The instability of liquid films with temperature-dependent properties flowing down a heated incline - Pascal, Jean-Paul; D’Alessio, Serge; Rubaida Zafar, Syeda (AIMS mathematics, 2019)
We investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral collocation method. Comparisons with nonlinear simulations are also made and the agreement is good.