Temperature dependent viscosity and surface tension effects on deformations of non-isothermal falling liquid film

Theoretical and numerical investigations of the heat transfer and hydrodynamics in a liquid film flowing along an inclined substrate under the action of gravity with a local heat source have been performed. A two-dimensional model, based on the thin layer approximation, has been developed describing deformations of the film interface. Equation of a non-isothermal thin-film flow with linear dependence of viscosity and surface tension on temperature is derived. A generalized analytical formula for the film thickness as a function of liquid flow-rate is obtained. Marangoni flow, due to local temperature changes, opposes the gravitationally driven film flow and forms a horizontal bump near the upper edge of the heater. Attention is paid to the viscosity effect on the shape of the bump and the film thinning on the local heaters. A second order deformation of the free surface before the bump up to flow may exist. The criterion for the appearance of this deformation is found analytically. (c) 2011 Elsevier Ltd. All rights reserved.