Flow and heat transfer in a nano-liquid film over an unsteady stretching surface

The unsteady film flow and heat transfer of nanofluids caused by a linear stretching velocity over a horizonal elastic sheet is investigated. By means of similarity variables, the boundary layer equations describing the momentum and energy conservations are reduced to a set of ordinary differential equations with an unknown constant. The homotopy analysis method (HAM) is then applied to give exact solutions for this particular kind of equations. A linear relationship between the film thickness β and the unsteadiness parameter S is found. Besides, the effects of the unsteadiness parameters S, the solid volume fraction of the nanofluid ϕ and the Prandtl number Pr on the velocity and the temperature distributions are presented and discussed, respectively. It is found that the usage of nanoparticles in the base fluids can effectively improve on the heat transfer characteristics.