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13 Linear Stability of Thin Liquid Films flows down on an Inclined Plane using Integral Approximation Hajar Farhan Ismael hajar.math@yahoo.com Faculty of Science, University of Zakho Zakho – Kurdistan-Region, Iraq Received on: 28/4/2013 Accepted on: 11/10/2013 ABSTRACT In this paper, the stability and dynamics of a thin liquid films flowing down on an inclined plane are investigated by using integral approximation. The strong non-linear evolution equations are derived by the integral approximation with a specified velocity profile. The evolution equations are used to study the linear stability for liquid films. As a result, output of this research, we showed that the effect of inclination of films is an unstable factor.