The breakup of coaxial liquid jets in a co-flowing gas stream under the radial thermal field is studied by the linear instability theory. A simplified physical model is established, and an analytical dimensionless dispersion relation for temporally axisymmetric perturbations is derived and solved numerically. The outer liquid-gas surface tension coefficient is assumed to be a linear function of temperature. Due to the radial temperature gradients, the time-dependent spatial variation of surface tension gives rise to a shear stress and induces Marangoni force upon the flow. The effects of different process parameters on the characteristics of unstable modes including the para-sinuous mode and the para-varicose mode are explored. It is found that the para-sinuous mode always dominates the jet instability in the parametric regions and the increasing temperature ratio of the surrounding gas stream and the inner liquid jet (T31) can reduce the maximum growth rates of unstable modes and corresponding dominant wavenumbers. The Reynolds number destabilizes the jet instability, and the Weber number suppresses it at relatively long wavelengths for both isothermal and non-isothermal situations. The Marangoni number and the Peclet number have a destabilizing effect for T31 < 1, but it is opposite for T31 > 1. These theoretical predictions would provide insight into underlying physical mechanisms of thermal jet breakup and compound droplet formation.
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