Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces

In this paper the convergent series solutions for the non-similarity flow of viscous fluid with nanoparticles are given. Fundamental equations employed in the mathematical modelling include the novel aspects of Brownian motion and thermophoresis. Non-similarity flow is induced by a stretching sheet with arbitrary velocity. The so-called homotopy analysis method (HAM) is applied to gain the convergent series solutions of the nonlinear partial differential equation. It is noticed that flow field, temperature and nanoparticle volume fraction profile are greatly influenced by the physical parameters such as Prandtl number, Brownian motion parameter, thermophoresis parameter and Lewis number. To the best of our knowledge, the present analysis seems to be a first attempt to non-similarity boundary layer flows of viscous fluids with nanoparticles.