The aim of this paper is to investigate numerically the steady boundary layer flow and heat transfer characteristics of nanofluids using Buongiorno's model past a permeable exponentially shrinking/stretching surface with second order slip velocity. Using appropriate similarity transformations, the basic nonlinear partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters, stretching/shrinking parameter 2, suction parameter s, first order slip parameter a, second order slip parameter b, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb and the thermophoresis parameter Nt using the bvp4c function from Matlab. A stability analysis has been also performed. Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the shrinking (lambda < 0) as well as for the stretching case (lambda > 0) for certain values of the parameter space. The stability analysis indicates that the lower solution branch is unstable, while the upper solution branch is stable and physically realizable. In addition, it is shown that for a regular fluid (Nb = Nt = 0) a very good agreement exists between the present numerical results and those reported in the open literature. The present results are original and new for the boundary-layer flow and heat transfer past a shrinking/stretching sheet in a nanofluid. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids. (C)2014 Elsevier Ltd. All rights reserved.