Unsteady thin-film flow over a heated stretching sheet

The unsteady flow in a thin viscous liquid film over a heated horizontal stretching surface are analyzed considering the stretching velocity and the temperature distribution in their general forms. An evolution equation for the film thickness, that retains the convective heat transport effects, is derived using long-wave theory of thin liquid film and is solved numerically for some representative values of non-dimensional parameters. It is observed that the thermocapillary effects are responsible in shaping the film thickness. Further the thermocapillary effects are more pronounced for lower values of Prandtl number and Biot number.