Finite-element simulation of a heated thin fluid layer

This investigation deals with finite-element modeling and numerical approximation of thermocapillary effects in long-wavelength evolution of inclined heated thin liquid layers. We consider several aspects, including model development, scaling and perturbation analysis, variational formulations, finite-element approximation, and application studies. A linear stability analysis of the thermocapillary problem for the layer at small inclination angle is also developed, and its implications are explored numerically over the related parameter space.