STABILITY OF LIQUID FILM FLOW DOWN A POROUS INCLINED PLANE

Abstract

The linear stability characteristics of the Flow of Liquid down a Porous Inclined Plane have been studied. In this work porous medium is modeled as Brinkman porous medium. The eigenvalue problem was formulated after carrying out the perturbation analysis and linearization of governing Navier-Stokes equation. Thereafter two numerical methods, spectral collocation and shooting methods were used to solve the eigenvalue problem. The spectral collocation method is used to find the eigenvalue spectrum and shooting method is used to find the effect of various parameters on the stability of the flow. The stability of the flow is governed by four parameters : Reynolds number (Re), inclined angle (13), depth ratio (a ) and permeability. At high Re and high wave numbers shear mode of instability was observed and at low Re and low wave numbers, surface mode of instability was observed. Instability increases as inclined angle increases from lower to higher value. Porous medium has destabilizing effect on the flow.