Unsteady boundary layer flow of a nanofluid past a moving surface in an external uniform free stream using Buongiorno's model

The unsteady boundary-layer flow and heat transfer of a nanofluid past a moving surface in an external uniform free stream with leading edge accretion or ablation is studied theoretically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution of the flow, heat transfer and nanoparticle volume fraction involving steady-state rates is presented. The non-linear coupled differential (similarity) equations are solved numerically using the function bvp4c from Matlab for different values of the governing parameters. It is found that dual, upper and lower branch solutions exist of the similarity equations, and these solutions depend on the leading edge accretion/ablation parameter. It results in from the stability analysis that the upper branch solutions are stable (physically realizable), while the lower branch solutions are not stable (not physically realizable). It is also found that there is a qualitative change in this boundary layer solution compared with the Rayleigh and Blasius problems for nanofluids. (C) 2014 Published by Elsevier Ltd.