .