Viscous correction for the viscous potential flow analysis of Kelvin–Helmholtz instability of cylindrical flow with heat and mass transfer

We study the linear Kelvin–Helmholtz instability of the interface between two viscous and incompressible fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface in presence of mass and heat transfer across the interface. Here we use an irrotational theory known as viscous correction for the viscous potential flow theory; in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. Both asymmetric and axisymmetric disturbances have been studied and stability criterion is given in terms of a critical value of relative velocity. It has been shown that the irrotational viscous flow with viscous correction gives rise to exactly the same dispersion relation as obtained by the dissipation method in which the viscous effect is accounted for by evaluating viscous dissipation using the irrotational flow. It has been observed that heat and mass transfer has destabilizing effect while irrotational shearing stresses stabilize the system.