Nonlinear evolution of nonuniformly heated falling liquid films

The present theoretical study focuses on the dynamics of a thin liquid film falling down a vertical plate with a nonuniform, sinusoidal temperature distribution. The results are compared to those obtained in the case of the uniform temperature distribution. The governing evolution equation for the film thickness profile based on long-wave theory accounts for two instability mechanisms related to thermocapillarity. The first mechanism is due to an inhomogeneity of the temperature at the liquid-gas interface induced by perturbations of the film thickness, when heat transfer to the gas phase is present, while the second one is due to the nonuniform heating imposed at the plate and leads to steady-state deformations of the liquid-gas interface. For a moderate nonuniform heating the traveling waves obtained in the case of a uniform heating are modulated by an envelope. When the temperature modulation along the plate increases the shape of the liquid-gas interface becomes frozen and the oscillatory traveling wave regime is suppressed. The enhancement of the heat transfer due to permanent deformations and traveling waves is also assessed. The latter is found to have no significant effect on the heat transfer coefficient, while the former can increase it significantly. A good agreement between the theoretical model and the experimental data obtained for a step-wise temperature distribution at the plate is found and the reason for discrepancies is explained. (C) 2002 American Institute of Physics.