Instability and energy budget analysis of viscous coaxial jets under a radial thermal field

Temporal linear instability of viscous coaxial jets under a radial thermal field is carried out by considering axisymmetric and non-axisymmetric disturbances. The interfacial tensions of different fluids are taken to be temperature dependent. The para-sinuous, para-varicose, and helical unstable modes are identified in the Rayleigh regime. The energy budget is also employed to explore the relative importance of thermal-induced stresses on the jet instability at the most unstable wavenumber by changing the dimensionless parameters. It is shown that decreasing the temperature ratio of inner fluid to surrounding fluid (T₁₃) promotes the jet instability. For coaxial jets at T₁₃ > 1, the Marangoni flow makes coaxial jets more stable, and increasing the fluid thermal conductivity suppresses the jet instability. For coaxial jets at T₁₃ < 1, however, their influences on the jet instability are opposite. Compared with the thermal-induced stresses at the inner and outer interfaces, the inner interfacial tension is the main factor dominating the flow. Increasing either inner interfacial tension or outer surface tension and decreasing viscosity of any fluid can promote the instability of coaxial jets. The variations of thermal conductivity and specific heat capacity of either inner or surrounding fluids apparently influence the jet instability of the para-varicose mode, but hardly influence that of the para-sinuous mode. This work would provide great insight into the physical mechanism of thermal jet instability in various applications.