Thermocapillarity Effects on Power-Law Liquids Thin Film Over an Unsteady Stretching Sheet

This paper investigates the effects of thermocapillarity on the flow and heat transfer in power-law liquid film over an unsteady stretching sheet. The surface tension is assumed to vary linearly with temperature, and the thermal conductivity of the fluid is assumed power-law-dependent on the velocity gradient with modified Fourier's law. The local similarity solutions are obtained numerically, and some interesting new phenomena are found. Results indicate that the thermally induced surface tension provides an opposite force in the direction of the stretching sheet which may cause the fluid adjacent to the free surface to flow in the opposite directions. The effect of thermocapillarity tends to decrease the thin film thickness and results in a smaller temperature distribution. With the increasing unsteadiness parameter, the thin film thickness has a local maximum, and thermal boundary layer is confined to the lower part of the thin film for bigger Prandtl number, while the temperature in the thin film remains equal to the slit temperature with Prandtl number close to 0.