Kelvin–Helmholtz instability of confined Oldroyd-B liquid film with heat and mass transfer

Abstract

This paper investigates the Kelvin–Helmholtz instability of an annular viscoelastic liquid film confined in a tube with a hotter, central viscous gas when the heat and mass transfer, which plays a significant role in determining flow instability and injector spraying characteristics, are taken into considered. The liquid is assumed to satisfy the Oldroyd-B model. The non-dimensional dispersion relation equation between the dimensionless growth rate and the wave number is obtained by linear stability analysis. In this work, heat and mass transfer are characterized by the heat transfer flux ratio of conduction-to-evaporation heat transfer at the interface. Maximum growth rate and range of unstable wave number both increases with an increase in heat transfer flux ratio of conduction-to-evaporation heat transfer. When the Reynolds number of the gas increases, the maximum growth rate also increases while the range of the unstable wave number is lowered. The effects of other non-dimensional parameters at the gas-to-liquid interface are also discussed.