Nonlinear Study of Kelvin-Helmholtz instability of cylindrical flow with mass and heat transfer

In this work, a viscous potential flow theory is used to study the nonlinear Kelvin-Helmholtz instability of the interface between two viscous, incompressible and thermally conducting fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface and when there is mass and heat transfer across the interface. The method of multiple time expansions is applied and it is shown that the evolution of amplitudes is governed by a nonlinear first order partial differential equation. The various stability criteria are discussed both analytically and numerically, stability diagrams are studied graphically. It is observed that the heat and mass transfer has destabilizing effect on the stability of the system in the nonlinear analysis.