Article ID Journal Published Year Pages File Type
1897920 Physica D: Nonlinear Phenomena 2008 12 Pages PDF
Abstract

The main object in this paper is to study the stability of a viscous film flowing down a vertical non-uniformly heated wall under gravity. The wall temperature is assumed linearly distributed along the wall and the free surface is taken to be adiabatic. A long wave perturbation method is used to derive the nonlinear evolution equation for the falling film. Using the method of multiple scale, the nonlinear stability analysis is studied for travelling wave solution of the evolution equation. The complex Ginzburg–Landau equation is determined to discuss the bifurcation analysis of the evolution equation. The results indicate that the supercritical unstable region increases and the subcritical stable region decreases with the increase of Peclet number. It has been also shown that the spatial uniform solution corresponding to the sideband disturbance may be stable in the unstable region.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
Authors
,