Spatio-temporal Stability Analysis of Falling Film Over Heated Inclined Plane

Linear stability analysis of a thin liquid film falling down a uniformly heated slippery inclined plane has been performed. The spatial growth rates for thermocapillary P mode and S mode have been estimated by solving a coupled set of boundary value problems employing Chebyshev spectral collocation method. Marangoni number is found to destabilize both the P mode and S mode, and Biot number seems to have a dual influence on the S mode instability. The S mode gets stabilized with the increase in spanwise wavenumber, whereas the P mode gets destabilized. The hydrodynamic shear mode has also been captured analytically for inviscid flow, which indicates a slight stabilizing effect of Marangoni number on it.