Instability of liquid film flowing down a linearly heated plate

O3; The full-scale linear stability equations for a liquid film flowing down a linearly heated inclined plate are derived from the N-S equations, and the stability characters of both temporal and spatial modes are computed by using Chebyshev spectral collocation method. The effects of Weber numbers and Marangoni numbers on growth rate, marginal curve, critical Reynolds number, etc. Are investigated. An explicit dispersion relation under long-wave approximation, which is in exact agreement with Miladinova's one, is obtained and the limits of long-wave approximation are discussed.