Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.
The focus of this paper is on linear stability analysis of
steady state solutions developing in horizontal or nearly
horizontal pipes. Continuity and momentum equations for
incompressible and isothermal flows are derived considering an
arbitrary number of fluids. It is shown that the linearization of
the governing equations around the steady state solutions and
the assumption of a particular form of the perturbations yield an
eigen-value problem, the roots of which represent complex
wave speeds of the perturbations. The coefficients of the eigenvalue
problem are derived for the most general case and given
in analytical form. The effects of inertia of the fluids, gravity,
interfacial tensions, shear stresses and wave length are included
explicitly in the stability coefficients. Some general properties
of the eigen-value problem are outlined.