Stability analysis of heated thin liquid-film flows with constant thermal boundary conditions

To answer the questions on the behavior of liquid flows under complicatedly combined actions of stresses, evaporation and temperature-dependent surface tension effects, thin liquid layers flowing under gravity down an inclined plane uniformly heated from below are considered There may be two thermal boundary conditions on the hot plate, i e , either constant heat flux or fixed temperature By using long-wave approximation, the nonlinear evolution equations governing the two-dimensional surface waves have been derived upto O(ε²) and O(ε) for the constant heat flux and the fixed temperature case, respectively Here the small parameter ε(l) is the ratio of the characteristic length scale parallel to the flow to the initial basic film thickness The linear and the nonlinear stability analyses are also performed by using numerical calculations Consequently, the flow subjected to the constant heat flux can be marked as a more stable system than the flow mechanism at a fixed-tem-perature boundary condition.